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User manual in PDF format - Kovach Computing Services

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1. Data Editor BAX 4 B E D likai Type Angles _x Anales _x angles Angles x Angles Name January February March April May 52 3 000 303 000 200 000 205 000 53 217 000 4 000 251 000 204 000 3 54 54 000 351 000 318 000 280 000 2 55 289 000 356 000 103 000 316 000 1 56 156 000 23 000 119 000 53 000 2 57 69 000 46 000 77 000 114 000 3 58 102 000 64 000 275 000 167 000 1 BS 281 000 25 000 113 000 357 000 60 100 000 243 000 129 000 52 000 2 61 188 000 200 000 187 000 1 62 342 000 128 000 327 000 2 63 223 000 123 000 72 000 1 64 171 000 304 000 100 000 1 65 325 000 310 000 158 000 1 66 257 000 233 000 67 85 000 5 000 1 68 301 000 3 000 1 69 101 000 208 000 70 191 000 339 000 aly lt Paired Data Oriana version 2 introduced a new method of structuring the data that allows much more flexibility With this new method each column is a separate variable rather than set of observations You might have one column with all the directional or time data plus another with a variable that you can optionally use to divide the data into subgroups For example with the arrival time example above the first column would have all of the arrival times and the second would have the day that each arrival time was recorded The data are paired so that each row of the data matrix gives all the data about a single event Here is the data matrix Getting Started Data Editor Joey B a A Type Time _x Day of week xl Name Arrival D
2. Two Sample Plots Main Graph type Scatterplot Select Axes Q Q Plot Colors Lines amp Patterns Subgroups on single plot Symbols Titles Fonts ok Cancel If you have a subgrouping variable in use then by default a separate graph is created for each subgroup You can tick the Subgroups on single plot to have them all plotted on a single plot with different colors or symbols for each subgroup as specified on the Colors and Symbols pages The Select page is identical to that in the Graphs Histogram 1133 dialog box The Axes page lets you customize the axes of the plot Two Sample Plots AX Main 7 V Scale circular data 0 360 Include symbol on angles Select Reverse X axes x Axis Decimal places Auto x Log scale for linear variables Colors P y Number of grid lines Auto Manually scale Lines amp _ Patterns Labels angle of Symbols Titles Y Axis Decimal places Auto iv Log scale for linear variables Fonts Number of grid lines Auto x Manually scale Labels angle of When the Seale circular data 0 360 option is ticked all axes for circular data depict the whole range even if the data are restricted to a certain section of the graph Otherwise the axes are scaled to fit the data range The Reverse X Y axes lets you change the samples that occur on the two axes The Include symbol on angles opt
3. Eg E Oriana Results Loe Es 1 BASIC STATISTICS 2 Datafile F StatData Oriana Ori2 Ti 3 Hourly wind data garden weather stz w 4 Analysis begun 10 November 2008 14 13 z v l gt Statistics Modified 0 Note that any windows that are iconized when the command is chosen remains iconized the other windows are adjusted so that there is room for the icons at the bottom 6 7 7 Window List of open windows Any windows that are open on the Oriana desktop will be listed at the bottom of the Windows menu This lets you easily switch between the windows particularly when you are using keyboard control 5A 6 8 6 8 1 6 8 2 6 8 3 6 8 4 Menus 155 Help This menu allows you to look at information about the program Help Index This command will load the Oriana help file and display the Contents page Help Check for updates This will allow you to check on the Kovach Computing Services web site to see if a new version of Oriana is available When you chose this menu item a wizard will appear that will take you through the process of checking over the Internet to see if there is a new version If there is the new version number and information about the update will be displayed and you can continue on with the wizard to download and install the new version By default Oriana will check every month to see if there is a new version It performs this check when you start up the pr
4. This option allows you to plot two different types of distribution graphsl 88 These are helpful for assessing whether your data fit a theoretical distribution The data can be compared to either the Uniform or von Mises distribution Distribution Plots Main Distribution type Uniform Select Axes Yon Mises Colors Lines amp Patterns Symbols Subgroups on single plot Titles Fonts OK Cancel Help If you have a subgrouping variable in use then by default a separate graph is created for each subgroup You can tick the Subgroups on single plot to have them all plotted on a single plot with different colors or symbols for each subgroup as specified on the Colors and Symbols pages The Select page is identical to that in the Graphs Histogram 1133 dialog box The Axes page lets you customize the axes of the plot Distribution Plots Main Extent of Uniform Axes Basic 0 1 Select STA Extended 0 2 1 2 Colors Number of grid lines Auto v Lines amp Patterns X Axis Symbols Decimal places Auto lw Titles Labels angle ole Fonts Y Axis Decimal places Auto v Labels angle oe OK Cancel Help The Extent of Axes option allows you for uniform distributions to have the axes of the graph extended so that any patterns that overlap the wrap around can be seen more easily see the section on distribution graphsl 88 for a
5. 12 00 Note that the scale is now a squared scale rather than a linear one With compass direction data the wedges of the diagram are shifted slightly so that they are centered on the compass direction For example in the diagram below the wedge for North directions is centered on the vertical axis 0 or N rather than having its left edge starting at that point This type of placement can also be optionally specified for graphs of angular or time data through the Center circular bars on 0 option on the Axes page of the Graphs Histograms 133 dialog box Direction 5 2 Circular Histograms These graphs are similar to the rose diagram but they are made up of parallel sided bars that show the number of observations within each class range The actual width of the bars the width of the class range can be set when the graph is drawn The graph below has a bar width of 10 degrees Arrival 00 00 5 3 Raw Data Plots These circular diagrams plot individual symbols for each datum in the sample This allows you to assess the sample size at a glance as well as seeing the distribution of the data Here is an example of one traditional way of presenting the raw data with the points stacked from the outer rim of the circle towards the middle You can also have the points stacked on the outer rim pointing outwards Arrival Finally you can have the points stacked from the middle pointing outwards 5 4 A
6. Mean Group Length of Mean Vector r 0 2845 Median 235 Median Group Concentration 0 5936 Circular Variance 0 7155 Circular Standard Deviation 90 8442 Standard Error of Mean 2 0794 95 confidence interval for pL 222 6424 230 7955 99 confidence interval for p 221 3619 232 076 The mean vector will have two properties its direction the mean angle u and its length often referred to using the letter r The length will range from 0 to 1 a larger r value indicates that the observations are clustered more closely around the mean than a smaller one The concentration is a parameter specific to the von Mises distribution and measures the departure of the distribution from a perfect circle or a uniform distribution It is related to the length of the mean vector The value reported by Oriana is the maximum likelihood estimate of the population concentration calculated using the formula in Fisher 1993 p 88 and Mardia amp Jupp 2000 p 85 6 The circular variance and circular standard deviation are equivalent to their linear counterparts but are calculated in a much different way Variance is calculated from the length of the mean vector through the simple formula V 1 r standard deviation is then calculated by S 2 In r The result S which is in radians may then be converted to degrees by multiplying by 180 n The standard error of the mean is also calculated based on the lengt
7. 74 77 45 124 11 153 170 Oriana 4 _R radians 115 Rao s spacing test 68 raw dataplots 81 raw data plots plots 142 Rayleigh s uniformity test 67 135 Moore s modified 66 70 76 77 redo 102 replace 119 results window 8 rose diagrams 47 49 54 55 79 85 133 138 r vector 48 63 79 85 128 129 134 aS sample labels 29 savingdata 38 saving files 54 59 93 94 scatterplots 89 145 scatterplots circular 57 87 114 140 search 118 second order statistics 77 126 seconds 149 select data 44 113 sorting data 115 spreadsheet 7 stacked amp stepped histograms 52 54 85 133 138 standard deviation 63 standard error 63 standardize 115 standards for data and time format 160 statistics 8 41 45 63 120 basic 63 123 printing 58 second order 70 76 126 status window 7 70 76 subgrouping variable 7 19 21 43 49 54 57 85 86 109 112 120 130 131 135 141 143 145 summarizing data 60 symbols 54 58 129 130 T tests chi squared multisample 72 chi squared one sample 69 correlations 75 125 Hotelling 66 70 76 Hotelling paired 74 77 Hotelling two sample 77 Kuipers 69 Mardia two sample 77 Mardia Watson Wheeler 73 Moore s modified Rayleigh 66 70 76 Moore s paired 74 77 multisample 71 124 one sample 67 123 paired 74 77 Rao s spacing test 68 Rayleigh s 67 135 second order 76 77 126 uniform scores 73 V test 69 Watson s U multisample 74 77 Watson s U2 one sample test 68 Watson
8. Number of Means 14 95 Confidence Interval for GM 217 706 175 987 99 Confidence Interval for GM 190 341 176 758 Hotelling s Test F 19 776 Hotelling s Test p 1 59E 4 Moore s Modified Rayleigh Test R 1 018 Moore s Modified Rayleigh Test p 0 1 gt p gt 0 05 The first statistics are the calculation of the grand mean vector or the mean of means This is calculated in a similar way to the mean of each variable with the means for each variable being used as the data rather than the original angles Also each mean is weighted by its r value the length of the mean vector The result is a grand mean angle and its resulting length r Also provided are the 95 and 99 confidence limits calculated using the method of Batschelet 1981 also described in Zar 1998 p 611 Note that unlike the confidence intervals for the sample means these are not necessarily symmetric around the grand mean Also the confidence intervals often cannot be calculated when the number of means are small e g less than 4 5 Two hypothesis tests are also calculated Hotelling s one sample test Zar 1998 p 638 Batschelet 1981 p 144 tests whether the whole population has a significant mean direction The null hypothesis is that there is no mean direction A 4 2 4 2 1 probability less than your chosen significance level usually 0 05 indicates that there is a common mean direction to the population It is assumed that th
9. Press OK The test will be calculated and the results placed in the Results window In the first column are the names of the samples and the numbers of observations The F statistic the associated probability p and the two degrees of freedom are in the following columns A p below your chosen alpha level usually 0 05 means that the null hypothesis that the samples have the same mean can be rejected In this case the p is 0 0104 so we can accept the alternative hypothesis that the samples do not all have the same mean Variables amp observations df Est Mean Multi sample test using Seti 100 Set5 50 Set6 50 Set8 48 Set10 50 Set 4 92 3 0446 0 0104 6 Let s now investigate each pair of samples Repeat steps 2 4 but this time choose the pairwise option and press OK The results are reported with a line of values for each pair of variables The F and p values are also reported ina matrix format at the bottom of the results page for easier comparisons 3 13 Tutorial Results in matrix format F scores lower half and probabilities upper half Setl Seth Set6 Set8 Setl0 Setl4 Setl 0 0307 0 3811 0 0915 0 0125 0 6631 Set5 4 7624 0 0812 0 7147 0 8385 0 0079 Set 0 7718 3 1037 0 2626 0 0134 0 4205 Set 2 8856 0 1344 1 2697 0 5468 0 0548 Seti0 6 3883 0 0418 6 337 0 3656 0 0007 Setl4 0 1903 7 2562 0 6528 3 7527 11 9512 We can see that most of the pairs do not have
10. at the top of the graph near the axes and over the legend The tick boxes to the left of each title let you suppress the display of the titles If the text editing box for a particular title is left blank then Oriana will create a default title if appropriate The Append subgroup and filtering value checkbox controls whether these values are added to the main title If subgrouping is in effect the particular subgroup being plotted will be added to the title If filtering is active the filtering criterion will be added to the title e g Month June Note that the X and Y axes titles are only displayed on graphs with X and Y axes e g scatterplots distribution plots etc The have no effect on circular diagrams The legend title is only displayed on those graphs that have a legend e g stacked plots 132 Oriana 4 Histograms 2 x Main V Main Title Options Wind Direction Select V Append subgroup and filtering value 6 5 1 5 Fonts This page allows you to customize the fonts used for various labels on the graphs Clicking on any of the buttons will bring up the regular Windows font dialog box 144 allowing you to select the characteristics of the new font Histograms mx Main Main Title E Solan xampie Select Title Box Style None v Axes Axes Titles Example Colors Large Axis Labels Example Lines amp Patterns Small Axis Labels Example Symbols Titles
11. is checked during calculations and a warning is printed if more than 20 of the classes have expected frequencies less than 5 If this occurs you can try using large class widths so that more observations are in each class You can also use the Drop Classes with 0 Observations option on the Options page of the analysis dialog box This will ignore any classes that do not have any observations This is particularly useful if your observations are clustered fairly closely around the mean with the result that a large portion of the circle will not have any data Mardia Watson Wheeler Test The Mardia Watson Wheeler Test Fisher 1993 p 122 Mardia amp Jupp 2000 p 147 Batschelet 1981 p 101 Zar 1999 p 633 also called the Uniform Scores Test is a non parametric test for determining whether two or more distributions are identical The basic idea is that the samples are pooled together sorted into increasing angles and are then evenly distributed around the circle by calculating a uniform score or circular rank If the distributions of the samples are identical then the new uniform scores for the samples should be evenly interspersed around the circle and their resultant vector lengths R should be short and similar Any significant difference between the Rs will lead to a large W test statistic and rejection of the null hypothesis of identical distributions difference is between the two samples It is important for this test th
12. make them a bit wider 8 By default using Month as the subgrouping variable means that a separate graph is created for each month If you instead wish to have all data on the same graph with different colors or symbols representing the different subgroups you can tick the Subgroups on single plot option on the Main page For scatterplots you can choose to use different colors symbols or both with the Represent subgroups with option on the Symbols page Printing graphs and results The contents of most window types can be printed using the File Print command You must first make sure that the window you want to print is the currently active window In the Print Range section you can select to have just the current graph printed or all graphs You can specify which printer to use and change other options with the File Printer setup 00 command The size of the 3 21 3 22 Tutorial margins on the printed page can be changed with the File Page setup 10h command Saving graphs and results to file The contents of the graph and results windows can be saved to a file using the File Export 97 command You must first make sure that the window you want to save is the currently active window and that the page with the graph or results you want to save is visible If you tick the Export all pages option on the dialog all graphs or result pages will be exported For graphs each files is exported to a separate file The file name
13. 1 01 Moore s paired p 0 1 gt p gt 0 05 Number of pairs 7 Hotelling s two sample test Zar 1999 p 641 642 Batschelet 1981 p 150 154 compares the grand means of two populations The null hypothesis is that the means of the two populations are equal A probability less than the chosen significance level usually 0 05 indicates that the two means differ As with other variations on the Hotelling test this assumes that the data are not grouped and that the data are from a bivariate normal distribution with similar variances However this two sample test is somewhat more robust to departures from normality than the one sample and paired tests A nonparametric alternative to the above is Mardia s two sample test Zar 1999 p 643 645 Batschelet 1981 p 154 156 With this test the differences between the individual means and the grand mean for both samples is further analyzed using one of the circular two sample tests In Oriana Watson s U is used for the analysis The null hypothesis is that the two samples come from the same population The alternative hypothesis is that the populations that differ in some way in the distribution mean direction or other parameter This test cannot be used on grouped data These tests are followed by Hotelling s paired two sample test 74 and Moore s nonparametric alternativel 74 These are identical to the paired tests described above in the Multisample Test section except that they a
14. 129 130 titles 51 131 two sample plots 89 145 two variable histograms 52 55 86 114 138 graphs 79 127 145 two variable vector plots 57 87 140 uniformity plots vector plots 57 von Mises distribution plot 88 143 gridlines 50 grouped 65 grouped data 26 107 grouping variable 7 19 21 43 49 54 57 85 86 109 112 120 130 131 135 141 143 145 H histograms 49 54 55 79 81 84 85 86 114 133 138 Hotelling 66 70 76 Hotelling paired 74 77 Hotelling two sample 77 lls importingdata 39 94 insertingdata 104 introduction 3 ISO 8601 15 16 160 keyboard 159 Kuiper s test 69 E labels 19 29 51 linear 18 linear histograms lines 53 129 log transform 115 lunar phase 16 152 M Mardia Watson Wheeler test 73 margins 101 mean 48 63 79 85 128 129 134 135 88 143 84 133 grand 70 76 ofmeans 70 76 weighted 18 65 114 141 mean ofmeans 70 76 median 63 menus 91 merging data 100 missing data 26 modifying graphs 147 monochrome 128 month of year 8 15 26 31 34 44 108 122 136 164 Moore s modified Rayleigh 66 70 76 Moore s paired multisample tests notepad notes 11 one sample tests 123 opening files 38 91 93 94 159 options 147 149 Bey page setup 101 page size 101 paired data 20 pairwise 45 pasting data 102 103 patterns 53 129 percentage circular 14 preferences 149 printer setup 100 printing 58 100 proportional circular 14 Q Q plots 89 145 quitting 101
15. 2 11 000 3 10 000 4 357 000 5 6 7 M lt IEA Entering data To begin entering data you must open the Data Editor 7 window if it isn t already Do this by choosing Data Edit Data from the menu A spreadsheet like editor will appear Initially the cell in the upper left corner will have a dark line around it This is the active cell and is where any characters or numbers that are typed will appear You can move the active cell around the spreadsheet using the mouse to select a new one or by using the arrow keys Other keystrokes are also recognized for navigating the spreadsheet see the section on using the keyboard h59 for a full list Data Editor BAX A B E D T la Type Angles _x Date _x Day of week x Time z Name Wind Direction Date DOW Time 32 208 000 p9 15 06 2002 Saturday 21 40 33 145 000 A26 15 06 2002 Saturday 22 00 34 259 000 4 921 15 06 2002 Saturday 22 20 35 194 000 2 684 15 06 2002 Saturday 22 40 36 229 000 3 132 15 06 2002 Saturday 23 00 37 230 000 3 132 15 06 2002 Saturday 23 20 38 253 000 4 474 Saturday 23 40 ncrement 39 227 000 2 684 Date _ Sunday 00 00 40 256 000 5 369 breerzth2 Sunday 00 20 41 192 000 3 132 16 06 2002 Sunday 00 40 42 211 000 7 158 16 06 2002 Tap 01 00 43 265 000 6 263 16 06 2002 Suh Datum 01 20 44 231 000 3 132 16 06 2002 Sunday 01 40 45 232 000 6 263 16 06 2002 Sunday 02 00 46 224 000 8 724 16 06 2002 Sunday 02 20 47 248 000 3 132 16 06
16. 6 260 15 06 2002 June 3 232 000 8 050 15 06 2002 June 4 186 000 5 370 15 06 2002 June TA 5 222 000 5 820 15 06 2002 June N 6 252 000 3 580 15 06 2002 June k lt 7 239 000 10 960 15 06 2002 June 8 250 000 10 960 15 06 2002 June 9 237 000 6 260 15 06 2002 June i aa aar ann eax Sine tena x lt l u l gt 0 Note that any windows that are iconized when the command is chosen remains iconized the other windows are adjusted so that there is room for the icons at the bottom 154 Oriana 4 6 7 4 Window Close all This command will close all the windows on the Oriana desktop If you have any results or changes to the data that haven t been saved you will first be prompted to save them The current data file will also be closed 6 7 5 Window Minimize All This will minimize all windows within the Oriana program frame to icons at the bottom of the frame 6 7 6 Window Tile This command rearranges and resizes the windows on the Oriana desktop so that they are all visible at one time The following picture illustrates this Oriana 3 0 Wee File Edit Data Analyses Graphs Options Window Help DnE gs AD SaS C8 Aa Pee z o x JG 2 Data file A B gg F StatData Oriana Or2 Test Data Wind200 Eo Ea zke W 5 variables and 4495 cases 1 9 1 2 248 000 6 2 Hourly wind data garden weather station 3 232 000 8 0 amp Jun Dec 2002 4 186 000 5 3 5 222 000 5 8 lt gt
17. BE FisherB5 ori BmardiasuppP2 o1 E B arrivalExample ori S FisherB7 ori E MardiaJuppP93 1 Desktop Baxisdemo ori SB FisherB8 ori BE mardiaJuppP99 1 Weatsch10 08i BrFisherBs ori DB mardiaJuppP 106 B Batsch117 ori Wrishers11 ori PB mardiasuppp149 BE BatschP26 ori BB FisherB13 ori EE mardiaJuppP 150 BE BatschP6n ori WrisherB14 ori EE mardiasuppp246 My Documents N g f B BatschP68 ori Wrishers16 ori Bmegagen ori BeatschP7sa ori Wrishers21 ori BE megaspor ori 33 lt a gt My Computer File name Bimodal ori v Files of type all Oriana files ori odk v Cancel 5 My Network Recent folders F StatData Oriana ori2 Test Data v C Open as read only Recent Title Zar 1996 p 606 607 File Variables 1 Cases 390 Information A panel at the bottom of the dialog shows information about the currently selected file so that you can be certain you are opening the correct file Above this is a Recent Folders drop down list which shows the most recently visited folders This makes it easy to move to different folders scattered around your hard disk or network without having to browse through the whole directory structure Note that this list does not appear under Windows Vista or later as the standard dialog boxes in these operating systems have their own Recent Places folder on the left hand side that performs the same function When you have specified a file to open click on the Open button to ope
18. It is a low volume list with at most one or two messages a month To join the KCS ANNOUNCE mailing list send an e mail message to listserver kovcomp com with the following text as the subject or first line of the body of the mail message subscribe kcs announce Getting Started zz 2 Getting Started 2 1 What is Oriana Oriana is a program for Microsoft Windows that analyzes orientations and other circular data It will calculate a variety of the special types of statistics necessary for working with data measured in degrees time of day or other circular scales It will also graph the data in a number of different ways Oriana will calculate basic statistics 63 such as the circular mean and median various measures of circular dispersion such as mean vector length r concentration and circular variance and standard deviation along with confidence intervals for the mean A number of single sample statistics are available for testing whether the data adhere to uniform or other distributions There are also several multisample tests for determining whether two or more samples differ significantly from each other Finally the program can calculate correlations between circular samples as well as between sets of circular and linear data A number of graph types 7 are available for plotting the data These include variants of the histogram for circular data including rose diagrams circular histograms linear histograms and arr
19. Reset to English Compass New ce V9 crescent Phases rar Aaa S quarter Anas gi o gibbous e i Aly ites ey Waring Gibbous ee 2 quarter Waning crescent Default time zone GMT Greenwich Mean Time Dublin Edinburgh Lisbon London x 6 7 6 7 1 6 7 2 6 7 3 Menus 153 Window This menu makes it easier to arrange the various windows on the Oriana desktop Window Show Notepad This option will open the Notepad window 1 for keeping notes about the analyses of the current data file Selecting it again will close the window Window Arrange Icons When you iconize windows on the desktop they can be moved around to any point on the desktop This command will rearrange them so that they are all neatly lined up at the bottom of the desktop window Window Cascade This command rearranges and resizes the windows on the Oriana desktop so that they are all the same size and are arranged in an overlapping manner with the title bars of all windows visible The following picture illustrates this Oriana 3 0 Jog Eile Edit Data Analyses Graphs Options Window Help E A E gt SOS CE Bp X E CHARS 7NOR AA 6 X D g z i x F gt Gi Data Editor Joe az 5 A B Dis ly Type Angles x linear _x Date z Month of yez Name Direction Speed Date Month amp 1 9 170 15 06 2002 June 2 248 000
20. Set Subgrouping Variable By default Oriana will calculate statistics and draw graphs using all the data from each variable However you may sometimes want to calculate separate statistics and do separate graphs for subsets of the data You can do this by using a subgrouping variable This is a separate variable that contains data specifying to which subgroup each case or row in the data matrix belongs This dialog box allows you to specify which variable to use for subgrouping If a date variable is selected then the Summarize Dates As section becomes available and Menus 113 you can choose a variety of ways to have the dates summarized Select Subgrouping Variable Group By OK None Cancel Yariable Date Summarize Dates As No Summary Day of the Week Month of the Year Week of Year numeric D Day of Year numeric 6 3 8 Data Filter Data This command lets you restrict the analyses or graphs to a certain subset of data Set Data Filtering No filtering Filter data Variable Month v Greater than or equal Not equal Less than or equal Greater than Contains Less than Doesn t contain Value September When you tick the Filter data button you can choose a variable to use for selecting the data to analyse You can then choose a comparison type e g Equal or Greater than and enter a 6 3 9 value to use for comp
21. Williams 45 71 time 15 31 136 163 title file 105 titles graphs transform data two sample plots two variable histograms 86 138 two variable vector plots 140 U undelete 51 131 115 89 145 52 55 57 87 103 Index 171 undo 34 101 103 week of year 16 44 uniform scorestest 73 weighted means 18 65 114 uniformity plots 88 143 141 windows 4 5 7 8 9 11 153 V N 154 variable selection 120 S X variables 13 109 angle 114 X Y coordinates 25 111 angles 14 axial 12 14 47 65 85 changing type 59 107 109 circular percentage 14 circular proportional 14 compass 14 26 50 80 136 151 164 date 8 18 31 44 122 163 day of week 8 15 26 31 34 44 108 122 136 164 dayofyear 16 44 directional 14 grouping 7 19 21 43 49 54 57 85 86 109 112 120 130 131 135 141 143 145 labels 19 linear 18 114 lunar 16 152 month of year 8 15 26 31 34 44 108 122 136 164 subgrouping 7 19 21 43 49 54 57 85 86 109 112 120 130 131 135 141 143 145 time 15 31 136 163 week of year 16 44 variance 63 vector 25 111 114 von Mises distribution plot 88 143 V test 69 W Watson s U2 multisample 77 Watson s U2 multisample test 74 Watson s U2 one sample test 68 Watson Williams F test 45 71
22. a significant result so the null hypothesis is not rejected but there are a few with p values below 0 05 For those pairs where the null hypothesis is not rejected then Oriana also reports the estimated population mean of the two samples 7 Comparing these results alongside the basic statistics calculated through Analyses Stats we can see that there appear to be two groups of samples some with means around 172 174 and some with means from 177 181 note that sample Set1 has the mean reported as 0 6443 but since these are axial data the mean could also be considered to be 180 6443 Variable Set10 Number of Observations 50 Data Grouped No Group width amp number of groups Mean Vector p 0 6443 172 9989 177 7285 174 2485 172 4901 179 469 8 We can test this by doing multisample tests of these two groups Again follow steps 2 4 but this time go to the Select page of the dialog box and untick Set1 Set6 and Set14 The results of the F Test on just Set5 Set8 and Set10 gives p 0 8329 so we retain the null hypothesis that these three samples have the same population mean which Oriana estimates as 173 187 We can reverse the state of the checkboxes so that we calculate the F Test on Set1 Set6 and Set14 which gives p 0 6198 and an estimated mean of 179 491 Plotting graphs Diagrams are produced through the Graphs 127 menu We will produce some rose diagrams and a distribution plot of t
23. and should only be used if your drawing program only imports WMF files you would normally use the more flexible EMF format The last four options are bitmap formats where the file contains an exact picture of what is on the screen made up of a series of pixels The elements of a bitmap cannot be as easily modified as a metafile although you can use a painting program to add new things to the graph or erase some parts Note that the size and length width ratio of the bitmap will be exactly the same size as that of the window containing the graph If you wish to have a larger bitmap simply resize or maximize both the Oriana main window and the graph window so that they are the appropriate size The BMP files are Windows native bitmap format Most programs can import these although they can t be placed in web pages The size of BMP files is usually much bigger than any of the other options PNG files are in a compressed format and are much smaller than BMP files Most modern painting programs can import these but this format isn t as widely used as the BMP format PNG files can also be used in web pages but older versions of web browsers may not be able to display them GIF files are also compressed and are more widely used so will work with all web browsers but have a limited range of colors JPEG files can also be used in web browsers even older versions and can be imported by most graphics programs These are also compres
24. are within the range of 0 180 Circular Proportional This is also similar to the Angles type but instead of entering data in the range of 0 360 the data are entered as a proportion of the whole circle ranging from 0 1 So a value of 0 5 would be the same as 180 The range of 0 1 is also used for labeling graphs and output Circular Percentage This is like Circular Proportional but the data are ona percentage scale ranging from 0 100 Compass Direction This data type presents angular data as directions of the compass Data are entered into the editor as letters indicating the direction e g N for North SW for South west NNE for North north east etc You can use up to 16 compass points including the three letter ones such as NNE or restrict the data to the four or eight main points e g N or SW Oriana will automatically detect which you are using and adjust the histogram bar widths and chi square class widths accordingly Getting Started The underlying data are still angular and all calculations are performed on and reported as angles For mean and median directions the corresponding compass direction is also reported The actual angle stored is the midpoint of the compass sector so North would be 0 East 90 South east 135 ete You can customize the abbreviations used for compass points e g NNE to match your own preferences or local language through the Options Preferences 149 menu item Time The T
25. commonly used for linear data As with Pearson s this coefficient ranges from 1 to 1 with the former indicating a perfect negative correlation the later a perfect positive correlation and 0 indicating no correlation The formula used for the calculation is the alternative form given in Fisher s 1993 equation 6 36 The significance of the correlation is tested by using the jackknife method described in Zar 1999 p 649 650 With this the correlation is calculated multiple times each time with one pair of data being dropped The confidence limits of the series of calculated coefficients is then calculated if 0 does not fall within the limits then the null hypothesis that the correlation is 0 is rejected and the 4 3 2 4 4 4 4 1 alternative that the correlation is significantly different than 0 is accepted Note that the jackknife calculation can take a long time for large data sets so this is an option in the Analyses Correlations 125 dialog box Circular linear correlation The circular linear correlation coefficient Fisher 1993 p 145 Mardia amp Jupp 2000 p 245 Zar 1999 p 651 calculates the correlation between a circular variable and a linear one Examples of data where one might want to calculate this type of correlation could include wind direction and ozone level or direction of travel of an animal along with the distance traveled This correlation coefficient ranges from 0 to 1 so there is no ne
26. follow these steps 1 Create a new blank file in Oriana as described in the File New191 section You can simply create a file with a single column of any type 2 Go to the program that you wish to copy the data from for example a spreadsheet Use the mouse to select the data you wish to copy and choose the Edit Copy command for that program clicking on the upper left corner of the sheet headers will select all data 3 Switch back to Oriana place the cursor in the second row of the data editor the one with the row label Name Then choose Edit Paste The data will then be pasted into the editor Oriana tries to guess the correct data type for each column as described in the section on the Edit Paste 10 command 3 9 Calculating statistics Once a data file has been created or loaded you can then perform analyses The Analyses 120 menu lists the various types of analyses available Selecting any one of these will cause a dialog box to be displayed giving the various options for the analysis When the OK button is pressed a new page will be added to the Results window and the analysis will be performed Here is an example of the steps required to calculate basic statistics 1 Open 38 a data file the Wind2002 ori example data file distributed with Oriana can be used 2 Select Analyses Stats 12A from the menu A multi page dialog box with tabs along the side will appear The first page contains options to select th
27. following sections 6 5 1 1 Colors This page lets you customize the colors used for various graph elements Histograms Ze Main Backgrounds Lines Options Chart white v Axes H black v E Grid l White im Grid LESS v ae Title C white Stats H Black v Legend C whi fa Inace Stats a fes Legi C White v I Red v i Plot Series Colors ae g Monochrome Graphs Series 1 Blue a A Symbols Series 2 Red Seneca Series 3 Yellow E sue v Titles Series 4 Fuchsia Series 5 Silver Series 6 Lime Fonts Series 7 Aqua Series 8 Black Series 9 Maroon Mij Cancel Help The Background section lets you change the color of the background of the whole chart the gridded portion within the main axes of the graph the box behind the graph title and the box behind the legend A new color can be chosen from the drop down boxes The Lines section allows you to change the color of the lines used for the main axes the grid within the axes and the line used to indicate the statistics of the data the mean and confidence limits The Inace Stats choice lets you change the color that is used for the confidence limits when there is a small sample size and or low concentration By default this is red to warn those viewing the graph that the limits may be unreliable The Monochrome Graphs option switches the graph to being produced in black and white for reproduction
28. for the next occurrence by clicking on Find Next again The dialog box remains open until you press the Cancel button The dialog box is non modal which means you can switch back to the data editor and make changes if you wish while the Find dialog remains open 6 3 14 Data Replace This dialog box searches for values in the data editor in an identical way to Data Find and lets you optionally replace the found value with a new one Replace Find what 200 Replace with 200 1 C Match whole word only C Match case Once a data value has been found you can click the Replace 120 Oriana 4 button to replace it with the value in the Replace With box The program will then automatically search for the next occurrence Clicking on the Replace All button will cause the program to scan through the entire file replacing all occurrences of the find text with the replace text The resulting replacement is first checked for whether it is valid given the variable type If it is not valid then the value is not changed For example replacing 2003 in a date variable with ABCD will leave all values as they were as ABCD is not valid in a date Likewise changing day to dog will not affect any of the values in a Day of Week variable as Mondog is not a valid day of the week 6 4 Analyses This menu contains the analyses functions When you choose one of these you will be presented with a di
29. graph is saved at its current size so if you want a larger bitmap with higher resolution and fewer jagged edges increase the window to its maximum size This format can be edited in a painting type of program such as the Paint program included with Windows but only on a pixel by pixel basis e The metafile formats EMF and WMF saves the graph as a vector based drawing This means that the graphic elements such as lines and circles are saved as descriptions of those elements rather than as a collection of pixels Thus the graph can be resized or printed in another program at the highest resolution available Also the graph can be modified in a vector based drawing package This would allow you for instance to change the dashed line to a dotted one or change the text of the labels The format used for saving the file is specified using the List Files of Type option on the File Export dialog box A graph can also be transferred to another program using the Windows clipboard Just choose the Edit Copy menu item when the graph window is the active window You can then switch to another program and use Edit Paste to make the transfer Oriana places both bitmap and metafile versions of the graph on the clipboard so you can paste either one into your other program 2 2 1 6 Notepad The Notepad window provides a space for you to make notes about the analyses you ve done and any trends you ve noticed It is a simple text editor wi
30. in monochrome publications All lines will be black and the graph elements 6 5 1 2 Menus 129 such as histogram bars and symbols will be filled with the patterns selected on the Lines amp Patterns page The Plot Series Colors section lists the different fill colors used for filling bars and symbols in color graphs The first color is used in most graphs and subsequent colors are used for further data series in stacked stepped histograms The colors can be changed by selecting the desired series and using the Set Series Color option to the right Lines amp Patterns This page lets you customize the lines and patterns used for various graph elements 7 zE Histograms Main Axes Stats lines f Style Solid Style Solid v Options width E v width 2 v Select Grid Axes Style Dot ly Outline around bars E V Draw Grid Colors width 1 v Ea tines amp Plot Series Patterns Set Series Pattern Patterns Series 1 Solid HE Solid Symbols Series 2 Clear Series 3 Horizontal Titles Series 4 Vertical Series 5 Diagonal Right Fonts Series 6 Diagonal Left Series 7 Cross Series 8 DiagCross OK Cancel Help Axes Style changes the style of the lines forming the main axes of the graph and Axes Width changes the width of these lines Note that width can only be adjusted for solid lines The Grid Style and Grid Width options do the same for the
31. numeric data both positive and negative These data can then be plotted along with the circular data on the two variable histograms 138 circular linear plots 87 or the two sample scatter plotsl144 and compared to the circular data with circular linear correlation 128 When the linear variable represents the length of a vector e g wind speed or distance traveled then you can define an angle variable and a linear variable as a vector pair through the Data Define Vector Pairh menu item This allows you to calculate weighted mean values where the mean angle is weighted by the length of the vectors in the basic statistics as well as add a weighted mean vector to circular plots Getting Started 9 This data type is also used for specifying the frequency of different values when data are being entered in a frequency table format 22 and for specifying the r value when means and mean vector lengths are being input for second order statistical analysis 76 Labels The label variable type can contain any type of text and is normally used for labeling cases to identify them Subgroup This variable type is similar to the Labels type in that you can type any text into it However it is specialized to be used for dividing cases up into subgroups 43 so that each subgroup can be analyzed separately When text is entered into a Subgroup variable in the data editor that text is added to an internal list of possible subgroups Tha
32. points Raw data plots Je Main Type Data points arranged Options Select from margin inwards Axes from margin outwards Colors from center outwards Lines amp Patterns symbols Subgroups on single plot Titles Fonts coo e_ When Data points arranged is set to from margin inwards then the points start at the outer rim of the circular graph and are stacked inwards The from margin outwards also starts at the outer rim but stacks the points outwards instead The circle 6 5 6 Menus 143 of the graph is much smaller with the labels in the inside to give plenty of room for the points The third option from center outwards starts from the middle of the graph and stacks the points outwards The points actually start from a circle plotted a small distance outside the center of the plots because if all points started at the very center they would overlap too much You can adjust the size of this circle with the Basal circle diameter option on the Axes page If you have a subgrouping variable in use then by default a separate graph is created for each subgroup You can tick the Subgroups on single plot option to have them all plotted on a single plot with different colors or symbols for each subgroup as specified on the Colors and Symbols pages The Options and Select pages are identical to those in the Graphs Histogram 33 dialog box Graphs Distribution
33. similar to that in the Graphs Histogram 3A dialog box with two exceptions The Weighted Mean options works slightly differently If the weighted option is selected for the r Value statistic then the length of the weighted vector arrow will reflect the native units of the weighting variable so it can be compared to the individual data points on the graph rather than being scaled 0 1 like the unweighted r As a result if you change the scaling of a graph 142 Oriana 4 the length of the weighted r arrow will also change to match the data Also there is a new statistics option The Standard deviation ellipse option plots the weighted mean as a centroid point along with an ellipse that depicts the standard deviation of the data along the two major axes the exact values of the centroid and standard deviations are given in the Analyses Stats h2 output as the angle length and SD of the Weighted Mean Vector These are calculated from the weighted sines and cosines data This option along with the Plot only 0 180 option on the Axes page is commonly used in ophthalmological studies see Holladay et al 2001 The Select page is similar to that for two variable histograms 133 6 5 5 Graphs Raw Data Plots This graph type allows you to plot raw data plots 81 where each data point i e row in the data matrix is plotted on the graph with a symbol stacked up in a histogram like format There are three methods of placing the
34. the same but skip Saturdays and Sundays The Week option will increment the value by one week i e seven days The Month option will increment the month by one for each row If the day portion of the starting date is one that occurs in only some months such as 31 the day used for shorter months will be the last one e g 28 or 29 for February The Year option will increment the date by a year for each row All the above date filling types take the Increment value into account e g if the increment is 3 and the fill type is Month then the dates generated will be three months apart Data Find This displays a standard Windows find dialog to search for particular data values Find xi Find what 2001 C Match whole word only Direction C Match case OUp Down Type in the text you wish to find and press the Find Next button The program will search through the data in the direction chosen then will highlight that data cell scrolling it into view if necessary The search proceeds columnwise searching either to the bottom or the top of a column before moving on to the next one to the left if Up Direction is chosen or to the right if Down is selected Ticking the Match Whole Word Only box will restrict the search to only finding a cell if the Find text matches the entire text in the cell The search can be made case sensitive by ticking the Match Case box Once a value has been found you can search
35. the windows and their contents letting you pick up where you left off in your analyses You can have Oriana automatically save and restore your desktop each time you exit or start the program The Options Preferences 149 dialog box allows you to turn this feature on or off When it is on your desktop will saved each time you exit Oriana When you next run Oriana the desktop will be returned to the same state File Import Oriana imports data through an import preview dialog box This shows you a preview of how the data will be imported and allows you to change various options so that the data are imported correctly Oriana can import data from the following formats Excel ver 2 1 through 2010 Lotus 1 2 3 ver 1 0 5 0 Symphony ver 1 0 1 1 Quattro Pro ver 1 0 6 0 dBase all versions Paradox ver 3 0 7 0 With all these formats Oriana assumes the data are column oriented that is the data for each variable or set of observations should be in a column with an optional column label at the top of the column e plain text files When you choose the File Import option you will first be shown a standard Open File dialog box The Files of type section will list all the possible import formats Set this to the correct format and select a file When you press Open Oriana will import a portion of the file You may see a warning dialog box saying that only a certain number of data rows were imported for preview not the w
36. this by explicitly saving the data with File Save Data If you try to exit the program or open create a new file when the data have not been saved you will be warned and asked if you wish to save the data Selecting spreadsheet cells Normally the spreadsheet will have a single active cell while you are working on it The active cell can be selected by positioning the cursor which is a op when it is over the spreadsheet over the desired cell and clicking the left mouse button Alternatively you can move the selected box around using the arrow keys This image shows the active cell in column A row 2 A B E D Type Axial Axial Axial Axial 00 Name ISOETES PAXILL SELAG ERLAN 1 94 000 112 0 38 000 2 aay 102 000 120 000 T 3 88 000 80 000 155 000 i 4 94 000 80 000 123 000 1 5 92 000 110 000 157 000 1 6 92 000 69 000 54 000 l 7 80 000 105 000 84 000 1 8 87 000 119 000 43 000 Pa at To select a number of cells in preparation for deleting them or copying them to the clipboard you can simply hold down the left mouse button and drag the cursor over the desired cells Alternatively hold down the shift key while you move the cursor with the arrow keys The resulting selected block of cells will look like this Tutorial SELAG ERLAN PASILL 112 000 36 000 0 120 000 1 0 155 000 7 123 000 1 157 000 1 6 92 000 69 000 54 000 j fi 80 000
37. users to the Oriana or Windows manuals for more basic queries Please note that free technical support only applies to questions on the actual use of the program and its features it does not extend to help on the statistical techniques themselves or interpretation of the results The user should refer to the literature 153 about circular statistics However Kovach Computing Services does offer data analysis consulting services at reasonable rates Please contact us for details Bug reports If you encounter a problem that you think may be a bug in Oriana yes all programs have the occasional bug in them please contact us so that we can try to track down the cause Please send as much detail about the problem as possible what you were doing at the time the exact wording of the error message a detailed description of what happened when the problem occurred details of your system configuration and other software that was running on your machine at the time and a copy of the data file if possible If the problem involves an error message then the message dialog box will usually have a button labeled Report If you press the button and follow through the steps this will automate the process of sending information about the error to us Upgrades Existing users of Oriana will be eligible for special prices on major new versions of the program e g upgrading from version 3 to 4 Minor upgrades e g from 4 0 to 4 1 can be down
38. variable for subgrouping results Modified 0 Note that most of the commands from the menus are also represented as buttons on the toolbars at the top and left hand side in the image above These toolbars can be customized to show just the buttons you want and can be positioned anywhere you would like There are eight different toolbars that you can display one for each top level item in the main menu You can choose which toolbars to display by right clicking the mouse in an empty area next to one of the toolbars and clicking on the name of the desired toolbar The buttons displayed on each toolbar can be customized by clicking on the downward pointing triangle on the right hand side of the toolbar hovering the mouse over the Add or Remove Buttons item then over the toolbar name A list of all possible buttons for that toolbar will appear with a checkmark next to those that are visible You can then click on the items to check or uncheck the desired buttons The toolbars themselves can be moved around by clicking and holding the mouse on the bar at the left end of the toolbar indicated above The toolbars can be moved around to different positions at the top or left hand side of the main window as shown above They can also be placed on the right hand side or bottom of the window by dragging them to those positions Finally you can drag the toolbar to float over the center of the window or float outside of the win
39. variables are displayed as columns with the observations for each sample filling the rows Each column can have different numbers of observations 2 2 1 4 Data Editor BAX A B c D A Type Angles _ Linear y dRate v _ Month of year min Name Direction Speed y Change Data Month 1 1 9 171 Type 462 June 2 248 000 6 263 15 06 2002 June X 3 232 000 8 053 15 06 2002 June X 4 186 000 5 369 15 06 2002 June bd 5 222 000 5 816 15 06 2002 June X 6 252 000 3 579 15 06 2002 June v E 239 000 10 961 15 06 2002 June X 8 250 000 10 961 15 06 2002 June X 9 237 000 6 263 15 06 2002 June v 10 236 000 5 369 15 06 2002 June X an 145 000 4 026 15 06 2002 June ad 12 229 000 3 132 15 06 2002 June E le lt gt The first row headed Type displays the data type for that column You can change the type of the data by simply clicking on the down arrow labeled Change data type above The data are displayed in a format that matches the data type MA You can adjust certain aspects of the format such as number of decimal places or whether seconds should be displayed through the Options Preferences 149 dialog box The display of certain data types such as date or Day of Week will be displayed in your local format and language as set up in the Windows Control Panel Results window The results of the statistical analyses are displayed in a tabular format in the Results window This is basically a spreadsheet and works in a sim
40. you to set the number of entries on the Reopen menu Display grid in This lets you choose whether to have grids displayed in the data editor and results spreadsheets Theme This lets you change the visual appearance of the Oriana Menus 151 window including different colors and visual effects By default a scheme is chosen that will match your current Windows theme as well as possible The drop down box for this option lets you change it to a different one The new theme will be applied immediately after you select a new one so that you can easily see the effects of the different themes but the change is only made permanent when you press OK If you press Cancel the theme will revert to the original one The second page of the dialog box labeled Warnings lets you set whether certain warning messages are shown When these warnings are displayed they have a check box labeled Don t show this again that suppresses future display of the warning This dialog box lets you turn them back on again Program Preferences General By default Oriana displays warning messages during various operations Warmi Experienced users may wish to skip these warnings by unchecking the arnings appropriate boxes below Compass V Incompatible variable type conversions V Missing data after conversions WV Frequency editing will change the order of data Desktop not saved V Prompt to consolidate Oriana ver 1 files V Only a subs
41. 0 to just less than 20 etc 12 00 Note that the above graph has a black line running from the center of the diagram to the outer edge at approximately 17 00 This is the mean angle of the data The arcs extending to either side represent the confidence limits of the mean They can be either the 95 or 99 confidence limits depending on the setting in the Graphs Histograms 133 dialog box Note that sometimes the confidence limits can be unreliable when the combination of the sample size and the concentration is low In these cases the confidence limit arc can be displayed ina different color By default this is red rather than black but the color can be changed with the Inace Stats option on the Colors page of the dialog box As an alternative the mean can also be depicted as an arrow the length of which represents the value of r which is described in the section on Basic Statistics 63 The above type of graph can be misleading because our visual perception takes the whole area of a wedge into account when comparing them rather than just its length A wedge that is one third the radius of another actually appears far less important since the area of the smaller wedge is only one ninth the area of the larger one To avoid this problem the wedges can be drawn so that the frequency is represented by the area of the wedge The following graph uses the same data as the one above but the area option has been selected
42. 105 000 84 000 1i 8 87 000 119 000 43 000 l oor You can select whole rows or columns by clicking on the row or column headers Multiple rows or columns can be selected by dragging the cursor across the headers The current row can also be selected by pressing Shift Space a column can be selected with Ctrl Space The following images show the result the sre is positioned over the header that was clicked to perform the selection A B c D Type Axial Axial Axial Axial Name ISOETES PAXILL SELAG ERLAN 1 94 000 112 000 38 000 i 2 88 000 102 000 120 000 1 3 60 0 00 4 94 000 80 000 123 000 1 5 92 000 110 000 157 000 1 6 92 000 69 000 54 000 80 000 105 000 84 000 1 8 87 000 119 000 43 000 l A Z Axial ISOETES SELAG ERLAN 1 94 2 000 38 000 2 88 0 120 000 1 a 88 000 155 000 4 94 8 0 123 000 1 5 92 0 000 157 000 1 6 92 6 0 54 000 i 0 84 000 1i 8 43 000 l a X 4 3 4 The entire spreadsheet can be selected by pressing the button in the upper left corner of the spreadsheet You can also select the whole spreadsheet using the Edit Select all command or by pressing Shift Ctrl Space The result looks like this we A B C Wia eel Axial Axial Name ISOETES PAXILL SELAG ERLAN x 2 3 4 5 6 co Editing data There are a number of editing actions you can perform on e
43. 2002 Sunday 02 40 y The spreadsheet has column headers labeled A B C etc and row headers labeled 1 2 3 etc These headers indicate the position within the spreadsheet and also can be clicked to select the whole row or column for editing purposes You can change the width of the columns and height of the rows Tutorial by using the mouse to drag the separator between the headers Normally each row or column is changed individually However holding down the shift key while you resize a row or column causes all others to be changed to the same size The first two rows are shaded The first row contains the indicator of the type of the variable You can change the variable type say from Angles to Time by clicking on the little arrow next to each cell labeled Change data type above and choosing a new type The second row contains the name of each variable These labels are used on the output to identify the variables or sets of observations New variables are by default given the same name as their data type You can change these by making the appropriate cell active and typing any characters Spaces may be included and the labels may be up to 60 characters long although shorter labels allow you to keep the columns widths narrow and see more data on the screen Typing in data Once labels have been entered you can start typing in the numeric data This is done by making the appropriate cell active and typ
44. 23 Ea calculating statistics 41 45 63 120 Cartesian coordinates 25 111 changing variable type 59 chi squared multisample test 72 chi squared one sample test 69 circular histograms 81 133 138 circular percentage 14 circular proportional 14 circular scatterplots 57 87 114 140 circular circular correlation 75 circular linear correlation 76 circular linear plots 57 87 114 140 closing files 93 colors 52 128 comparing samples 45 compass 14 26 50 80 136 151 164 concentration 63 confidence interval 48 63 79 128 129 134 41 45 coordinates Cartesian X Y 25 111 correlations 125 circular circular 75 circular linear 76 Index 167 creating datafiles 29 91 creating graphs 9 47 79 127 cut and paste 32 102 103 104 D data approximate 26 Cartesian coordinates 25 111 deleting 34 deviations 24 display format editing 30 34 exporting 97 filling 116 149 filter 44 113 frequencies 22 36 43 106 120 grouped 26 65 107 grouping see also subgrouping variable importing 94 inserting 34 merge 100 missing 26 modifying 34 paired 20 radians 115 random 116 saving 38 select 44 113 sorting 115 standardize 115 summarizing 60 transform 115 types see also variables 13 variables see also variables 13 65 43 112 X Y coordinates 25 111 data editor 7 29 32 grid 149 data file creating 29 structure 161 title 105 dataformat 12 13 19 107 109 dataimport 39 d
45. Direction and Distance N The vector type of circular linear plot is superficially like the Arrow Histogram 83 but in this case each arrow corresponds to a single observation The direction the arrow is pointing is taken from the selected circular variable while the length of the arrow is determined by the chosen second variable So you could for example use this graph to plot the direction and distance traveled for each animal observed or the orientation and length of individual toolmarks in sedimentary rocks 5 9 Direction and Distance WW s0 40 30 20 10 Seep 20 30 40 S01 E Instead of arrows you can also choose to have the linear variable represented by bars or wedges Distribution Plots Distribution plots allow you to assess the departure of your data from a certain distribution such as uniformity Each datum is plotted against the value expected for that datum given the desired distribution The points on the plot should lie alonga 45 angle the diagram has a reference line at this angle Departures from the distribution can be seen as departures from this line The following graph compares arrival time against a uniform distribution it is clear that there are departures from uniformity Arrival o oo Shh at DERE tee 9 Caan o D o ps MEE SO AN ENEE E Sample Quantiles o 0 2 0 4 0 6 0 8 1 Uniform Quantiles o Since the data are circular and the starting point o
46. Legend Example Fonts Legend Position Top Right v Legend Box Style Single v C Ce Coe The various graph elements are 6 5 2 Menus 133 e Main Title The title that appears at the top center of the graph e Axes Titles These are the titles that appear alongside the X and Y axes of graphs like linear histograms scatterplots etc They do not appear on the circular graph types e Large Axis Labels These are the larger axis tick mark labels These are used for labeling the tick marks along X and Y axes of scatterplots etc This font is also used for labeling the four point on circular diagrams e g the 0 90 180 and 270 points and the minor divisions e Small Axis Labels These are used for labeling the steps of the circular grid in circular diagrams e Legend This is used for labeling the entries in the legend The title of the legend will use the same font but in boldface and underlined The Title Box Style and Legend Box Style drop down boxes allow you to customize or remove the box that is drawn around these two graph elements The Legend Position adjusts where the legend is drawn Graphs Histograms This option allows you to plot a variety of histograms 79 Choosing this option will cause the following dialog box to be displayed Histograms Main Type Frequency shown as Options Rose Radius of wedge Select Stacked Rose Area of wedge Axe
47. Moore s Paired Samples The analyses on this dialog box assume that the data consist of pairs of variables one a circular variable that contains means calculated from samples of raw observations and a linear variable that contains the length of each mean vector You can use these analyses when you have been supplied with data in the form of means or have calculated them yourself Note that if your data are raw observations you can use the Basic Statistics23 command to calculate the means for each set of observations column in the data matrix That dialog box has an option to save the means to a file which can then be opened and analysed with this second order stats command Graphs This menu contains the graph functions When you choose one of these you will be presented with a dialog box that allows you to select the samples to graph and the options for how the graphs should be plotted Each graph will be created in a separate page of the graph window The size of the graph may be adjusted by resizing the window If you wish to change the type of graph on a page choose the Graphs Edit graphl 4 option you will then be presented with the dialog box originally used to create the graph 128 Oriana 4 6 5 1 Common elements of graph dialogs All dialog boxes for creating graphs have five pages that control various aspects of the appearance of the graph The options on these pages are described in the
48. Oriana Version 4 Users Manual 1994 2011 Kovach Computing Services All Rights Reserved Published by Kovach Computing Services Pentraeth Wales U K Last revised October 2011 Oriana Copyright 1994 2011 Kovach Computing Services All Rights Reserved LIMITED USER LICENCE Kovach Computing Services the licensor grants the purchaser the licensee a licence for the computer program Oriana the program in accordance with the terms and conditions contained in this agreement The program is owned by us and is protected by copyright law and we reserve ownership of all Intellectual Property Rights in it and all rights other than those expressly granted by this Agreement The program is licensed for use by one user The program may be transferred between computers or users so long as there is NO POSSIBILITY that the program will be used by more than one user at any one time The licensee may make additional copies of the software for archival purposes only Any accompanying printed user documentation may not be copied in any way You must keep any activation or registration code provided to you confidential You must take reasonable steps to protect the Software from unauthorised copying publication disclosure or distribution The licensee shall not use copy rent lease sell modify decompile disassemble otherwise reverse engineer or transfer the licensed program except as provided in this agreement Any such unautho
49. This option allows you to calculate correlations between variables in your data This will cause the following dialog box to be displayed See the section on correlations 75 to learn more about each test 126 Oriana 4 Correlations Main f Select Circular Circular Correlation Calc jackknifed probabilities Circular Linear Correlation OK Cancel Help When Circular Circular Correlation is chosen you can also select whether to have probabilities calculated using a jackknifed procedure using the option labeled Calc jackknifed probabilities This can take a long time for large data sets so you may wish to leave it turned off When you press the OK button the tests you have chosen will be calculated and the results placed in a table The results will be printed with the number of decimal points specified in Options Preferences 149 6 4 5 Analyses Second Order Stats This option allows you to calculate second order statistics 76 on your data This will cause the following dialog box to be displayed 6 5 Menus 127 Second Order Statistics eg Main Note these analyses assume that the values in the data editor are means and vector lengths not raw data Select V Grand Mean Angle V Grandr Y Confidence Intervals V Hotelling s One Sample V Moore s One Sample V Hotelling s Two Sample V Mardia s Two Sample nonparametric V Hotelling s Paired Samples V
50. Transform This command allows you to perform various transformations on your data You can transform a single variable by choosing the variable from the drop down list labeled Variable below or transform all variables of the appropriate type either Angles Axial or Linear by choosing the All Variables option at the top of the drop down box 6 3 12 Transform Data Variable Speed ily 2 Cancel Circular D Radians to Degrees Linear Log base 10 Use Log X 1 Log base e Standardize _ Square root For circular data the only available transformation is from radians to degrees Oriana assumes that data in Angles or Axial variables are in degrees However you may already have data in the form of radians This transformation will allow you to import or paste radians data then transform them to degrees so they can be analyzed Linear data can have a variety of transformations applied including logarithmic base 10 and e square root and standardization When log transforming data zero values can cause problems as the log of 0 is undefined If your data have zeros you can tick the Use Log X 1 option to add 1 to all values thus allowing the log transformation to occur If any negative values are found for either log or square root transformations then the transformation will not be performed Data Fill This command lets you fill a variable with a variet
51. Windows applications It closely follows the modern Windows standards for menu structures and the behavior of the Windows elements It also allows you to easily move data results and graphs between Windows programs so that you can paste data from another application into Oriana or transfer a table of results and a graph into your word processor Oriana also tailors itself to the way you work so that your favorite program options are saved automatically and reinstated later You can also save whole sets of graphs and results using the KCS Desktop Metaphor 4 allowing you to return to work at the point where you left off This program is meant to be a tool rather than a teaching program this manual does not purport to teach you about circular statistics You should make sure you understand the basic theory and assumptions behind the methods presented in this package There are a number of good books and papers listed in the Referencesh5 section that will help you in learning about these methods KCS Desktop Metaphor Oriana uses the KCS Desktop Metaphor You can spread out your data the statistical results and the graphs in front of you while you study them just like paper on your desktop Each piece of paper is collected into notebook like windows one for graphs and one for results These have tabs to access each page There is also a notepad window that allows you to keep notes about the analyses you are performing All these wind
52. acing Test Mardia amp Jupp 200 p 108 Batschelet 1981 p 66 also takes as its null hypothesis that the data are uniformly distributed This is tested by looking to see if the spacing between adjacent points is roughly equal around the circle using the equations on the above cited pages For uniform distribution the spacing between points should be roughly 360 n If the actual spacings deviate too much from this value then the likelihood that the data are uniformly distributed is reduced This test can be more powerful than Rayleigh s test For example the data in the graph below seem to be non uniform appearing to be bimodal However the length of the mean vector is very small note the short mean arrow on the graph and Rayleigh s test gives a non significant result with a probability of 0 811 However Rao s spacing test gives a probability less than 0 01 and the null hypothesis of uniformity can be rejected 270 x 90 Watson s U2 Test Fisher 1993 p 84 Mardia amp Jupp 2000 p 104 Zar 1999 p 657 Batschelet 1981 p 79 performs a goodness of fit test against a specified distribution either uniform or von Mises It does this by calculating the mean square deviation for the fitted distribution If the deviation is too high resulting in a high U and a low probability then the null hypothesis that the data fit the chosen distribution is rejected When the uniform distribution is selected the modifi
53. adsheets used for data editing and displaying the results the selected 3Z cells are copied Edit Paste Choosing this option will paste data from the Windows clipboard to Oriana The data will be inserted at the currently highlighted cell and will overwrite any existing data You must have first copied some text or data to the clipboard before choosing this command otherwise the Edit Paste command will be disabled The data in the clipboard may have been copied from the Oriana data editor or from another spreadsheet program Data may also be pasted from programs such as word processors However Oriana expects that the data for different cells are separated by tabs with carriage returns separating data that belong on a new row If no tabs or carriage returns are encountered Oriana will paste as much as possible into a single cell When pasting data from other programs into empty columns Oriana will do its best to guess the type of data and convert the variable accordingly If the column already contains data then the newly pasted data must match the variable type Any data that doesn t match the type for example pasting date format data into an angle variable will be left out and the cell will remain blank A warning message will be displayed if this happens Edit Delete Choosing this option will delete the currently selected B data leaving the cell or cells blank If you accidentally delete some data then decide yo
54. al j 12 T Terminator Two x 14 O Times NewRoman 16 M Effects Sample C Strikeout F AaBbYyZz C Underline eo Color HMB Black Script Western With the graph window different fonts can be used for the numeric labels on the graphs and the axes labels and title When this window is active you will be shown the Font page of the Graphs Edit Graphl14 dialog which allows you to change these fonts individually Clicking on each of the buttons below will produce a font dialog like that above Histograms eax Main Options Select Axes Colors Lines amp Patterns Symbols Titles m Title Box Style Legend Position Legend Box Style Example Example Example Example Example Top Right v Single v C Ce Coe 6 6 2 Options Format This dialog lets you change the various options for how data are displayed in the data editor and results window Data Format OK Lk Help Decimal places 3 Cancel C Include seconds in time Windows Format settings Time First is the setting of the number of Decimal Places for numeric data followed by an option as to whether to Include seconds in time data These are followed by three buttons that take you directly to the Windows format setting dialog boxes for setting the format of Numbers Times and Dates Changing these three options wi
55. alculate tests as option lets you decide whether to compare the columns of the data matrix in a pairwise fashion where each column is compared to one of the others or multisample where all columns are compared in a single analysis When you press the OK button the tests you have chosen will be calculated and the results placed in a table The results will be 6 4 4 Menus 125 printed with the number of decimal points specified in Options Preferences 145 The Options page contains two options related to the Chi squared analysis Multisample Tests Main Chi squared options Options 10 0 class Width Select Drop Classes with 0 Observations E Cancel Help The first option Class Width lets you set the class width in degrees that is used in creating the frequency table for the chi squared analysis The chi squared test assumes that the expected frequencies in most classes are greater than five a warning will be printed if too many of them are below this level However your measurements may be restricted to a portion of the full circle e g between 45 and 135 degrees In this situation many of the classes will be empty and the frequencies will be zero The Drop Classes with 0 Observations option lets you automatically drop all classes which have no observations thus restricting the analysis to that portion of the circle that is of interest Analyses Correlations
56. allowing you to enter the observations and their frequency Once you are done the column of the data editor will be filled with data representing all the observations summarized in the frequency table in a single column 2 You can also enter frequency data directly in the data editor To do this you need to have two variables the first being one of the circular types and the other a Linear type variable You can then enter the data in the same form as the table above as in this example a E Data Editor KJ B n Type Angles x Linear xl Name Direction Frequency 1 15 000 2 15 000 25 000 3 30 000 35 000 4 45 000 45 000 5 60 000 35 000 6 75 000 25 000 fa 90 000 15 000 8 180 000 15 000 195 000 25 000 210 000 35 000 225 000 45 000 240 000 35 000 255 000 25 000 gt When this method is used for entering frequency data you must specify that the data are in frequency format on the Select pageli20 of the Analyses or Graphs dialog boxes Note that the second method can only be used for basic statistics and histograms If you need to do multisample comparison tests then you will need to use the first method or use Data Change Data Structure to convert the frequency table to raw data Deviation Data Occasionally data are measured as deviations from a particular direction For example it might be expected that bees would fly in a particular direction and observations are made of the actual angle of travel compare
57. alog box that allows you to select the samples to analyze and the options for how the analysis should be performed A table will be created ina separate window to contain the results 6 4 1 Select page All the dialog boxes displayed by the commands under the Analyses and Graphs menus contain a tabbed page entitled Select It allows you to select which variables sets of observations to analyze and whether to use a subgrouping variable Menus 121 Statistics ax Main Raw D Frequency Subgrouping Select Variable None 4 tection coh See seteonans Use variable lal Time Summarize Dates As No Summary Day of Year numeric OK Cancel l Help The box marked Variable on the left hand side lists all the circular variables in the data file For most analyses and graphs all of them will initially be ticked indicating that they will be used in the analysis or graph You can remove a variable from analysis by clearing the checkbox Oriana will remember the selection state of the variables during the current analysis session so that you don t need to reset them for every analysis and graph In the above example a file with paired datal 20 is being used and the Raw option at the top is selected If your data have been entered directly in the spreadsheet as frequency datal 22 you can select the Frequency option then select the two variables with your circu
58. analyses and Oriana s particular implementation is given For details and a greater understanding of the analyses you should look to some of the circular statistics literature The references 158 section of this document lists many references and in the following text page references are given to some of the textbooks that describe the analyses Statistics Oriana calculates a variety of special circular statistics on each sample These are mainly descriptive statistics similar to those provided by other general statistics packages but they are special versions designed for circular data There are also a number of one sample tests of probability The statistics included in Oriana are described briefly in the next two sections See the section on the Analyses Stats 123 command for details on how to run these analyses Basic Statistics Many of the basic statistical parameters are based on the concept of the mean vector A group of observations or individual vectors have a mean vector that can be calculated by combining each of the individual vectors the calculations are explained in most books 158 about circular statistics BASIC STATISTICS Data file E StatData Oriana Ori2 Test Data Wind2002 ori Hourly wind data garden weather station Jun Dec 2002 Analysis begun 29 May 2003 15 40 28 Variable Direction Number of Observations 4495 Data Grouped No Group width amp number of groups Mean Vector p 226 7189
59. ar data 3 23 Summarizing data You may sometimes wish to summarize a variable to allow for particular types of analyses For example if you have recorded the exact date of an event you may wish to summarize these by month so that you can look at trends throughout the year You can do this by creating a new variable from the original date one This is done with the Data Change Variable Type command 1 Place the cursor in the column of the desired date variable in the data editor and choose the Data Change Variable Type menu item tutorial ot Change Variable Type Variable l Date x Data are grouped roug Tees Basic Type D Angles D Day of year D Axial D Compass Direction Circ Proportional Date Circ Percentage Linear Time Label Day of week SubGroup Month of year Lunar D Week of year 2 Inthe Basic Type section choose the desired type of the new variable Month of year in this case 3 Ensure that the Create new variable option is ticked 4 Click OK A new variable will be inserted next to the date variable containing the month of year corresponding to each date 4 1 4 1 1 Analyses There are several types of analyses that Oriana can perform Some procedures will give you basic statistics on each sample whereas others will allow you to compare samples to test whether they differ significantly In the descriptions that follow the basic concept behind the
60. arisons in the Value box For example if you wish to only analyse data from September you would set up the dialog box as shown above with the variable Month and the comparison type Equal selected and the word September in the Value box You could also use the abbreviated value Sep If you instead wanted to restrict the analysis to measurements where the wind speed was greater than 20 miles per hour you would select the variable Wind Speed the Greater than comparison type and enter 20 in the Value box If the variable you are using is a Label or Subgrouping variable then you can use the Contains and Doesn t contain options to base the selection on a part of the data in that variable For example if you had observations labels like Sample1 1 Sample1 2 Sample 1 3 Sample2 1 Sample 2 2 Sample 2 3 and you wanted to restrict the analysis to just the first three you would select Contains and enter Sample1 in the Value box When you press the OK button Oriana will check that the value entered in the Value box is appropriate given the variable type chosen If not a message will be displayed and you will be given the opportunity to fix it Data Define Vector Pair Circular data are often accompanied by a second variable describing length speed or other data measured on a linear scale The two variables together describe a vector If you have data in this format you ca
61. at any ties between samples e g identical angles such as 135 in two or more samples are broken Oriana does this by randomly assigning different ranks during the ranking procedure The actual ranks assigned will be the same for subsequent runs of the test so long as the order of the original data remains the same However if you re sort the data and run this test again you may get a different result for W because the randomly assigned ranks will differ If this is likely to cause problems you may wish to break any ranks manually before running the test You can do this by replacing the identical values with two slightly different values e g replace two 135 observations with 134 999 in one sample and 135 in the other You must remember though that this may cause unwanted effects in other statistical procedures 4 2 4 4 2 5 4 2 6 This test cannot be performed on grouped 26 data Watson s U2 Test Watson s U2 Test Mardia amp Jupp 2000 p 150 Batschelet 1981 p 114 Zar 1999 p 630 is a two sample analogue of the single sample Watson s U2 68 test instead of comparing a set of data to a theoretical distribution two sets of data are compared using mean square deviations The null hypothesis is that the two samples have the same distribution A significant p value leads to the rejection of this hypothesis and the acceptance of the alternative hypothesis that the samples are from populations that differ in some
62. at the expected frequencies in each class are 2 or greater If you wish to perform the chi squared test on data that are not grouped you will have to first declare them as grouped and set the class width using the Data Change Variable Typel107 dialog box The V Test Fisher 1993 p 69 Mardia amp Jupp 2000 p 98 Batschelet 1981 p 58 Zar 1999 p 618 is a variant of the Rayleigh test but instead of testing the null hypothesis of uniformity against an unspecified alternative the V test tests against an alternative hypothesis that the distribution is a non uniform one with a specified mean direction The specified mean direction is a hypothetical one chosen in advance for example the expected vanishing direction of released homing pigeons 4 1 3 Note that Zar 1999 calculates V from R the total length of the resultant vector of the data rather than from r the length of the mean vector which is what most other authors and Oriana use However Zar s formula for u corrects for this thus u and p will be the same for all methods Second Order Statistics If two or more circular variables are present in the file or if a subgrouping variable is being used to analyze sets of data then second order statistics are also calculated These are statistics that focus on further analyses of the basic statistics for each variable Second Order Statistics Grand Mean Vector GM 171 64 Length of Grand Mean Vector r 0 505
63. ata structure 19 109 datatypes 12 13 91 107 date 8 18 31 44 122 163 day of week 8 15 26 31 34 44 108 122 136 164 dayofyear 16 44 decimal places 149 deletingdata 102 103 105 description of datafile 105 desktop 4 54 94 159 automatically reloading 149 deviations 24 directional 12 14 distribution plots 88 143 fy ee editing data 7 30 32 34 102 103 104 105 106 107 editing graphs 147 exiting 101 exporting data 97 _F files backup 149 closing 93 exporting 97 importing 94 merge 100 opening 38 91 93 94 159 recently used 93 saving 54 59 93 94 fillingdata 116 filter data 44 113 find 118 fonts 51 132 147 format 149 frequencies 22 36 43 106 120 frequency table 106 135 f test 45 71 4G grandmean 70 76 graph types 9 47 79 127 graph windows 9 graphs 79 127 145 arrow plots 83 axes 50 circular histograms 81 133 138 circular scatterplots 87 114 140 circular linear plots 57 87 114 140 colors 52 128 creating 47 customizing 47 49 51 128 distribution plots 88 143 editing 147 fonts 51 132 grid 53 gridlines 50 histograms 47 49 54 55 79 81 84 85 86 114 133 138 labels 51 linear histograms 84 133 lines 58 129 modifying 147 monochrome 128 patterns 53 129 printing 58 Q Q plots 89 145 raw dataplots 81 142 rose diagrams 47 49 54 55 79 85 133 138 scatterplots 89 145 scatterplots circular 57 87 140 stacked amp stepped histograms 52 54 85 133 138 symbols 54 58
64. ata under a new name choose File Save Data As 935 which will produce the dialog box described above Make sure that the Save file as type section of the dialog is set to Data files ORD Opening an existing data file Existing data files can be loaded into Oriana using the File Openl 91 dialog box Alternatively you can choose a previously used file from the File Reopen 93 menu or use the drag and drop 159 feature of Oriana You can also load a whole set of windows related to a data file using the desktop 44 functions You can keep your data files in any location you wish The File Open dialog box allows you to switch to any disk or directory accessible to your machine and will remember the last location at which you looked for a data file If you wish you can have separate directories for each project The Oriana program only allows a single data file and its related results and graph windows to be open at any one time You can start a second copy of Oriana if you wish to have a second data file open If you already have a data file open when 3 8 Tutorial you choose the File Open command it will be closed before the new file is opened Oriana comes with a number of example data files You can use these to try out the program or to see the correct format for the data files They can be found in the SampData folder of the Oriana program directory usually C Program Files Oriana Importing data Data can be i
65. atistics for each month The Subgrouping box also has options for summarizing dates If the variable you select as subgrouping variable is a Date one then these options are enabled allowing you to group the data by Day of Week Month of Year Day of Year or Week of Year Filtering data There are often times when you want to analyze just a subset of your data rather than all of it You may want to analyze data from just a single month rather than the whole year or only those data for which an associated linear variable exceeds a certain value You can do this through the Filter Datal113 dialog box You can access this in two ways either choose the Data Filter Data menu item after a data file has been opened or click on the Filtering button on the Select page of any analysis or graph dialog box To define the subset of data you wish to use you must select a variable that contains the data you want to use to define the subgroup then declare the criterion to filter on Lets say we want to calculate statistics of the wind data in the Wind2002 ori example data file in September alone To do this Open 38 the Wind2002 ori data file Choose the Data Filter Datal113 menu item Click on the Filter Data button Select the variable Month in the Variable drop down box 5 Inthe Comparison Type section click the Equal button 6 Inthe Value box enter sep for September a ce he 3 12 Tutorial Variable Mo
66. ay 2 16 51 Thursday 3 19 10 Saturday 4 17 17 Wednesday 5 19 21 Thursday 6 ii 8 09 14 Thursday 00 17 Tuesday 02 01 Saturday g 16 03 Saturday 10 14 48 Monday 11 05 27 Wednesday iz 16 39 Sunday 13 16 19 Sunday 14 23 50 Wednesday 15 07 20 Wednesday m 1R NN 33 Thursday i Row 1 records the arrival of a patient at 18 42 on a Sunday Row 2 records an arrival at 16 51 on Thursday etc With this format you can for example produce a rose diagram of all the arrival times then produce a series of diagrams one for each day With data of this type each column must have the same number of rows since the data are paired However Oriana can handle missing data so if one of the variables doesn t have data for a particular observation you can just leave that cell blank Oriana will deal with the missing data in the most appropriate way for the given analysis or graph For example if some of the values in the Day column above are missing then when producing graphs for each day a separate graph will be produced for those where the day is not known Any missing circular data are just ignored and not included in the graphs or statistics With this type of paired format you can also add other variables allowing you to subgroup the data in different ways or to correlate the circular data with other types of data Here is an example of some wind data E Data Editor BAX B E D E E Is Type An
67. beessecgabh co ea neea 4 Second Order Statistics jcecccccsesaccsssceersiceacincseetovies E EANN E 76 Part V Graphs 79 b Rose Didbraims tcc aiieed A an ng its ces dk een A ee 79 2 Circular Histograms we 81 3 Raw Data Plots we 81 4 Arrow Graphs 83 De Linear HistO grams cci2 eree a a a dh Sevaeedevistdens EE EEE A 84 6 Stacked and Stepped Histograms ccccccsccsssccssseceeneeceseeeeseeeeeeeeseeeesaees 85 7 Two variable Histograms 86 8 Circular linear Plot n 87 9 Distribution Plots 88 10 Tw s mple Graphs vcs icedcig csi ccceccoacsstennvessaseethenvocka ndeneadeaaesaceatendaureareasednaeed 89 Part VI Menus 91 gt Wiles ices Pregl optsh Cee aed Nees een el Aachen E E OE 91 mi Oriana 4 Graphs Options Window Hepu evacasivnat easdegassessdh e seschbag cas tvaaeeeadeeceganedeckevdeh coated coded teaveessieombete Part VII Technical Support T Technical Supportiwss 2 51 cic ieee ain ee Adee ada aaa 2 Further reading about circular statistics Part VIII Appendices ONDAN T Dr p and Drop sneseno nerien SEE EEE ETN A a 2 Using the keyboard 3 ISO 8601 0 4 Data file structure 5 Example data files Index Introduction i 1 Introduction Welcome to the manual for Oriana the circular statistics program for Windows This manual will explain how to use the program what each menu item does and gi
68. box will appear again If you wish to change any of the options or even the graph type you can do it here We can change the current graph into a circular histogram type by choosing the Circular type on the Main page Also on the Options page we can change the mean direction indicator into a vector the length of which reflects the r value for this set of data by selecting the R Vector option Go to the Fonts page by clicking on the tab at the side labeled Fonts Click on the button labeled Main Title A standard font dialog will appear Use this to change the font to be used for the graph title then press OK Just below this is a drop down box labeled Title Box Style Use this to change the box style to Drop Shadow som J Example Title Box Style Drop Shadow x Example 4 Press OK The graph will now be changed to a circular histogram with an r vector the font of the main title will be changed to the chosen one and a box will have appeared around the title These new settings will have been saved so all future graphs will be of this appearance until you change them again 5 Many other options can be changed to alter the appearance For example we can change the text of the title that appears at the top of the graph By default this is the name of the variable Choose the Graphs Edit Graph menu item again go to the Titles page and change the Main Title to Wind Direction You could also remove the title completely
69. by clearing the checkbox next to the title J Main Title Wind Direction 6 Now goto the Colors page The bars segments of the histograms are currently plotted in blue You can change this by going to the list box titled Plot Series Colors selecting Series 1 then changing the color with the drop down box labeled Set Series Colors If this plot were a stacked or two variable graph 54A then you could use the other series to change the colors of other segments of the bars Backgrounds Chart CO white x Title Cwe fx tutorial 53 Lines a Me D Grid H black v Stats HM Black v Inacc Stats E Red v Plot Series Col OF ES oa Monochrome Graphs Series 1 Blue a Series 2 Red Series 3 Yellow Series 4 Fuchsia Series 5 Silver Series 6 Lime Series 7 Aqua Series 8 Black Series 9 Maroon ow Set Series Color L Blue 7 You can also use this page to change the background color of various parts of the graph and also of the lines Click OK to see the results 8 You may wish to produce a monochrome graph with shaded areas rather than colored ones for reproduction in a print journal You can do this by going to the Colors page and ticking the Monochrome Graphs option This will disable the color selection options 9 Now goto the Lines and Patterns page where you can use the Plot Series Patterns and Set Series Pattern option to configure the various shading patterns in a similar
70. cale option lets you choose to have the circular concentric grid or Y axis on linear graphs scaled logarithmically base 10 rather than linearly The Percentage scale option will label the scale with the percentages of the total frequencies rather than the frequencies themselves 6 5 3 Graphs Two var Histograms This dialog box allows you to create two variable histograms 86 which allow two variables to be plotted together on a single graph with the second variable being represented as stacked segments of each bar or wedge Two Variable Histograms Wain type S n Frequency shown as 3 A Options Stacked Rose Radius of wedge q Area of wedge Select Stacked Circular Axes Stepped Circular Linear Width Colors Stacked Linear Normal width Lines amp HalF width Patterns Double width Symbols Titles Fonts OK Cancel Help The options are similar to those on the Graphs Histogramli33 dialog box but with only the relevant graph types listed The Options page is similar to that for regular histograms except for the addition of a few new options Menus 139 Main Statistics Segments Options None Automatic r vector Number of Segments 5 Select x Mean Log scale Axes x V Confidence intervals Segment for each unique value Colors 95 Manual Lines amp 99 Patterns Weighted r Mean vectors only Symbols Segment means Titles Rayleigh critical
71. ch sector is 30 wide with January being 15 February 45 and December 345 Day of Year DOY This circular type stores the numeric day of the year ranging from 1 to 365 or 366 for leap years with day 1 being 1 January and day 365 or 366 being 31 December They are actually entered into the data editor as numbers and the results are reported as angles although as with DOW and MOY the equivalent numeric Day of Year is also reported for means and medians By default all analyses assume that there are 365 days in the year so that each day represents 0 9863 of the circular range Thus Day 1 would be represented by the midpoint of the sector 0 49315 However if you enter any values of 366 then that is taken as the range and each day represents 0 9836 Day 1 would then be 0 4918 Week of Year WOY This data type works in a similar way to DOY with the circular range divided into either 52 or 53 weeks The calculation of WOY follows the ISO 8601 68 international standard This states that a week is a seven day period beginning on Monday The first week of the year is that which contains the first Thursday of the year This means that Week 1 could contain some days from the end of the previous year 31 Dec 2002 was actually in Week 1 of 2003 Likewise the last week of a year can contain some days from the next year 1 Jan 2000 was in week 52 of 1999 The above standard means that although we normally think of a
72. d The Options Preferences 149 dialog also allows you to customize the names used for different phases of the moon These names are used on the graphs and the basic statistics output Please note that no correction is made for local summer or daylight savings time differences when calculating the dates of the moon phases The remaining variable types are non circular types They can be used for labeling data cases specifying subgroups and providing linear data for correlation with the circular types Date The Date variable type allows you to specify the date on which an observation took place This could be auxiliary data which allows you to group your circular data observations according to calendar periods Or it could be your main data which will later be summarized 60 into circular types such as days of the week or months of the year then analyzed statistically and graphically The format of the date including the order of the year month and day portions follows that specified as the short date format in the Windows Control Panel Normally this would be an all numeric type such as 2003 05 27 27 05 03 or 05 27 2003 Currently the data editor requires numeric format for direct data input However if you are pasting or importing data from another source that is in mixed format such as 27 May 2003 Oriana will recognize this and convert it to numeric format Linear The linear data type can be used to store any type of
73. d you will only be able to reverse actions that have occurred since the window was reopened The Undo option will be disabled if there is nothing to undo 6 2 2 Edit Redo If any editing actions have been undone this command will reinstate that action For example if some text was deleted then restored by choosing the Undo item the Redo item will delete it again 6 2 3 Edit Cut Choosing this option will delete the currently selected 3 data leaving the cell or cells blank Anything deleted will be placed in the Windows clipboard so that it can be pasted into another application or to another spot within Oriana If you accidentally delete some data then decide you want to restore it choose the Edit Undo option The data editor and the notepad are the only windows that allow the user to delete data so this option is disabled when any other window is activated Text or graphics from other windows can be placed in the clipboard using the Edit Copy command 6 2 4 Edit Copy Choosing this option will copy text data or graphics to the Windows clipboard so that it can be pasted into another application or to another spot within Oriana With graphs the entire diagram is placed in the clipboard in both bitmap and metafile formats With bitmaps the graph is copied at its current size so if you want a larger bitmap with fewer jagged edges increase the window to its maximum size 6 2 5 6 2 6 Menus 103 In the spre
74. d Wales Contents i Table of Contents Introduction 0 Part I Introduction 1 Part II Getting Started 3 Tt Whatis Oriana omessa neei EE E a EAEEREN R 3 2 KCS Desktop Metaphor 9 Oriana Concepts inertni aan e EEE EEE aR EEN EREET EEAS Part III Tutorial 1 Creating a d ta fille eiiisciccssasiesecssess caus eniai caviencs a a 2 Entering data 3 Selecting spreadsheet cells bch 4 Editing data occ wi 4 5 Entering frequency data we 36 6 Saving data ceeceeceseeeseees 1 38 7 Opening an existing data file we 38 8 Importing data 0 ee 39 9 Calculating statistics ee Al 10 Selecting a subgrouping variable we 48 WL Filter amp datasenter eeta OENE E dea ER EEA EERE EEEE E 44 12 Comparing samples araeo iii KEE E E casei E A AER AE 45 13 Plotting graphs AT 14 Adjusting graph axes 49 15 Customizing graphs 51 16 Saving the desktop 54 17 Stacked histograms 54 18 Two variable histograms 55 19 Circular linear plots aD 20 Printing graphs and results 58 21 Saving graphs and results to file we BD 22 Changing variable type we 59 23 SUM Marizin gs datas esieelis clseessbeacdeseiddebaceaieavcnseiecedscaveveaccgusdeahonaedshedeceuveesedes 60 Part IV Analyses Statistics eroen aean E an aituer vac eves dette esi en eee aia 2 Multisample Test Bi Correlation S a iinde ca tun cg tn ea cede on cesadece di
75. d it for estimated concentrations between 1 and 2 Chi Squared Test Oriana can perform pairwise or multisample Chi squared Tests Batschelet 1981 p 109 on the samples This test determines whether the samples differ significantly from each other in some unspecified way The test is the basic chi squared test as used for a variety of purposes The data must first be grouped into classes For data that are already grouped 2 their specified class width is used otherwise the class width can be set through the option on the Options page of the Analyses Multisample Tests 24 dialog box A contingency table is then constructed and the expected frequencies determined based on the row and column totals The Chi Squared statistic is then calculated based on the differences between the observed frequencies of the samples The p value printed for each test is the probability associated with the null hypothesis that the samples are drawn from the same population If this probability is less than your chosen significance level usually 0 05 then the null hypothesis can be rejected in favor of the hypothesis that the samples are from different populations that differ in some way The difference may be in the distribution mean direction or other parameter further investigation will be needed to determine what the 4 2 3 The Chi squared test assumes that most or all the expected frequencies used in the calculation will be greater than 5 This
76. d to the expected Thus some observations might be negative numbers flight to the left of the expected direction and others positive Oriana expects angular data to be in degrees ranging from 0 360 so the data editor does not allow entry of negative data for angular variables However this can be worked around by entering the deviation data into a variable of the Linear type which allows numbers of any type Once the data have all been entered the type of the data variable can be changed 59 to Angles When this is done Oriana will automatically convert the negative data to the equivalent on the 0 360 scale So 10 would be converted to 350 The following shows the data before and after conversion Getting Started Data Editor BAX B Kad Type Linear Angles Name Deviations Angles 2 11 000 11 000 3 10 000 10 000 4 3 000 357 000 5 12 000 348 000 6 24 000 24 000 7 27 000 27 000 8 6 000 6 000 a 20 000 340 000 10 6 000 354 000 if 27 000 27 000 12 30 000 30 000 13 14 000 14 000 1 v lt Mm IEJ X Y Data Usually circular vector data are entered directly as measured angles and the length of the vector However sometimes it may be more convenient to measure and record the X Y coordinates of the beginning and ending of the vector For instance in the following example you may record the X and Y coordinates of the dots at either end of the vector rather than the angle and length of the vec
77. dow Getting Started 7 At the bottom of the window is the status bar that provides information about the program The large section to the left displays hints giving a fuller description of the menu item or toolbar button currently under the mouse pointer It also describes the current status of the program when it is doing calculations or other long operations The next section displays the word Modified if the contents of the window that is currently on top the graph window above have been modified Next to this is a button that lights up when the program is doing long operations such as loading large files or doing long calculations You can stop the current activity by clicking on this button Finally there is a progress bar that indicates how much of the current operation has been completed 2 2 1 2 Status window The status window is opened every time a data file is opened It displays some information about the file its name and title the number of variables and cases the current subgrouping variable and defined vector pairs if any and the descriptive title Closing this window causes the data file and all other associated files to be closed c3 Currently open file BAX Data file F DelphiiOriana3 SampData Wind2002 ori 5 variables and 4495 cases Hourly wind data garden weather station Jun Dec 2002 2 2 1 3 Data editor This window is a spreadsheet that allows you to edit 34 your data The
78. e Folder control to select the folder containing your files then tick the box next to each file that you wish to combine When you press the OK button you will be prompted for a name for the new file File Print This option allows you to print the contents of the currently active window When you choose the File Print command the standard Windows Print dialog box will be displayed You may change the required printer its properties and the number of copies and pages to be printed With graphs you can choose to have just the current graph printed or all graphs in the graph window File Printer Setup The standard Windows Printer Setup dialog box can be displayed by choosing the File Printer Setup option You may choose which printer to use for printing the current window as well as modify its properties Each type of window in Oriana allows you to specify a certain printer So for instance you can always have graphics go to a high quality color printer whereas results and data are always printed to a monochrome laser or inkjet printer The specific printer chosen in this dialog box will apply to the currently active window These choices of selected printers are saved and restored next time you run Oriana 6 1 14 File Page Setup The File Page Setup command allows you to specify the margins to be used on your printouts You would normally have margins of about 2 3 cm or 0 5 1 inch although you may prefer oth
79. e basic statistics you want calculated Statistics Select V Mean Angle Save to File V Variance V Standard Deviation V Length of vector r Standard Error Median Angle Concentration Confidence Intervals V Rayleigh Uniformity Test Chi Squared V Rao s Spacing Hotelling s Watson s U Moore s Kuiper s Y Test To discover what each option does you can press the large button labeled Help to display a help page describing all the options By default all circular variables in the file are included in the analyses If you wish to drop some of the variables go to the Select page of the dialog All the circular variables will be listed on the left with a tick mark before each To drop a variable just click the box containing the tick mark so that it is cleared We want to calculate statistics on just the Direction variable so clear the checkmarks on the other variables Hint You can clear all checkmarks by right clicking on the list and choosing Deselect All from the context menu Variable Press OK The Results window will open if it isn t already visible A new page will be added to which the results will be written Once the analysis is finished you can look at and print the results or export them to a file for inclusion in another program Direction 3 10 Tutorial Note if you are working with frequency data where the data file contains a frequency tab
80. e data are not grouped and that they conform to the bivariate normal distribution Note that the test is particularly sensitive to departures due to skewness A nonparametric test is also available Moore s modified Rayleigh test Zar 1998 p 641 is an analogue of the Raleigh test that is based on weighting the mean angles with the rank order of the r values of each The null hypothesis is that the means of the population are uniformly distributed around the circle A significant probability indicates that the data are not distributed uniformly and that they show evidence of a preferred direction Multisample Test The multisample tests in Oriana allow you to compare two or more sets of data to determine if their distributions differ Most tests can be performed either as pairwise where each pair of samples are compared or as multisample where all samples are compared at once The tests included in Oriana are described briefly in the next sections See the section on the Analyses Multisample Tests 124 command for details on how to run these analyses Watson Williams F Test Watson Williams F test Fisher 1993 p 126 Mardia amp Jupp 2000 p 129 Batschelet 1981 p 95 Zar 1999 p 625 compares two or more samples to determine if their mean angles differ significantly The test can be performed ina pairwise fashion so that the selected samples are compared with each other a pair at a time or an overall test can be calculat
81. e navigation bar at the left side allows you to select which graph you would like to view Each time you create a graph or series of graphs a bar is created giving the graph type and the time of creation Below this is one or more tabs labeled with the variable s used in the graph If more than one graph is created because you either have multiple variables selected or you are using subgroups then these all occur grouped together under the same graph type bar You can show or hide the individual tabs under each bar by clicking on the downward pointing black triangle on the left hand side of the bar If you click the right mouse button over this navigation bar you will see a menu with the options Open all to open up all the bars to show all the tabs and Close all to close all the bars so all tabs are hidden There are also options to delete the graph page corresponding to the tab clicked and to delete the whole group of pages clicked Right clicking on the graph itself will give a menu with the option to delete that graph A graph can be saved to disk for transfer to another program using the File Export 9 command When the contents of this window are saved they are written to the file in one of several graphic formats e Bitmap BMP Portable Network Graphics PNG GIF and Getting Started 1 1 JPEG JPG formats save the graph as individual pixels The resolution is limited to what you see on the screen Note though that the
82. e that this method can only be used when calculating basic statistics and plotting histograms If you need to do multisample comparison tests then you will need to convert the frequency data into raw data columns of individual observations You can do this using the Data Change Data Structure command to convert the frequency tables to raw data You can also use the Data Edit Frequencies 104 option to enter data as frequencies but have them saved as columns of raw data 3 6 3 7 Saving data Data are saved through the File Save Data 93 menu item If you have created a new data file and the status window says Unnamed for the filename you will then be presented with a Save As 93 dialog box You can choose the appropriate disk and directory then type a name into the File name edit box and press OK If the file already has a name which will appear in the status window then choosing File Save Data will save any changes directly with no dialog box If no changes have been made to the data the Save Data menu item will be dimmed and cannot be selected You can tell if the data have been modified by looking at the status bar when either the status window or data editor are the topmost window the word Modified will appear in the second panel from the left note that if the results graphs or notepad windows are topmost then this modified indicator will reflect their modified status not that of the data To save the d
83. e_tc catalogue_detail htm csnumber 40874 8 4 Data file structure The data files used by Oriana are plain text or ASCII files This has the advantage that you can modify or edit them witha simple text editor as well as through the Oriana data editor It also means that it is possible to transfer data from any other program to Oriana so long as the other program can create an ASCII file Header The first three lines of the file is the header which contains necessary information about the file This is an example data file header 162 Oriana 4 ORI2 5 4495 Hourly wind data garden weather station Jun Dec 2002 Direction Speed Date Month Time Angles Linear Date Month of year Time 15 The first line gives some overall information about the file First is a tag that identifies the file as an Oriana version 2 files ORI2 If this is not found then Oriana will assume that the file is an Oriana version 1 file and will try to read the header in that format If the first line does not fit the format of a version 1 file then an error message will be displayed Next is the number of columns in the data file followed by the maximum number of rows note that for paired data each column must have the same number of rows whereas with unpaired data the length of each column can differ Everything after the number of rows is taken to be a descriptive title of the data file this w
84. ects linear histograms By default the labels are oriented parallel to the bottom of the graph You can use this option to rotate the labels to any angle up to 90 either way Angular X Axis By default the Angular grid is oriented so that the 0 or North point is at the top of the graph In some disciplines it is more usual to have the graph oriented differently so you can use the Placement of 0 N option to set the position on the circle where the 0 should occur e g to the right or at the bottom The next option Rotation sets whether the scale should increase clockwise or counterclockwise With clockwise and the 0 point at the top the 90 point will be on the right whereas with counterclockwise it will be on the left By default Oriana will divide the graph into four sectors with boundaries at 0 90 180 and 270 We might want more gridlines than this We can use the Minor divisions option to customize the minor division You can set the minor divisions to be every 45 22 5 or 10 or their equivalents in Compass or Time variables or you can leave it at the Basic level every 90 You can also turn off all divisions so there is no grid radiating from the center Note that for Time variables the finest division occurs every 1 00 hour rather than the time equivalent of 10 This option has no effect on the date based variable types such as Day of Week as they always have their own angular divisions If you wa
85. ed for all samples The F test basically proceeds by comparing the lengths of the mean vectors for each sample with that for the pooled data of the two or more samples The resulting F statistic is the same as Fisher s variance ratio statistic which is commonly used in linear statistics including analysis of variance The p value printed for each test is the probability associated with the null hypothesis that the two mean angles are equal If this probability is less than your chosen significance level usually 0 05 then the null hypothesis can be rejected in favor of the 4 2 2 hypothesis that the means are different If the null hypothesis is not rejected i e the probability is greater than 0 05 then Oriana will report the overall mean for all samples in the test which can be used as an estimate of the overall population mean This test assumes that the two samples are independent and drawn at random from a population with a von Mises distribution It also assumes that the concentrations of the two samples are similar and that they are sufficiently large gt 2 If the concentration is too low a warning is printed Finally the data may not be grouped 26 The formula for the F test can incorporate a correction factor based on the concentration to correct for bias Some authors only use this when concentrations are low whereas others use it for all calculations Oriana ver 2 takes the latter approach Oriana ver 1 only use
86. ed statistic as shown in Fisher s 1993 formula 4 36 or Mardia amp Jupp s 2000 formula 6 3 36 is used This test cannot be calculated on grouped 20 data nor can it be used for sample sizes less than 10 Kuiper s Test Fisher 1993 p 66 Mardia amp Jupp 2000 p 99 Batschelet 1981 p 76 takes the alternative approach of directly comparing the distribution of the data to the desired distribution either uniform or von Mises It can be viewed graphically by referring to the distribution plots 88 produced by Oriana The Kuiper s V statistic is based on the largest vertical deviations above and below the diagonal line representing the desired distribution Too great a deviation giving a high V and low probability leads to rejection of the null hypothesis that the data fit the distribution The formula used in Oriana incorporates the correction factor shown in Fisher s 1993 equation 4 12 and Mardia amp Jupp s 2000 6 3 30 As with Watson s U2 this cannot be calculated on grouped 26 data For grouped data the Chi squared Test Batschelet 1981 p 72 Zar 1999 p 656 is instead calculated This simply performs a standard chi squared test based on the expected number of observations in each class given a uniform distribution A probability below the chosen alpha level usually 0 05 leads to the rejection of the null hypothesis that the data are distributed uniformly The sample size must be sufficient so th
87. endar for the moon phase to be calculated correctly This can be done by adding a certain number of days depending on the date range A table in the Wikipedia topic on the Proleptic Gregorian Calendar gives the required number of days Note too that you can specify the time zone in which the lunar dates were recorded The exact point in time at which the moon phase becomes new or full is the same all over the world but because of differing times zones the clock time and perhaps the date will be different For example a new moon occurred on 4 March 2011 at 20 46 UTC Thus the date of the new moon would have been 4 March in Great Britain However when that new moon occurred it was 07 46 on 5 March in Sydney Australia The difference in dates can affect how graphs are drawn and statistics calculated By default Oriana will use the time zone specified in the Windows system on which it is running which can be changed through the Control Panel or the clock on the Task Bar If you are regularly analyzing data from a different time zone you can change the zone that Oriana will use through the Default Time Zone option on the Lunar Phases tab of the Options Preferences i49 dialog You can also change the time zone for individual variables through the Data Change Variable Typel 0 dialog The time zone for each variable is saved in the data file so if you send the file to a colleague in a different time zone the original time zone will still be use
88. eparate columns e g if there are two data columns plus a subgrouping variable with four groups the result will be eight separate columns four for each original data column If there is more than one subgrouping variable only the first one counting from the left will be used any others will be separated out like the other variables If the multiple data columns in a subgrouped data file are of different types then you can still separate them into individual columns However you will not be able to consolidate them back to their original form This is because Oriana always consolidates data into a single data column and will not be able to combine the different data types You will be given a warning message if you do try to separate out data of different types Converting raw data to frequency table This will take a column of data and turn it into a frequency table with one column containing the unique data values in the original data and a second containing the frequency that each of those values occur So if the original variable has three 45 values the restructured data file will have one 45 in the data column and a 3 in the frequency column If a data file has more than one variable then each of those will be converted to frequency tables If a subgrouping variable is found then that will be used to create a frequency table for each subgroup The frequency tables will all occur in the same columns and a subgrouping variab
89. er settings If you wish to have printouts of graphs that do not fill the page then just increase the margins For example if you are using 8 5 x 11 paper and want graphs 2 5 wide set both the left and right margins to 3 8 3 2 5 8 5 Page setup Margins 1 00 Left Inches Cancel Centimeters 1 00 Right 1 009 Top 1 00 Bottom Print border 6 1 15 File Exit Choosing this menu option will end your Oriana session If the data have been changed or new results have been generated but not saved you will first be prompted to save the files if you wish 6 2 Edit This menu contains functions for editing the current window as well as transferring text and graphics between Oriana and the Windows clipboard 6 2 1 Edit Undo This reverses the last editing action performed on data or graphs Oriana will save all of your editing actions during the current session allowing you to undo them one by one Note that this menu item changes its caption to give a better idea of 102 Oriana 4 what type of action will be undone When the cursor is over this item the message area on the status bar will give greater detail of the action Note that each window maintains a separate list of editing actions that can be undone Choosing this menu item will undo the last action performed in the currently active window Also note that if the data editor is closed and then later reopene
90. et of imported data are being previewed V Closing window will lose all graphs results V Suggest alternative variable type for imported data Lunar Phases Enable All Disable All The Compass page lets you customize the abbreviation used on graphs results and in the data editor for the compass directions By default the standard English abbreviations are used e g N for North SE for southeast You can change these to the equivalents in your own language by just typing the new abbreviations into the table You can reset the abbreviations to their defaults with the Reset to English button 152 Oriana 4 Program Preferences General Customize compass abbreviations Warnings 2 Reset to English T N Lunar Northmorthest ssa MNE Phases The Lunar Phases page contains options related to the Lunar variable type The table at the top lets you customize the names used for the various lunar phases in a similar way as the compass abbreviations above The Default time zone option lets you change the time zone that Oriana assumes when calculating lunar phases see the description of the Lunar variablef6 to find out why you might need to do this This defaults to the current Windows time zone but if you change it the new setting will be remembered next time you run Oriana Program Preferences General Customize lunar phase names Warnings
91. f the plot is arbitrary you could have important patterns becoming less noticeable if they occur split over the wrapped around part of the plot i e going off the graph at the upper right and wrapping around back to the lower left This can be alleviated by extending the axes and repeating 20 of the points at either end The following graph is the extended version of the one above Arrival wn 15 H H H H 2 1 25 f 4 4 S ql oO 6 0 75 OD ee al ele oes ee ee 025 ERE a E f iii 0 25 i 1 0 25 0 02505 075 1 124 15 Uniform Quantiles The next graph compares the data to the von Mises distribution Here you can see a close correlation suggesting that the data follow the von Mises distribution Arrival Sample Quantiles 1 0 5 0 0 5 1 Von Mises Quantiles 5 10 Two sample Graphs The Graphs Two sample 143 command produces scatterplots and two sample Q Q plots With the Scatterplots option you can plot any two variables against each other This is useful to give a graphical representation that can be used in interpreting the results of a correlation 75 analysis Options on the dialog box allow you to reverse the X and Y axes and also to specify whether the whole 0 360 range for circular data is plotted or only that part of the scale that actually has data Ozone 0 90 180 270 360 Wind Dir Q Q plots are ones that let you compare the distribution of two samples much like
92. fferent symbols used for different groups of symbols on the graphs The first symbol is used in most graphs and subsequent symbols are used for further data series when subgrouped data are being plotted The symbols can be changed by selecting the desired series and using the Set Series Symbol option to the right The Outline around symbols arrows option lets you set whether to have a black outline drawn around the symbol When this is not checked the symbol will just be a solid color The Represent subgroups with option lets you decide 6 5 1 4 Menus 131 whether the different subgroups should be represented by different symbols or whether the same symbol should be used for all but with different colors You can also choose to use both different colors and symbols The way the symbols are drawn can be set with the Rotate symbols around origin option With this ticked the symbols will be rotated so that the top of the symbol e g the top tip of the triangle always points outward on circular graphs When this is not ticked the symbols will all be oriented the same way You can change the size of the arrowheads for the r vectors arrow and vector plots with the Arrowhead size option The Variable arrowhead size option makes the arrowheads towards the center of an arrow plot progressively smaller so that it is easier to see the shorter arrows towards the center Titles This page allows you to customize the various titles that appear
93. g If the data in a variable were collected in the USA Eastern Time Zone the label would be Lunar 300 indicating a time zone difference from GMT UTC of 300 minutes 5 hours If any of the columns are of the Subgroup data type then the header will contain further lines giving the actual text for the various subgroups Subgroup data are entered in the data editor by the user as text e g GroupA GroupB GroupC etc but are stored internally and in the data files as integer numbers e g 0 1 2 etc These extra header lines provide the text for each subgroup An example subgroup header line is SubgroupLabels 1 3 GroupA GroupB GroupC The word SubgroupLabels indicates that this is a subgroup text line and must be present and match exactly Next isa number indicating the position of the variable in the file in the above example the subgroup variable is the first column Next is the number of different groups three in the above case followed by the text for each group If there are more than one subgroup variables then there will be a similar line for each variable Data The rest of the file contains the data The variables are arranged in columns just like in the data editor and the data are separated by spaces or tabs Any data that are missing are stored as periods Numeric data such as angles axial angles and linear data are written as floating point numbers with a period representing the dec
94. g box You can then modify the data as required Note that you can now also enter frequency data directly into the spreadsheet See the tutorial 3 for more details Warning Editing data in frequency mode can change the order of your data values If your data in the data editor are paired i e each row is a single case and each column contains different data about that case such as a label subgroup or linear data then editing in frequency mode will change the order of one variable so that they are no longer paired Only use the frequency editor if the columns are independent 6 3 4 Data Change Variable Type This option allows you to change the type of datal12 contained in each column The following dialog box will be displayed hange Variable Type Ta Variable Date x Basic Type Angles D Day of year Axial Compass Direction Circ Proportional Date Circ Percentage Linear Time Label Day of week SubGroup Month of year Lunar Week of year The Variable drop down box allows you to select the variable to change You can then use the options in the Basic Type box to change the type Oriana will do its best to convert existing data to the new variable type Conversion from angles to other circular types is done by converting to the nearest angular equivalent e g 90 becomes 06 00 or March or week 13 or compass direction E Conversions back to angles will give the angle that is the mid point f
95. g the File Open Desktop command Oriana can be set up to automatically save your desktop when you exit and reload it next time you run the program This option can be turned on in the Options Preferences 149 dialog box Stacked histograms Data sets that have a subgrouping variable defined can be plotted as stacked or stepped histograms 85 where a single diagram is produced for all the groups with each group s portion of the bar depicted in different colors 1 Open the Wind2002 ori file ifit isn t already loaded 2 Choose the Graphs Histograms menu item 3 First goto the Select page and ensure that Use variable is ticked under Subgrouping and that the Month variable is selected in the drop down box 3 18 4 5 Tutorial Variable Subgrouping Direction None Use variable xj Month Go to the Main page and select the type of stacked stepped graph you wish to produce say Stacked Rose Press OK and the graph will be produced Two variable histograms Let s now try plotting a two variable 86 rose diagram This is a rose diagram with each bar divided up into segments that represent a frequency table of a second variable We can use this to show both the wind direction and wind speed from our Wind2002 ori file N e Open the Wind2002 ori file if it isn t already loaded Choose the Graphs Two Var Histograms menu item On the Main page of the dialog choose the Stacked Rose optio
96. gative correlation The calculation of the significance of the correlation follows Mardia amp Jupp 2000 in using their approximation of the F distribution in equation 11 2 2 Second Order Statistics The Basic Statistics analysis in Oriana will provide second order stats e g the grand mean if there are more than one variable of raw data It will do this by calculating the means and mean vector length for each variable then calculating the second order statistics However you may already have your data in the form of means and mean vector lengths so may wish to calculate the second order statistics directly on those means The analyses in Oriana s Second Order Statistics command will do this To run these analyses your data file needs to have pairs of variables one circular and one linear which contain the polar coordinates of the mean vectors the means and their associated lengths You can have a number of pairs of variables but Oriana will always assume that the first linear variable is associated with the first circular one the second linear with the second circular etc Basic Second Order Statistics The first section of the Second Order Statistics output is similar to that produced when calculating the basic statistics 7010n raw data The grand mean and its length the confidence intervals 4 4 2 and Hotelling s and Moore s tests are output If the data file contains more than one pair of variables containing the
97. gles x linear _ Linear _ Linear _x Date _x Time Name Wind Direction Wind Speed Temp Pressure Date Time 1 9 171 17 200 1010 043 15 06 2002 12 00 2 248 000 6 263 16 100 1010 043 15 06 2002 13 00 3 232 000 8 053 16 900 1011 043 15 06 2002 14 00 4 186 000 5 369 16 100 1011 043 15 06 2002 15 00 5 222 000 5 816 15 600 1011 043 15 06 2002 16 00 6 252 000 3 579 16 000 1011 043 15 06 2002 17 00 7 239 000 10 961 16 600 1010 043 15 06 2002 18 00 8 250 000 10 961 15 400 1010 043 15 06 2002 19 00 9 237 000 6 263 15 100 1010 043 15 06 2002 20 00 10 236 000 5 369 14 700 1009 043 15 06 2002 21 00 11 145 000 4 026 14 800 1009 043 15 06 2002 22 00 12 229 000 3 132 14 700 1009 043 15 06 2002 23 00 13 227 000 2 684 14 300 1008 043 16 06 2002 00 00 14 211 000 7 158 14 900 1007 043 16 06 2002 01 00 15 232 000 6 263 14 700 1007 043 16 06 2002 02 00 lt gt Here each row represents an hourly wind measurement For each observation we have recorded the date and time of the observation along with the wind direction at that time the wind speed the temperature and atmospheric pressure We can now analyze all the wind direction data together We can also use the Date variable for grouping by various methods such as month of year day of week or year Finally we can use the Wind Speed variable to compare wind speed with wind direction This can be done with a two variable rose diagram 86 circular linear plots 8 or by circ
98. graph This is the angular mean that is weighted with the second variable For instance in wind data you may want to have the mean weighted by the wind speed so that if higher winds occur predominantly from a certain direction the mean will be weighted more towards that direction When the Weighted Mean option is selected along with the Mean type of statistic then it is depicted by an arrow that extends beyond the edge of the graph If the r Vector type of statistic is selected then the length of the mean Menus 135 weighted vector will reflect the weighted r of the mean scaled 0 1 If the Subgroup means option is ticked then separate statistics lines are drawn for each subgroup when a subgrouping variable is in use Otherwise just a single overall mean is drawn The Rayleigh critical value option lets you draw a circle on the graph showing the level of the Rayleigh critical value If the r vector extends beyond the circle this indicates that the Rayleigh test is significant at the chosen p value This option is only available when the r vector option is chosen and is not available if subgroup means are being plotted When the Print frequency table option is ticked a frequency table will be created in the Results window 84 showing the frequencies for each class that are used to draw the histogram as well as the percentages The Axes page allows you to make extensive customizations of the axes in the circular and linear
99. graphs There are two sections The first labeled Angular X Axis is for adjusting various aspects of the axis around the circumference of the circle which represents the angles time of day or other circular data The second section labeled Circular Y Axis is for changing the set of concentric rings that provide the grid representing the frequencies in the histogram Histograms Main Angular Axis Placement of O N Top Decimal places Auto Options EF WA Rotation Clockwise m Center circular bars on 0 Select g Label minor divisions m Minor divisions Basic 90 E 6 00 Label angles as compass Include symbol on angles l oes Plot only 0 180 Lines amp Patterns Circular Axis Symbols Manually scale Decimal places ato x Number of bars 36 Width 10 00 Titles Number of grid lines Auto yj Label grid lines fal four X axes x Log scale Fonts Percentage scale Cancel Help 136 Oriana 4 Both sections have options called Decimal places This adjusts the number of decimal places used for numeric labels on either axis When set to Auto the shortest number possible will be used e g there will be no decimal portion if the number is a whole number If set to a specific number of decimal places then all numbers will have that many places The second option occurring in both sections is Linear labels angle This only aff
100. grid lines of the graph and the Stats lines options affect the lines drawn for mean r vector and confidence limits Outline Around Bars sets whether there should be black lines drawn around the bars in a histogram The Draw Grid option selects whether to draw gridlines on the graph 130 Oriana 4 The Plot Series Patterns section lists the different fill patterns used for filling bars and symbols in monochrome graphs The first pattern is used in most graphs and subsequent patterns are used for further data series in stacked stepped histograms The patterns can be changed by selecting the desired series and using the Set Series Pattern option to the right 6 5 1 3 Symbols This page lets you customize the symbols used on raw data and scatterplots Raw data plots Jeg Main Symbol size 2 Options Plot Series Symbols Set Series Symbol Select Series 1 Circle Tal Circle Series 2 Triangle Series 3 Down Triangle Axes Series 4 Left Triangle Series 5 Right Triangle Outline around symbols arrows Colors Series 6 Square Series 7 Diamond i Ps i i 4 Lines amp Saree Gross Arrowhead size Patterns Series 9 Plus M Symbols v Variable arrowhead size Represent subgroups with symbols x Rotate symbols around origin Titles Fonts OK Cancel Help The Symbol Size option changes the size of the symbols used in the plots The Plot Series Symbols section lists the di
101. groups into separate columns 2 Convert raw data to frequency table Convert frequency table to raw data The dialog box that is displayed gives an explanation of the process that is about to take place This is so that you don t inadvertently run this command which makes major changes to your data structure Your data will be examined to determine which types of changes are feasible and the appropriate options will then be enabled Consolidating data If the current data file has two or more columns of the same data type with no subgrouping variable then you are given the option to consolidate the data into a single data column with an associated subgrouping variable The labels from each of the old columns are used in the subgrouping variable to identify to which group each of the data points belongs If you wish to consolidate data but the variables are not all of the same type then you must first convert all data to the same type or delete the incompatible variables See the section on changing variable type 59 for information on how to do this Separating data If the data do contain a subgrouping variable then you will be given the option to convert these to separate columns with one column for each subgroup Each column will have a label created by taking the label for the single data column and appending the name of the subgroup If there are more than one data columns then each will be split into a set of s
102. h of the mean vector r and the concentration and is calculated using formula 4 42 in Fisher 1993 It assumes that your data adhere to the von Mises distribution The 95 and 99 confidence intervals are then derived from the standard error as would be done for the normal distribution i e multiplying by 1 9604 or 2 5762 When the standard error is calculated a check is made of the concentration for the sample as well as the sample size The standard error can be unreliable if the combination of these is low If this occurs a warning will be printed The circular median direction can be difficult to calculate due to the problem of choosing an appropriate axis on the circular scale which wraps around In Oriana the median is calculated by minimizing the function d 0 2 gt r 0 6 N j This is from equation 2 32 of Fisher 1998 note that earlier hardback printings of that book accidentally leave out part of this equation and finds the absolute difference between the test median direction 0 and all the data values 8i This minimization process can take a long time for large data sets so it is advised that you leave the Median option on the Analyses Stats 23 dialog box unticked unless you need the median When circular data are grouped 26 a bias can occur in the calculation of r This can be corrected by multiplying r by a correction term Zar 1999 p 601 Mardia amp Jupp 200 p 23 calculated as ce cw 2 si
103. he Make up names option to have names in the form of C1 C2 etc created Max preview rows When you change options on this dialog and press the Update Preview button the data will be reimported to reflect the new 6 1 10 choices With large files this could take a long time To avoid this you can limit the number of rows to preview to a smaller number such as 500 or 100 Text Options These options are only available for text file importing Field delimiter With text files the columns of data must be separated by some character Oriana will attempt to determine the type of character delimiting the columns but it may not be successful If you don t see columns of numbers in the preview box then check the setting of this option to make sure it matches your file If you aren t sure of the format you can experiment with different options to see which works best Be particularly aware that if the numbers in the imported file use a comma for the decimal point rather than a period full stop setting the delimiter to acomma will result in the data being imported completely wrong File Export The function of the File Export command will differ depending on which window within Oriana is the active one If either the data editor or the status window is the topmost one then this command will export the Oriana data to one of several formats These include e Excel ver 97 xls or 2007 2010 xlsx e Lotus ver 1 Quattr
104. he Wind2002 ori data 1 Open the Wind2002 ori data file 2 Choose the Graphs Histogram menu item A dialog box will appear 3 Onthe first page make sure that Rose is ticked as the graph Type Main Type Frequency shown as Options Rose Radius of wedge Select Stacked Rose Area of wedge Axes Circular 4 Click on the Options tab to go to that page In Statistics tick the Mean option along with Confidence Intervals Main Options Select Axes Colors Lines amp Patterns Symbols Statistics 2 None 2 g vector Mean Confidence intervals 95 5 99 5 Onthe Axes page set the Number of bars to 24 to produce a graph with 24 bars each 15 wide Circular Axis Manually scale Decimal places Auto Number of bars 242 Width 15 00 Number of grid lines 3 v Label grid lines All w of bars Log scale Percentage scale 6 Click on the Select tab then untick the Month and Time variables so that only Direction is ticked Main Options fa Variable Ean Tutorial 9 7 Press OK The Graphsl 9 window will open if it isn t already visible A new page will be added to which the plot will be drawn This diagram shows the wind direction distribution of all the data in the file Now let s try creating a rose diagram for each month 1 Again choose the Graphs Histogram menu item All the options will be at the same settings used
105. hole file This is to speed up the preview process when you actually import the data all rows will be imported You may simply click OK for this dialog box You will next be presented with the Import Preview dialog box This has a tabbed section at the top with various options that can be changed on different pages described in detail below At the bottom is a spreadsheet like area that shows you how the data will be imported The portion of the file that will be read as the variable column labels will be in the shaded row at the top Import preview Gandalf F StatData Oriana Ori2 Test Data Wind2002 xls Options Text Options mo nanes Max preview rows 500 Guess names 1 Names at row gt Make up names Update Preview Import statistics Columns 4 Rows 500 max preview File type Excel Direction Speed Date Time a 265 00 9 17 15406 2002 0 00 PM 248 00 6 26 15406 2002 1 00 PM 232 00 8 05 15 06 2002 2 00 PM 186 00 5 37 15 06 2002 3 00 PM 222 00 5 82 15 06 2002 4 00 PM 252 00 3 58 15 06 2002 5 00 PM 239 00 10 96 15 06 2002 6 00 PM 250 00 10 96 15406 2002 7 00 PM 237 00 6 26 15 06 2002 8 00 PM v lt gt wind2002 j Cancel Hep The actual data points will be below At this point you need to examine the previewed data to ensure that they are being imported correctly If they are not then adjust the options described below to correct any problems Once you have changed any o
106. ilar way to the Data Editor except that you cannot change any of the values Also this single window can contain the results of many different analyses each on different pages You can select the page you wish to view by clicking on the tab along the bottom Double clicking the tab lets you change the text on the tab Getting Started 9 riana Results ole A B E D E Ead 1 BASIC STATISTICS 2 Data file F StatData Oriana Ori2 Test Data Termites ori 3 Orientation of termite mounds Fisher 1993 Appendix B 13 4 Analysis begun 07 November 2008 15 33 31 5 6 7 Variable Seti Set5 Set6 Set8 8 Data Type Axial Axial Axial Axial 9 Number of Observations 100 50 50 48 10 Data Grouped No No No No 11 Group Width amp Number of Groups 12 Mean Vector u 0 644 172 999 177 728 174 248 13 Length of Mean Vector r 0 721 0 87 0 923 0 813 14 Concentration 2 142 4 165 6 756 3 023 15 Circular Variance 0 14 0 065 0 039 0 094 16 Circular Standard Deviation 23 182 15 088 11 485 18 46 1 Standard Error of Mean 2 306 2 128 1 623 2 638 18 95 Confidence Interval For u 356 125 168 828 174 547 169 076 19 5 164 177 17 180 91 179 421 20 199 Confidence Interval for p 354 705 167 518 173 548 167 451 21 6 584 178 48 181 909 181 045 22 Rayleigh Test Z 51 955 37 888 42 576 31 689 23 Rayleigh Test p lt 1E 12 lt 1E 12 lt 1E 12 lt 1E 12 Rao s Spacing Te
107. ill be displayed when you load the file and will be placed on all printouts The second line contains the labels or names for each column Each label is enclosed within double quotes so that the label can contain multiple words with spaces in between Each label is then separated from the next by at least one space or a tab The number of labels must match the number of columns given in the first line of the header The third line contains the data type of the column These are again enclosed within double quotes and separated by spaces or tabs The actual text of the data type must exactly match one of the following including capitalization Angles Day of year Axial Compass Direction Time Date Day of week Linear Month of year Label Week of year Subgroup Lunar If the data within a particular variable are grouped 261 then the data type indicator also contains a specification of the class width of the grouped data For example if times are recorded to the nearest hour then the data are grouped with a class width Appendices 163 of 15 360 24 This would be indicated in the data file as Time 15 This is the data type indicator followed by a single with no spaces and a number giving the class width in degrees For Lunar variables the time zone for that variable is indicated after the data type label in a similar way to the groupin
108. imal point The number of digits after the decimal point is controlled by the setting in Options Format for the data editor Very large or very small numbers will be represented in exponential form e g 0 0000025 or 2 5x10 6 is stored as 2 5E 6 Times and dates are stored in ISO 86011160 format The format for time is hh mm ss where hh is the hour mm is the minutes and ss is the seconds A colon is always used as the separator Dates are stored in the format YYYY MM DD where YYYY is the year MM is the month and DD is the day Days of the week are stored as the ordinal number for the day with Monday being 1 Tuesday 2 etc Months are also stored as ordinal numbers 1 for January 2 for February etc Day of the year and week of the year are stored as the actual number Compass directions are stored as the angle of the mid point of the compass sector e g 45 for NE 90 for E etc Subgroups are stored as their ordinal number starting from zero 0 for the first group 1 for the second etc Finally labels are stored enclosed in double quotes so that they can contain embedded spaces As the data are read they will be checked to make sure they are in an appropriate format for the data type If any entries are found that are inappropriate that particular cell will be set to missing and a warning message will be displayed If a subgrouping variable 114 has been set then the next line after the data will specify which va
109. ime data type presents the circular data as time in hours minutes and seconds on a 24 hour scale The data can range from 00 00 00 to 23 59 59 or 12 00 00 AM to 11 59 59 PM The format used to display the time depends on the settings in the Windows Control Panel As with other circular data the data are stored as angles However the mean and median times and the confidence limits are reported as time values Day of Week DOW This circular type divides the 360 range into 7 groups representing the seven days of the week The order of the days follows the ISO 86016 international standard where Monday is the first day and Sunday the last As with other circular data the underlying data are in angles with the midpoint of the sector being the angle stored Each sector is 360 7 or approximately 51 4286 wide so the first day has an angle of around 25 7143 and day 7 is ca 334 2857 Means and medians are reported in angles but the associated DOW is also reported The actual text displayed in the results graphs and data editor are in the user s local language as set up in the Windows Control Panel so Monday is displayed for the first day in English Lunes in Spanish etc Currently Oriana cannot properly display day names that do not use the Roman alphabet Month of Year MOY This data type works in a similar way to DOW except it is divided into 12 groups for the months of the year with January first and December last Ea
110. ing a data file The first step in using Oriana is to create a new data file Do this using the File New command from the main menu A multi step wizard dialog box will be displayed this helps you in setting up your data file You will be asked various questions about your type of data For now let s assume we just have one set of circular data You should 1 Choose Angles as the type of data you are working with then click on the Next button 2 Choose the Separate option on the data layout page then click on Next 3 Pick Circular data only and press Next 4 Make sure Number of columns is set to 1 5 Enter a label for this column of data in the Labels box and press Next 6 Enter a descriptive title for the file then Finish 7 The dialog will close and the status window 7 and data editor 7 will appear Now you can start entering data The data editor has a single column for typing in the single set of data New columns can be added by simply pressing the left arrow key or using the Edit Insert Column 104 command The spreadsheet will be empty except for two rows of grey cells across the top One contains the data type the other the label you entered in the New File wizard Data can then be typed into the main body of the spreadsheet The following image shows a new data matrix in which five data points have been entered 3 2 Data Editor BAX A amp Type Angles x Name Direction F 1 9 000
111. ing the numbers You then press the Enter or Tab key or the up or down arrow keys to finish entering the data the Enter key will also move the active cell to next cell down ready to enter the next datum while the Tab key will move to the cell to the right As you type in data the values are checked to make sure they are valid e g in the range of 0 360 degrees or 00 00 23 59 hours The program will beep and refuse to accept any values that are not valid Some data types such as Day of Week have a fixed list of possible values You can choose the desired entry by clicking on the down arrow labeled Change datum in the image above You can also go straight to an entry by just typing the first few characters of the desired entry With Date and Time cells a small scroller labeled Increment Date in the image above will appear next to the cell when you begin typing You can use this to increment and decrement the date or time With Date cells if you double click on the cell when the scroller is visible a monthly calendar will be displayed you can pick a new date from this 3 3 You can close the data editor at any time by again selecting Data Edit Data from the menu or clicking on its matching button on the toolbar or by clicking on the close button the one with the x in the upper right corner The data are maintained in memory and will appear when you open the editor again They are not saved to disk yet though You can do
112. ion determines whether the degree symbol is used when printing angles on the scales The X Axis and Y Axis sections both have a number of options that let you change aspects of either of the axes The Decimal places option adjusts the number of decimal places used for numeric labels on either axis When set to Auto the shortest number possible will be used e g there will be no decimal portion if the number is a whole number If set to a specific number of decimal places then all numbers will have that many places The second option occurring in both sections is Number of grid lines This option will allow you to specify how many grid lines are plotted on the graph When set to Auto it will use the optimum number of gridlines with the aim of producing a neatly scaled grid with values such as 10 or 25 if possible rather than 33 33 24 25 etc You can set a specific number of gridlines if you desire using this option 6 5 8 6 6 6 6 1 Menus 147 By default the labels are oriented parallel to the bottom of the graph You can use the Labels angle option to rotate the labels to any angle up to 90 either way If you are plotting linear data that are better expressed on a logarithmic scale with many very large values as well as small ones you can tick the Log scale for linear variables scale option to base the scale on a log scale e g 0 10 100 1000 Normally Oriana will scale the axes to the best value to acco
113. ions can t be made If you have a Label variable that you convert to Angles only those cells that have numbers between 0 and 360 or 180 to 180 will be converted Any cells with textual data or numbers outside the circular range will be converted to blank cells missing data If you wish to convert data to an alternative representation but keep the original data then tick the Create New Variable box For example if you have a date variable and wish to have a second one summarizing the month of each date you can use this option Finally you can declare that circular data are grouped 26 and set the width of the grouping 6 3 5 Data Change Data Structure This command lets you change the structure of the data between different layouts raw data in separate columns grouped data in a single column or frequency table data For a full explanation of these see the section on data structures 19 Change data layout This converts data between different layouts Sets of observations raw data in separate columns One column of data plus one subgrouping variable to distinguish the different sets A frequency table with one column of data and one column of the frequency of each data point plus an optional subgrouping variable Your data have been examined and the available options are enabled below Select the appropriate one and press OK Consolidate separate columns into one with subgrouping Separate out sub
114. ircular linear This dialog box allows you to create circular linear plots 87 which allow two variables to be plotted together on a single graph with the second variable determining the length or placement of each of the graph elements Circular Linear Plot Main Type Options Scatterplat Select Arrows Axes Bere Value shown as Colors Radius of wedge Lines amp Srea of wedge Patterns Wedges Symbols Titles Subgroups on single plot Fonts OK Cancel Help The section titled Type allows you to specify the graph type The Scatterplot will plot points on the graph so that the positioning around the graph represents the angle and the distance from the center of the graph represents the second linear variable You can also have the value of the second variable represented by an arrow bar or wedge When bars are used they by default are one degree wide You may use the Bar Width option on the Axes page to make them wider For wedges the Value shown as option lets you determine how the wedges as scaled just like in the rose diagrams in the Graphs Histograml 33 dialog box If you have a subgrouping variable in use then by default a separate graph is created for each subgroup You can tick the Subgroups on single plot to have them all plotted on a single plot with different colors or symbols for each subgroup as specified on the Colors and Symbols pages The Options page is
115. is no need to type them Clearing data in one or more cells Make the cell active and press the Del key choose Edit Delete from the menu or choose Delete from the context menu To clear several cells at once select the desired cells and use one of the above commands Pasting data from the clipboard Make active the cell at the upper left of where you wish the clipboard contents to be pasted Then choose Edit Paste press Ctrl V or choose Paste from the context menu The pasted data will overwrite existing data The data will be validated as they are pasted to ensure they are valid given the variable type Any data that are not valid are ignored and the cell remains blank A warning will be displayed if this happens If the column into which you are pasting does not yet have any data then Oriana will try to guess the most appropriate data type given the data on the clipboard If this guess is wrong you can set the column to the appropriate type make sure there is data in at least one cell then try pasting again If the data in the clipboard contains more rows or columns than will fit in the spreadsheet then more rows or columns will be added automatically Adding new columns and rows New rows or columns can be added singly by going to the last cell in the row or column and pressing the right or down arrow keys 3 5 To insert new rows or columns in the middle of the spreadsheet select a whole row or column then choose Edi
116. lar data and the associated frequencies like this 122 Oriana 4 Statistics era Raw yi Subgrouping fSeec Variable None ea so TA m 1 Direction A EEN Direction B Use variable Summarize Dates As No Summary Day of the Week Frequency Frequency 4 _ Frequency B OK l Cancel Help Note that this option will only be available if the data file appears to have frequency table data defined as pairs of variables one of which is Linear and contains the frequencies Also only one pair of data and frequency variables can be selected at atime This type of selection is not available for analyses and graphs that are used to compare two or more variables such as multisample statistics or two sample scatterplots If you need to do these you can use the Data Change Data Structureli09 option to convert the frequency data into columns of raw data Subgrouping and Filtering By default Oriana will calculate statistics and draw graphs using all the data from each variable However you may sometimes want to calculate separate statistics and do separate graphs for subsets of the data You can do this by using a subgrouping variable This is a separate variable that contains data specifying to which subgroup each case or row in the data matrix belongs You can select which variable to use for this purpose with the set of controls on the right entitled Subgroupi
117. le will be created next to the frequency variable For example if the subgrouping variable has three subgroups A B and C and each subgroup has a single value of 45 then the resulting frequency table will have three entries for 45 one for each subgroup with a frequency of 1 for each Converting frequency table to raw data This option will be enabled if it appears that the file contains Menus i i i one or more frequency tables To be recognized as a frequency table the file must have one Linear type variable holding the frequencies which must all be positive numbers one other data variable of any type and optionally a subgrouping variable If the file contains more than one frequency table the variables for all must be in the same order e g if one has the data variable before the frequency one then all of them must be the same When this option is selected each frequency table will be converted into a single data variable using the frequency column to determine how many of each value are in the column If a subgrouping variable is also found then a new one will be created and each data value will be assigned to the appropriate subgroup 6 3 6 Data Convert XY to Circular Usually circular vector data are entered directly as measured angles and the length of the vector However sometimes it may be more convenient to measure and record the X Y coordinates of the beginning and ending of the vector For instance in the fol
118. le depicted This is useful if you are working with axial data all in the 0 180 range Stacked and Stepped Histograms If your current data file has a grouping variable defined then normally separate graphs will be produced for each group However you can also produce a single graph that has differently colored segments for each group showing the relative proportions of each pow HB Monday BB tuesday E Wednesday HB thursday E Friday Oo Oo Saturday Sunday The above graph was produced by first ensuring that a grouping variable was selected DOW in this case and then choosing the Stacked Rose option on the Graphs Histograms 33 dialog box Choosing Stacked Circular will give a similar graph but with parallel sided bars and Stacked Linear will give a linear histogram 84 with stacked segments By default a single mean will be displayed for the whole data set However you can optionally specify that the mean for each 5 7 subgroup is displayed by selecting the Subgroup means option on the Options page of the Graphs Histograms 13A dialog box The Stepped Circular option will produce a circular histogram with each segment being somewhat thicker than the previous one This type of graph is commonly used for meteorological wind roses o o Angles Monday Tuesday Wednesday Thursday Friday Saturday Beougoms Sunday Two variable Histograms Segmented histograms like
119. le of Anglesey Wales current readings can be found at http www anglesey history co uk weather weather shtml They are hourly readings from 15 June 31 December 2002 The variables include wind direction wind speed in miles per hour date time and month Megaspor ori These data are from a study by Kovach 1989 Quantitative methods for the study of lycopod megaspore ultrastructure Review of Palaeobotany and Palynology 57 233 246 They represent measurements of the orientation of the elements that make up the wall of various fossil and modern lycopsid megaspores The data are measured in degrees and represent the orientation of the element relative to a base line drawn perpendicular to the spore surface Measurements were taken from several species of modern Selaginella and Isoetes as well as the Cretaceous aged fossils Paxillitriletes vittatus and Erlansonisporites erlansonii It was hypothesized that the orientation differed between the modern Selaginellaceae and Isoetaceae and that the fossil spores could be related to one of the two modern groups on the basis of this difference Termites ori This file has six of the data sets reproduced in Appendix B 13 in Fisher 1993 They are axial orientations of termite mounds of the species Amitermes laurensis at different sites in North Queensland Index By ee analyses see also tests 63 120 arrow graphs 83 axes 50 axial 12 14 47 65 85 B basic statistics 63 1
120. le summarizing your data then you will need to select the Frequency option on the Select page rather than Raw Then ensure that the variables selected in the Variable and Frequency sections of the page are the desired ones Raw Variable Direction A Direction B Frequency Frequency A Frequency B Selecting a subgrouping variable By default Oriana will calculate statistics and draw graphs using all the data from each variable However you may sometimes want to calculate separate statistics and do separate graphs for subsets of the data You can do this by using a subgrouping variable This is a separate variable that contains data specifying to which subgroup each case or row in the data matrix belongs For example the Wind2002 ori data file has a variable called Month which indicates in which month each observation was made See the section entitled Summarizing Datal60 to learn how this subgrouping variable was created To calculate separate statistics for each subgroup follow these steps 1 Follow steps 1 4 in the Calculating Statistics 41 section 2 On the Select page of the dialog box go to the Subgrouping box and tick the Use variable option 3 Inthe drop down box below this option chose the desired subgrouping variable Month in this case 3 11 Variable Subgrouping Direction None Use variable Month x 4 Click OK The results page will have a column of st
121. ll affect how these data are displayed in all Windows programs not just Oriana 6 6 3 Options Preferences This option lets you change a variety of settings that affect the whole of the program These settings are automatically saved for future use When you choose it the following dialog box is displayed 150 Oriana 4 Program Preferences General Automatically save amp restore desktop Warnings V Create backup data files or amp od Compass Convert Oriana Version 1 files to subgrouped data Lunar Phases Entries on recent file list 7 Display grid in V Data editor Result notebook Theme Office 2003 Silver v Automatically save amp restore desktop If you choose this option your desktop 4 will be saved when you exit Oriana It will automatically be restored to the same state next time you run the program Create backup data files or By default Oriana makes backup copies of your data files with the extension OR instead of ORI whenever you save your data Desktop files are also backed up to the extension OD instead of ODK You can turn this off using this option Convert Oriana version 1 files to subgrouped data When selected any Oriana ver 1 files that contain multiple columns samples will be converted into one column of data and another subgrouping variable containing the labels of the original samples Entries on recent file list This allows
122. loaded for free from our web site 158 7 2 Oriana 4 Further reading about circular statistics There are several books that are either dedicated to discussions of circular statistics or have substantial sections about the subject Many of these books are available from our web site at http www kovcomp com books html Batschelet E 1981 Circular statistics in biology Academic Press London 372pp Davis J C 1986 Statistics and data analysis in geology John Wiley New York 646pp Fisher N I 1993 Statistical analysis of circular data Cambridge University Press Cambridge 277pp Jammalamadaka S R amp Sengupta A 2001 Topics in Circular Statistics Series on Multivariate Analysis World Scientific Singapore 319pp Mardia K V amp Jupp P E 2000 Statistics of directional data 2nd Edition John Wiley amp Sons Chicester 429pp Reyment R A 1971 Introduction to quantitative paleoecology Elsevier London 226pp Upton G J G and Fingleton B 1989 Spatial data analysis by example Volume 2 Categorical and directional data John Wiley New York 416pp Zar J H 1998 Biostatistical Analysis 4th Edition Prentice Hall New Jersey 663pp Cabreram J Schmidt Koenig K and Watson G S 1991 The statistical analysis of circular data In Bateson P P G and Klopfer P H eds Understanding and animal awareness Plenum Press New York Fisher N I amp Lee A J 1983 A co
123. low you to specify how many concentric circles grid lines are on the graph When set to Auto it will use the optimum number of gridlines with the aim of producing a neatly scaled grid with values such as 10 or 25 if possible rather than 33 33 24 25 etc You can set a specific number of gridlines if you desire using this option or set it to 0 to remove all circular gridlines With circular histograms which use bars with parallel sides rather than wedges the bars actually extend outwards from a small circle around the middle of the graph rather than from the very center so that the bases of the bars do not overlap You can use the Basal circle diameter option to adjust the size of this circle The value is expressed as a fraction of the diameter of the graph so a setting of 1 5 means that the diameter of the circle will be 1 5 the total diameter The width of the bars will be adjusted so that they do not overlap The Number of bars option lets you set the number of bars in the histogram The width of each bar will also be displayed Note that this option is not available for data types with fixed 138 Oriana 4 class widths e g Day of Week or Month of Year The Label grid lines option lets you choose which of the four main angular grid lines have labels for each circular grid line By default all four angular grid lines are labeled but you can choose to have only a single of a pair of lines labeled or none at all The Log s
124. lowing example you may record the X and Y coordinates of the dots at either end of the vector rather than the angle and length of the vector itself 8 If your data are in this format then you can enter them into Oriana in the following way 1 Choose File New to create a new file If the File Creation Wizard comes up switch to Expert mode using the button in the lower left 2 Set the number of variables to 4 and press OK 112 Oriana 4 3 In the data editor change the variable type of all four variables to Linear 4 You can now use these variables to enter your data Put the X and Y coordinates of the start point of the vector in the first two columns and the X and Y coordinates of the end point in the other two columns 5 Once the data have been entered select the Data Convert X Y to Circular menu item Ensure that the four drop down boxes contain the names of the appropriate variables for the X Y coordinates Convert X Y Coordinates to Circular Vector Start point origin x xStart iv Y Start a End point xX XEnd v Y End v 6 Press OK Two new variables will be created named Angle and Length that will contain the angle and length of each vector Please note that in the conversion process the starting point is translated to the origin of the circular graph so the angle will be the direction towards which the end point is pointing 6 3 7 Data
125. means and lengths then a column of results is produced for each pair SECOND ORDER STATISTICS Data file F StatData Oriana Ori2 Test Data Zar2717_ori Analysis begun 16 August 2011 16 18 07 Variable Means1 amp Rs1 Means2 amp Rs2 Number of Means 7 10 Grand Mean Vector GM 152 166 123 82 Length of Grand Mean Vector r 0 596 0 659 95 Confidence Interval for GM 121 423 110 535 186 01 140 566 99 Confidence Interval for GM 96 366 105 464 216 08 149 262 Hotelling s Test F 16 663 42 043 Hotelling s Test p 0 006 5 70E 5 Moore s Modified Rayleigh Test R 1 428 1 697 Moore s Modified Ravleiah Test fol lt 0 001 lt 0 001 Two Sample Second Order Statistics If there are two or more pairs of mean and mean vector length variables in the data file then two sample second order tests are also calculated First in the table of results are the names of the two sets of means lengths that are being compared along with the number of means in each sample This is followed by a number of test results Two sample second order statistics Variables 1st sample means Means1 1st sample vector lengths Rs1 Number of means 7 2nd sample means Means2 2nd sample vector lengths Ris2 Number of means 10 Hotelling s two sample F 4 693 Hotelling s two sample p 0 028 Mardia s two sample U 0 158 Mardia s two sample p 0 1 gt p gt 0 05 Hotelling s paired F 2 564 Hotelling s paired p 0 171 Moore s paired Ri
126. mmodate all data However you may want to produce multiple graphs with the same scaling for comparison Ticking the Manually scale option will allow you to specify in the Minimum and Maximum boxes the extents of the axis The Symbol Size option on the Axes page lets you adjust the size of the points on the graph Graphs Edit graph Choosing this option allows you to modify the graph settings for the diagram in the currently active window A dialog box similar to that used when first creating the graph will be displayed You can change most of the options the graph will then be redrawn with the new settings when you press OK These dialog boxes will not display the Select page that allows you to select the samples for plotting If you wish to plot a different sample then you will need to create a new graph Also scatterplot and Q Q plots cannot be changed from one plot type to the other new graphs will also need to be created in this case Options This menu lets you change some of the options regarding how the program acts and looks Options Font This option allows you to change the font used in the currently active window It will also change the font that will be used in the future for that particular window type 5 Font Font Font style Size Tahoma Regular 8 O Tahoma a Regular 8 a O Tahoma Small Cap Italic 9 T Technology Bold 10 O Tempus Sans ITC Bold Italic 11 E Termin
127. mported into Oriana from a variety of sources including many spreadsheet and database formats as well as plain text See the section on the File Import 94 command for a full list of formats To import a file follow these steps 1 Choose the File Import command from the menu 2 An Open File dialog box will be displayed Use the Files of type drop down box at the bottom to choose the type of file you wish to import We will choose Excel for this example 3 Now select the file you wish to import We can try importing the ImportEx xls file that can be found in the Sample Data folder of the Oriana data folder usually found in your My Documents folder Once the file is selected press Open 4 You will now be presented with an import preview dialog box which shows a preview of your imported data You can use this to check that the data are being imported properly If they are not then you can use the options at the top to adjust various parameters With this example data set you should see six columns of data each with a column label Set1 Set5 etc in the shaded portion at the top of each column Import statistics Columns 6 Rows 100 File type Excel Set1 Set5 Set6 Set Set10 Set14 172 183 166 169 180 5 177 86 194 178 167 174 5 184 74 70 178 184 173 5 163 161 177 168 180 179 5 244 83 201 179 172 173 5 192 86 71 188 176 191 5 215 174 179 177 160 197 5 163 174 191 180 179 179 5 1An 190 179 1572 173 17A 5 5 This i
128. n see the section on stacked and stepped diagrams 85 for the difference between these Type ae Frequency shown as A Stacked Rose Radius of wedge Area of wedge Stacked Circular Stepped Circular Linear Width 5 Normal width Stacked Linear Half width Double width Now go to the Select page where we can specify the variable to be used as the second one This time the Variable box only allows a single variable to be selected We will select the Direction variable Variable Direction Month Time 5 Below this is a new listbox labeled Second variable Use this to specify the second variable that will make up the segments of each bar in the diagram We will choose the Speed variable which represents wind speed Second Variable Direction Speed Month Time 6 Let s now look at the Options page There is a new option here called Exclude 0 0 values With diagrams depicting wind speed it is customary to not include data when the wind speed is zero the associated direction could be unreliable as the wind vane could be pointing in any direction in becalmed situations When this option is ticked any zero values are not included in the rose diagram Instead the legend box will give the percentage of the zero values in the data set 7 You can choose to have Oriana automatically divide each wedge of the rose diagram into a certain number of segments using the Automatic option and the Number of Segments set
129. n declare which pairs of variables are supposed to be treated together as a vector These vector pairs can then be used to produce Two variable histogramsl 86 and Circular Linear plots 87 They can also be used to calculate weighted means where the mean is weighted by the linear variable To define vector pairs use the Data Define Vector Pair menu item The dialog box has two drop down boxes that list the circular and linear variables Simply choose the appropriate variables and press the Add button to add the variables to the list of vector pairs When you press the OK button the Status window 7 will be updated to show the defined vector pairs 6 3 10 6 3 11 Menus 115 Define Pair of Variables as Vector Circular amp Linear Vector pairs circular amp linear Circular Variable Month v Direction amp Speed Linear Variable 2nd speed iv Data Sort Data You can use this command to sort your data numerically or alphabetically You can sort on up to two different variables and can reverse the order of either Sort Data First Sort Variable Date ki Reverse order Second Sort Variable Time v C Reverse order Normally the entire data matrix will be reordered so that data paired in each row remain paired However if just certain columns are selected before choosing this menu item only those columns are sorted Data
130. n ew 2 where ew is the width of each class of the grouped data in radians For classes less than 30 in width this correction is negligible so is not applied If the variable typel 13 being analyzed is Axial then the data are doubled modulo 360 before being analyzed The resulting mean direction is then back converted to be within 0 180 The other mean related statistics are also back converted Weighted Statistics If your data consist of vectors where both the angle and the length have been recorded and you have defined vector pairs using the Data Define vector pair 112 command then a weighted mean vector will also be displayed This is the angular mean but weighted by the lengths of the vectors The length of this mean vector is also given first in the native units of the weighting variable then scaled 0 1 like the unweighted r This is followed by the X and Y components sin and cosine of the standard deviation ellipse This is an ellipse depicting the standard deviation that can be drawn around the weighted mean centroid on circular linear graphs 142 Basic statistics about the weighting variable will also be displayed Also displayed are two hypothesis tests Hotelling s test Batschelet 1981 p 144 tests whether the centroid of the end points of the weighted vectors differs from the origin effectively whether the weighted angles have a significant mean direction The null hypothesis is that there is no mean direc
131. n example The Number of grid lines option will allow you to specify how many grid lines to draw on the graph When set to Auto it will use the optimum number of gridlines with the aim of producing a neatly scaled grid with values such as 10 or 25 if possible rather than 33 33 24 25 etc You can set a specific number of gridlines if you desire using this option Since the main purpose of this graph is to compare the distributions on the two axes the same number of gridlines is used for both axes The X Axis and Y Axis sections both have options called Decimal places This adjusts the number of decimal places used for numeric labels on either axis When set to Auto the 6 5 7 Menus 145 shortest number possible will be used e g there will be no decimal portion if the number is a whole number If set toa specific number of decimal places then all numbers will have that many places The second option occurring in both sections is Labels angle By default the labels are oriented parallel to the bottom of the graph You can use this option to rotate the labels to any angle up to 90 either way You can use the Symbol Size option on the Symbols page to adjust the size of the points on the graph Graphs Two sample This dialog box lets you create two sample plots 89 either a standard scatterplot using either circular or linear data types or a Q Q plot that compares the distributions of two circular variables
132. n the file Oriana will then check to make sure the file exists is a valid Oriana file and can be opened with no problems The program will then read the data and open a status window telling you some information about the file Once this is displayed you can then choose one of the data editing graphing or analysis options You can also open a new file using the drag and drop 159 feature of Oriana 6 1 3 6 1 4 6 1 5 6 1 6 When this is selected a submenu is displayed showing the most recently used files You can reopen one of these files by clicking on it File Reopen The number of recent files displayed here can be changed in the Options Preferences 149 dialog box File Close This will close the current data file along with all other windows containing the graphs and results associated with this data file If the data have been modified but not saved you will be asked if you wish to save them If you have previously opened or saved the current desktop and have added new results or graphs to it then you will also be asked if you wish to save the desktop File Save Data Choosing this option will save the currently loaded data to a file If you have already specified a filename by saving it previously then the file will be saved straight away Otherwise you will be asked to enter a file name in the Save Data As 93 dialog box File Save Data As This option lets you save the currently loaded data t
133. ng Ticking the Use variable box will allow you to use the drop down box to select the variable you wish to use as the subgrouping variable If the selected variable is a date variable then the Summarize Dates As section can be used to select the method of subgrouping by date e g by month of year or day 6 4 2 Menus 123 of week The Filtering button opens the Filter Datal113 dialog box This lets you restrict the analysis to a certain subset of data When filtering is active the caption of this button is changed to Filtering Active See the description of the dialog box for more details Analyses Stats This option allows you to calculate a variety of statistics 63 on your data This will cause the following dialog box to be displayed See the section on Basic Statisticsl 631 to learn more about each option Statistics fan i V Mean Angle v Variance Select Save to File v Standard Deviation V Length of vector r Standard Error Median Angle V Concentration Confidence Intervals V Rayleigh Uniformity Test Chi Squared V Rao s Spacing Hotelling s Watson s U Moore s Kuiper s Y Test Choose the statistics you wish to have calculated by ticking the box before each one The ones above the horizontal line are basic statistics about the sample while those below are single sample tests Most statistics are calculated very rapidly but the Median Angle can take a l
134. ng data When this is chosen the Value box above turns to Start Value and the Increment box is enabled To fill an angular variable with a series of data such as 10 20 30 40 etc enter 10 in the Start Value box and 10 in the Increment box With circular data once the data fill reaches the upper limit e g 360 or 23 59 the values will start again at the lowest value 0 or 00 00 Random 6 3 13 This will fill the variable with uniformly random data When this is chosen the Value box above will become Min Value and Increment will become Max Value This allows you to specify the range of possible values that are randomly generated For circular types if these are left blank then the data are randomly generated from the whole circular range von Mises Random This will fill the variable with random data fitting a von Mises distribution When this is chosen the Value box above will become Mean and Increment will become Concentration This allows you to specify the parameters of the distribution If these are left blank the distribution used will have a mean of 0 and a concentration of 2 Date If the chosen variable is a Date variable then the Date option will become available in the Fill Type box When this is selected the Date Fill box becomes enabled allowing you to fill the variable with an incrementing series of calendar dates The Day option will increment the value by one day for each row whereas the Weekday option will do
135. nt the minor divisions labeled you can tick the Label minor divisions option The Center circular bars on 0 option specifies that the bars or wedges should be arranged so that the first one is centered on zero e g first bar would range from 350 10 instead of 0 20 Usually Angle and Axial data are plotted with the actual degrees e g 90 used as labels However if these data Menus 137 represent geographical directions then you may wish to have the graph labeled with the compass directions such as E for East instead You can do this by ticking the Label angles as compass option The Include symbol on angles option determines whether the degree symbol is used when printing angles on the circular scale The Plot only 0 180 option allows you to create a graph that only plots the data in the 0 180 range but which cover the whole of the circular graph This type of graph can be used in fields where data are always measured on a 0 180 scale such as the axis in ophthalmology Note that any data values greater than 180 will be ignored Circular Y Axis Normally Oriana will scale the Circular or Y Axis to the best value to accommodate all frequencies in the histogram However you may want to produce multiple graphs with the same scaling for comparison Ticking the Manually scale option will allow you to specify in the Maximum box the maximum extent of the circular Y axis The Number of grid lines option will al
136. nter 1001 2 2 1 1 Main window The Oriana program interface consists of a single main window a so called multiple document window A number of windows can be displayed within this main window as shown below All these windows relate to a single data file if you wish to have data and results from a second data file on your screen you can run Oriana again to create a second main window The image below shows a typical layout of the main window during an analysis session 6 Oriana 4 Oriana 3 0 Px File Edit Data Analyses Graphs Options Window Help Deon 68 B gt S06 CE o aeaaea i l E M Click and drag here Click here to e E customize toolbars g lt oy Data file mA B 1 c D r E F StatData Oriana Ori2 Test Data Winc 1 BASIC STATISTICS i 2 Data file F StatData Oriana Ori2 Test Data Wind2002 ori 5 variables and 4495 cases 3 Hourly wind data garden weather station Jun Dec 2002 4 Analysis begun 14 November 2008 09 35 09 Hourly wind data garden weather statio 5 5 E Oriana Graphs BAX Y Rose 09 7 i A 8 Direction D t Type Angles z linear z i Month Irection L Name Direction Speed time 0 om A 2 248 000 6 260 3 232 000 8 050 Vv E3 4 186 000 5 370 5 222 000 5 820 6 252 000 3 580 7 239 000 10 960 8 250 000 10 960 c 237 000 6 260 10 236 000 5 370 i 145 000 4 030 12 229 000 3 130 13 227 000 2 680 lt 7 Select
137. nth iv Filter data Comparison Type Equal Greater than or equal Not equal Less than or equal Greater than Contains Less than Doesn t contair Value sep 7 Click OK The Status window will now be updated to show you are filtering on the selected criterion Now when you calculate basic statistics as in the Calculating Statistics tutoriall 47 only those data recorded in September will be used The number of observations in the analysis will be just 700 rather than the 4495 in the full data set Comparing samples Oriana has several different methods for comparing samples within a set of data Descriptions of each test are given in the Analyses 63 section To perform these tests take the following steps 1 First open the file We will use the Termites ori example data file for this example 2 Select the Analyses Multisample Tests menu item 3 Onthe first page of the dialog box select the desired analysis We will use the Watson Williams F Test here 4 Most of these tests can be performed in either a pairwise fashion where the test is calculated for each pair of samples or multisample where a single test is calculated for all samples Let s first choose multisample by ticking the appropriate option in the Calculate Tests As section Main Choose test type Options Watson Williams F Test Select Chi Squared Test Mardia Watson Wheeler Test Watson U Calculate tests as Pairwise 5
138. o ver 1 Symphony ver 1 dBase II dBase ITI Paradox ver 4 Oriana ver 1 Comma delimited text e Tab delimited text e Fixed width text For many of the formats the data are saved in the earliest file format version possible as indicated in the list above so that they should be able to be read by the widest range of program versions When you choose the File Export command you will be presented with the standard Oriana save file dialog box To choose the format you wish to save in use the Files of type drop down list at the bottom of the dialog You can then switch to the appropriate folder and enter a name for the resulting exported file Graphs If the Graphs window is the active one then this command will let you export the currently visible graph to one of several common graphics formats By default just the currently visible graph is exported but if you tick the Export all pages option then all graphs will be exported They will each be exported to separate files Numbers will be appended to the file names to make them unique The available export graphics formats include e Enhanced Metafile emf e Windows Metafile wmf e Windows Bitmap bmp Portable Network Graphics png e GIF or Compuserve gif JPEG jpg The Metafile options save the graph as lines symbols and text so that it can be easily modified and rescaled in a drawing program The WMF format is an older one that is less flexible
139. o a file after specifying a filename When you choose the File Save Data As command the Save File dialog box will be displayed It looks much the same as the File Open Datal 97 dialog Once you have entered a valid file name in this box click on the Save button Oriana will first check to see if the file already exists if so you will be asked if you wish to overwrite the existing file The program will then write the data to the file Subsequent saves to the same filename can be done without having this dialog box appear by using the File Save Datal93 command 6 1 7 6 1 8 6 1 9 File Open Desktop This option allows you to reload a previously saved desktop file The data file will be reloaded and all the results and graphs windows will be recreated When this option is chosen you will be presented with a dialog box similar to that used in the File Open 91 option You can choose which desktop file you wish to open All currently opened data files and results and graphs windows will be closed before the desktop is restored You can also open a new desktop file using the drag and drop 15 feature of Oriana File Save Desktop Oriana uses a desktop metaphorl 4 in dealing with data analysis projects The Save Desktop option lets you save your current working environment to disk The position size and contents of each window currently displayed will be saved Later you can use the Open Desktopl 94 option to reload all
140. o not be cakated Rayleigh s Uniformity Test Fisher 1993 p 70 Zar 1998 p 616 Mardia amp Jupp 2000 p 94 calculates the probability of the null hypothesis that the data are distributed in a uniform manner The Z value is calculated simply as Z nr where n is the number of observations and r is the length of the mean vector A longer mean vector and the resulting larger value of Z means greater concentration of the data around the mean and thus less likelihood of the data being uniformly distributed The calculation of the probability follows Fisher s equations 4 17 and 4 18 A probability less than your chosen significance level usually 0 05 indicates that the data are not distributed uniformly and that they show evidence of a preferred direction the preferred mean direction is unspecified as opposed to the V test discussed below In the above example the Rayleigh Z value is very high and the probability vanishingly small so we reject the probability that the data are uniformly distributed Note that in the Results window a lt 1E 12 which stands for lt 1x10 means that the actual value is indistinguishable from zero at the maximum accuracy of the computer 15 16 significant digits Values that are somewhat larger but still smaller than the number of decimal places set in Options Format 149 are given in scientific notation e g 0 0000025 or 2 5x10 is displayed as 2 5E 6 Rao s Sp
141. ogram You can change the frequency of the check or disable it completely by clicking on the Options button on the update wizard Please note that Oriana will ask you first before checking for updates and that no information about your computer or software setup is transmitted to our web site This update check simply downloads a small file from our web site containing the version number of the latest version and information about the update Help Order Oriana This menu item takes you to the Kovach Computing Services web site to order a copy of Oriana Help About This will display a dialog box giving some information about this program primarily the version number copyright notice and the address of the author If you are using the evaluation version of the program it will also tell you how many days or runs you have left in the trial period and will provide buttons for ordering the program and entering the registration code Technical Support Technical Support Technical support Registered users of Oriana are eligible for free technical support on the use of the program for 90 days after purchase This is primarily meant to answer questions about installation of the program and getting started in using it Most questions will be answered in the manual and help files so look at those first before contacting us After 90 days we will generally try to help with more technical questions but we reserve the right to refer
142. ong time for large sets of data So you may wish to leave this one unticked unless you need it For the Watson s U2 and Kuiper s single sample tests you must select the desired Test distribution from the drop down box The V Test requires that an Expected Mean is entered as with this test the alternative hypothesis is that the data are 124 Oriana 4 not uniform but have a certain specified mean When you press the OK button the statistics you have chosen will be calculated and the results placed in a table The results will be printed with the number of decimal points specified in Options Preferences 145 If you have ticked the Save to File checkbox then you will also be prompted to enter a file name This file will be used to store the means and lengths of the mean vectors in a separate file You can then use these for further second order analyses 124 in particular for two sample and paired tests 6 4 3 Analyses Multisample Tests This option allows you to calculate a variety of multisample test on your data This will cause the following dialog box to be displayed See the section on multisample analyses 71 to learn more about each test gt Multisample Tests Main Choose test type Options Watson Williams E Test Select Chi Squared Test Mardia Watson Wheeler Test Watson U Hotelling s Paired Moore s Paired Calculate tests as Pairwise Multisample The C
143. or columns 6 2 9 6 3 6 3 1 Menus 105 Edit Delete Row Column When the data editor is active this command can be used to delete rows or columns into the spreadsheet The exact function of this command varies depending on how the cells in the spreadsheet are currently selected BA If a single cell is selected the dialog box below will be displayed allowing you to specify what you want deleted You can choose to delete either rows or columns and you can specify whether they should be deleted from the end of the spreadsheet or the current location Delete Rows Columns Delete Where Number to Delete 1 If you have selected 32 whole rows or whole columns then the dialog will not be displayed Instead if you have selected a whole row Oriana will delete that row Likewise if a whole column is selected that column will be deleted If you want to delete more than one row or column then just select the appropriate number of rows or columns Data The Data menu contains functions that allow you to make modifications to the currently loaded data file Data Edit Data Title Each data file has a title associated with it You can use this title to give your data file a description so you know what the data are The title will be printed whenever you print out data or results This command will open up a dialog box that allows you to 6 3 2 6 3 3 enter or edit the title for the file If y
144. or the sector of the circular type e g January will become 15 Conversions to and between date summary types tries as much as possible to give a sensible conversion For example if you convert a Date variable to Day of Week it will convert each datum to the appropriate day of week for that date Conversion from less specific to more specific date types is done with reference to the current year month or week If you convert from Day Of Week to full Date it will give the date for the DOW in the current week likewise conversion from Month Of Year to Date will give the date of the first day of that month in the current year Conversion of a Lunar variable works in a similar way as the Date type An addition for Lunar variables is that if the variable is converted to a Linear type the result will be the lunar day with a range of 29 or 30 depending on the length of that lunar month Day 1 represents the new moon day Also for each Lunar variable you can set the time zone in which the data were recorded see the description of the Lunar variable 16 to find out why you might need to do this The value entered into the Lunar time zone offset option is the number of hours difference positive or negative from UTC or GMT Coordinated Universal Time or Greenwich Mean Time If you aren t sure of the difference you can press the Zones button which will display a list of time zones from which you can select the appropriate one Some convers
145. ou have changed the title but not saved the file you will be asked if you would like to save it before you exit Oriana or open a new file If you wish to save the title straight away choose the File Save Datal 93 command Data Edit Data Choosing this option will open the Oriana data editor to allow you to enter or modify data See the section on modifying 34 data for more details Data Edit Frequencies Sometimes you may have recorded your data as a frequency table For example you may have recorded that there were 20 objects oriented at 10 30 at 20 etc To enter these data into Oriana you could go to the data editor and type in 20 10s 30 20s etc However Oriana has a frequency editing mode that makes it easier to enter this type of data This allows you to enter the value measured in one column and the frequency of those values in the second column Frequency Editor Value Frequency A 10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000 90 000 100 000 110 000 120 000 130 000 140 000 460 000 on onek Wn ea feat fen fom ea fee nrun ot PNON WN WON WON WD FY FA NY J Once you have entered your data in this form you can press the OK button The current column of the data editor will then be filled with the data Menus 107 If you open the Frequency Editor when the selected column in the data editor already has data then that data will be summarized in the dialo
146. ow plots plus raw data plots and vector plots for circular data There are also distribution plots for comparing data to theoretical distributions Q Q plots for comparing the distributions of two samples and scatterplots for plotting circular as well as linear data Oriana has powerful data handling capabilities It can work with a variety of circular data types in their native formats these include angles time day of the week month day or week of the year and compass directions You can also include any type of linear numerical data for example if you wish to record both wind direction and speed or direction of movement of an animal and distance traveled which can then be used in some of the graph types and in the circular linear correlation You can also include full dates which can later be summarized into the various circular types and labels for each observation There is also a subgrouping data type which allows you to assign each data point to one of the groups you define so that you can analyze each subgroup separately as well as all data together 4 Oriana 4 2 2 Data can be entered in a spreadsheet form with separate columns for each set of data or each variable as well as in the form of a frequency table Data sorting automated filling of data and search and replace facilities aid in entry and maintenance of your data Oriana is designed to be as easy to use as possible and to be compatible with all your other
147. ows are contained within the main Oriana program window and they all relate to a single data file The windows can each be resized minimized or moved around while you study them and generate new pages Each page can then be printed and or saved to a file if desired You can save your desktop to a file using the File Save Desktop command later you can restore it to the same state Getting Started os using File Open Desktop so each window is just where you left it with the same contents as before You can continue working where you left off Multiple desktops can be saved for different projects 2 2 1 Windows The Oriana desktop can have a number of different types of windows open at any one time These types of windows have different appearances and characteristics depending on their function In most cases you need not worry about these differences For example choosing the Print option will print the currently active window no matter what type it is you will notice no difference in the procedure The different windows automatically save their characteristics for future use For example if you resize the status window so that it is small and place it in the lower right corner new status windows will always be that size and position Other types of windows can have their own default size and placement Similarly each type of window has its own characteristic font 1147 and each can be set up to print to a different pri
148. previous section for two variable histograms However in this case the value of the second variable is represented by the length of the arrows or bars or by the placement of the points on the graph each of which represents a single case or row of the data matrix We can 3 20 demonstrate this graph type by again using the Wind2002 ori file 1 Open the Wind2002 ori file ifit isn t already loaded 2 Choose the Graphs Circular linear Plot menu item 3 Onthe Select page ensure that subgrouping is by Month as done in step 3 of the Stacked Histogram 5A tutorial 4 Also ensure that the primary and second variables are set to Direction and Speed respectively as in steps 3 4 of the Two variable Histogram 55 tutorial 5 Onthe Main page of the dialog you can choose to have the data represented as a scatterplot or with arrows bars or wedges 6 You can use the Symbol size option on the Symbols page to determine the size of the scatterplot symbols and the Arrowhead size option on the same page to adjust the arrowheads If the Variable arrowhead size option is ticked then arrowheads closer to the center of the graph will be made smaller Since shorter arrows have their heads packed more closely together this helps make the individual arrowheads more easily visible 7 Ifinstead you are using bars the width of the bar is controlled by the Bar width option on the Axes page By default this is set to 1 degree wide but you may wish to
149. previously so you don t need to follow steps 3 5 above unless you wish to change them 2 On the Select page in the Subgrouping box tick the Use variable button then select Month from the drop down box below it Variable Subgrouping Direction None Use variable Month x 3 Press OK Seven new graphs will be added to the Graphs window one for each month from June December These demonstrate the variation in the wind direction through the seasons with it being primarily southwesterly in the summer but more varied in the autumn and winter 3 14 Adjusting graph axes Oriana has a wide variety of options that allow you to customize the appearance of the graph Let s first try out some of the options for changing the axes of the circular graph Here is what our graph looks like so far Direction 1 With the graph window topmost showing the graph you want to change choose the Graphs Edit Graph menu item The Histogram dialog box will appear again 2 Now go to the Axes page This has two sections the first for adjusting various aspects of the Angular or X Axis This is the one around the circumference of the circle which represents the angles time of day or other circular data In the graph above it is labeled 0 90 180 270 The second section is for changing the Circular or Y Axis This is the set of concentric rings that provide the grid representing the frequencies in the histogram Circula
150. ptions you must press the button labeled Update Preview to have the data preview pane reflect the new settings Below the spreadsheet is one or more tabs Most modern spreadsheet programs allow multiple pages or sheets These tabs provide access to each page in the current spreadsheet When you select a different page by clicking on the tab that page will be previewed Note that only one page can be imported at a time Options Column names This tells import where to find the text labels used for each column variable The exact options available vary depending on the file type being imported Some file types don t offer any options here at all for example with database files the column names are taken from the field names Guess names for spreadsheets only will examine the spreadsheet skip over any blank rows or rows that have text in just a single cell e g titles at the top of a page and use the first row it finds with text in more than one column as the column names Names at row for spreadsheets only If the above doesn t correctly find your column labels then you can use this option to specify exactly which row they are in Data in rows before this are ignored Note that the labels should have at least one non numeric character When importing text files this option becomes Names at row 1 and any labels included should be in the first row of the text file If your file does not have column labels then you can choose t
151. quentially through the dialog box items Besides the above principles you can also use certain other standard keystrokes The following is a list of the keystrokes that can be used Menu Items etc 8 3 Ctrl O Open data file Ctrl S Save current window Ctrl P Print current window F1 Context sensitive help Ctrl F4 Close window on Oriana desktop Alt F4 Close Oriana main window Ctrl F Find datum Ctrl H Find and replace data Ctrl Tab Switch between windows within the main Oriana window Data editor amp results window Del Delete current cell Ctrl Z Undelete last deletion Shift Cut selected cells to clipboard Delete Ctrl X same as Shift Delete Shift Ins Paste clipboard contents at current cell Ctrl V same as Shift Ins Ctrl Ins Copy selected cells to clipboard Ctrl C same as Ctrl Ins F2 Turn on edit mode Esc same as F2 F3 In date or time fields when edit mode is on sets cell to current date or time F4 In date fields when edit mode is on displays calendar Edit mode can be exited by pressing Enter tab or one of the arrow keys Pressing Esc while in Edit mode will also exit but the cell will revert to its original value ISO 8601 The International Organization for Standardization has produced a document ISO 8601 that defines standards related to date and time notations Different countries around the world traditionally use different methods for these notations which can cause problems It is
152. r Axis Manually scale Decimal places Auto Number of bars 242 width 15 00 Number of grid lines 3 v Label grid lines all Ford Number A of bars Log scale Percentage scale 3 First lets change the Angular axis Notice that the first wedge in the histogram starts at 0 and goes to 15 With directional data particular those based on the compass like our wind direction data some people prefer to have this first bar centered on 0 rather than starting there We can do this with the Center circular bars on 0 option We can also tell Oriana to label the axis with compass directions e g N S etc rather than the actual angles Tutorial The Label angles as compass option will do this By default Oriana will divide the graph into four sectors for N E S and W We might want more gridlines than this We can use the Minor divisions option to specify that we want a medium number of divisions With compass labels this will give us 16 divisions We can also tick the Label minor divisions option so that the compass directions such as NNE and SW are used Finally we can reduce the number of circular gridlines in the Circular Y Axis section with the Number of grid lines option Let s set this to 3 Now press OK Our graph now looks like this Direction 3 15 Customizing graphs 1 Let s customize other aspects of the appearance of the graph Choose the Graphs Edit Graph menu item The Histogram dialog
153. r data e g day of week month of year day of year etc Oriana has a wide range of native circular data types to match the data with which you are working There are also several other non circular data types for associating other data such as text labels or data measured on a linear scale with your circular data You can find a summary of the data types in the section entitled Oriana Data Typesl 13 When you create a new data file 29 you specify the type of data for each variable You can later change the type of dataina variable using the Data Change data typeli0 menu option Oriana Data Types Each variable in an Oriana file is declared as one of 12 data types These determine the type of data that can be entered in the data editor The editor will restrict entry so that only valid data can be entered It also provides assistance in entering the data such as automatically entering the separators for times and dates or allowing you to enter day and month names from a drop down list or by typing just the first one or two letters The data types will also dictate how the data are handled during analyses and graphing For example some data types are inherently grouped see section on Grouped Circular Datal 26 Oriana will automatically adjust graphs such as the rose diagram to reflect the group width of the data e g Month of Year data will have 12 segments in the diagram each 30 wide Some analyses cannot be reliably pe
154. r this bias using recognized corrections or alternative calculations but some analyses simply cannot be calculated on these types of data After you have entered or imported a new set of data and before saving or analyzing the data Oriana will scan through them to see if they appear to be grouped If so Oriana will prompt you with a dialog box asking if the data actually are grouped and if so what the grouping interval is If you confirm that the data are grouped then Oriana will record this and will take the grouping into account in all analyses If you clear the Data Are Grouped tick box then Oriana will remember this and will always proceed as if the data are not grouped You can change this declaration later through the Data Change Variable Typelt0 menu item Missing Data Oriana can easily handle missing data There is no need to enter a special missing data marker simply leave a cell in the Getting Started spreadsheet blank and Oriana will consider that data as missing With all single sample statistics tests and graphs the missing data are ignored and not included in the results With pairwise tests missing data are handled by pairwise deletion leaving out any pair of data where one is missing For multisample tests listwise deletion is performed any row that contains one or more missing data is ignored 3 1 Tutorial Tutorial The following topics give step by step instructions on using Oriana Creat
155. re calculated on samples of means rather than raw data As with those it is assumed that the data are paired e g each row in the data matrix contains the means for the same population but measured before and after some treatment or change in circumstances 5 1 Graphs Oriana allows you to plot your data in a number of ways There are a variety of circular graphs as well as traditional linear histograms and scatterplots There is also a graph that plots your data against an expected uniform distribution to allow you to assess whether your data depart from uniformity and a similar graph that compares two sample distributions For more details about how to actually produce these charts see the tutorial section on graphing your data 47 Rose Diagrams This is one of the most commonly used types of graphs for circular data It is basically a histogram that has been wrapped around a circle Each section of the histogram which in this case is wedge shaped depicts the number of observations falling within that portion of the range In the graphs shown below each wedge represents 10 of the total circular range and the length of each wedge the radius from the center represents the number of observations falling within that range The data are tabulated so that the lower end of the range is included in the bar but not the upper end e g the first bar includes values ranging from 0 to just less than 10 the second one ranges from 1
156. recommended that particularly for a global audience the ISO 8601 standard be followed to avoid confusion For example the actual date represented by 5 2 2003 could be Appendices tot either February 5 or May 2 depending on the country ISO 8601 recommends representing dates in the unmistakable form YYYY MM DD where YYYY is the year in the usual Gregorian calendar MM is the month of the year between 01 January and 12 December and DD is the day of the month between 01 and 31 Internally Oriana follows the ISO standard in the way it stores dates and times However the format used for displaying dates and times in the data editor and results window follows the regional settings in the Windows Control Panel ISO 8601 specifies that Monday is used as the first day of the week Thus any lists of days of the week in Oriana e g the order they are listed on histograms follow this standard Also the calculation of the week of year follows the ISO standard see the section on Oriana data typesl 13 for details An excellent summary of ISO 8601 can be found in the Internet document A Summary of the International Standard Date and Time Notation by Markus Kuhn http www cl cam ac uk mgk25 iso time html as well as on Wikipedia http en wikipedia org wiki ISO_8601 The full text of the ISO standard can be downloaded from the International Organization for Standards at http www iso org iso iso_catalogue catalogu
157. rformed on grouped data and others must be adjusted to work properly so Oriana takes this into account Variables can be changed 5 between one type and another but data that do not fit into the range and assumptions of the destination type may be lost or converted to nonsensical values The characteristics of the different variable types are listed below Angles This is the basic circular type where data are measured within the range of 0 360 The data editor will not allow any values outside of this range to be entered Occasionally researchers find it useful to measure angles as a deviation from a home direction So for example if the expected direction of travel is 0 and one subject travels 10 to the left then a value of 10 would be recorded The Oriana Angles variable type will not allow negative numbers to be entered However you can get around this by entering the data into a Linear variable described below which will accept negative numbers Once all data have been entered you can change the variable typel 591 to Angles Any negative numbers will be converted to the appropriate degrees e g 10 will become 350 Axial This is similar to the Angles type but the data are bidirectional rather than unidirectional as discussed in the Circular Data A topic above Data can still be entered in the full 0 360 range but when analyses are performed the data are doubled and then back converted so that they
158. riable is the subgrouping one This line begins with the word SubgroupingVar which is followed by the ordinal number of the selected variable e g 4 for the fourth variable If the selected variable is a date variable and the date is to be summarized e g by day of week then the variable number will be followed by a dash and one of four indicator of the summary type DOW MOY WOY or DOY An example is SubgroupingVar 4 DOW If any vector pairsh 1A have been declared then the last line of the file will identify these The line begins with the word VectorPairs followed by one or more pairs of numbers separated by a colon that identify the numbers of the two variables in the vector pair The line is terminated with a 1 to indicate that the last pair has been written So if the first and second variable in the data file have been declared as a vector pair the last line will look like this VectorPairs 1 2 1 8 5 Appendices 165 Example data files Oriana includes three example data files These show you the structure of the data files as well as allowing you to test out the program before entering your own data These can be found in the folder SampData in the Oriana program directory Oriana should go to this folder first time you run the program Wind2002 ori These are data from a weather station in the back garden of the home of the owner of Kovach Computing Services in Pentraeth Is
159. rised use shall result in immediate and automatic termination of this licence This licence is non transferrable and non exclusive Kovach Computing Services warrants that it is the sole owner of the software and has full power and authority to grant the site licence without the consent of any other parties LIMITED WARRANTY Kovach Computing Services warrants the physical diskettes and physical documentation provided under this agreement to be free of defects in materials and workmanship for a period of sixty days from the purchase KOVACH COMPUTING SERVICES SPECIFICALLY DISCLAIMS ALL OTHER WARRANTIES OF ANY KIND EXPRESSED OR IMPLIED INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY AND OR FITNESS FOR A PARTICULAR PURPOSE The total liability of Kovach Computing Services for any claim or damage arising out of the use of the licensed program or otherwise related to this licence shall be limited to direct damages that shall not exceed the price paid for the program IN NO EVENT SHALL THE LICENSOR BE LIABLE TO THE LICENSEE FOR ADDITIONAL DAMAGES INCLUDING ANY LOST PROFITS LOST SAVINGS OR OTHER INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OF OR INABILITY TO USE THE LICENSED PROGRAM EVEN IF LICENSOR HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES This agreement does not affect your statutory rights The agreement shall be interpreted and enforced in accordance with and shall be governed by the laws of England an
160. rrelation coefficient for circular data Biometrika 70 327 332 8 2 Appendices 159 Appendices Drag and Drop Oriana supports drag and drop actions with data and desktop files This allows you to easily open files by dragging them around the screen rather than having to navigate the Open File 9M dialog box To do this simply drag a new data ori or desktop odk file from a Windows Explorer window onto the Oriana program window and it will be opened You can also drag a file onto an Oriana icon on the desktop this will cause a new copy of the Oriana program to be started Double clicking on a data file in Explorer or My Computer will also open a new copy of the program and load the file Using the keyboard Oriana like most Windows programs is strongly oriented towards using the mouse to control the program However great care has been taken to ensure that all functions can be performed using the keyboard as well All main menus can be accessed by holding down the Alt key and pressing the letter that is underlined on the menu So to call up the File menu press Alt F To access items on each menu just press the letter that is underlined while the menu is displayed To save a file press the s key while the file menu is displayed All items on the dialog boxes also have underlined letters You can access them by holding down the Alt key and pressing that letter Alternatively the Tab and arrow keys will move se
161. rrival 00 00 12 00 Note For samples with very large numbers of observations each symbol may represent multiple observations a note will be placed on the graph if this occurs If you want to reduce it to one symbol per observation you can try taking one or more of the following steps e Reduce the size of the symbols on the Symbols page of the graph dialog box e Switch to using a different type of raw plot e g from points arranged margin inwards to margin outwards Adjust the Basal Circle option on the Axes page to make it smaller for margin outwards and center outwards graphs only Increase the overall size of the graph by making the graph window and or the whole Oriana window bigger Arrow Graphs This graph is similar to a circular histogram 8 but instead of parallel sided bars it has arrows indicating the frequencies for each class 5 5 Linear Histograms Circular data can also be plotted on linear histograms In this case the mean vector and the confidence limits are show as vertical lines Arrival Time a a i ee em n lo eed amen ennn Frequency n 0 00 00 06 00 12 00 18 00 24 00 Hours If you wish to emphasize the cyclicity of the data you can choose to have the X axis doubled so two complete cycles of the data are plotted 5 6 Arrival Time nn errr E C EN Frequency nn 0 00 00 12 00 24 00 12 00 24 00 Hours You can also choose to have just half the sca
162. s Circular S22 Stacked Circular Lines amp Patterns Stepped Circular Symbols Arrow Titles 7 Linear Width i Normal width Linear Fonts Half Stacked Linear Double wid Cancel Hep The first page lets you choose which type of histogram to 134 Oriana 4 produce They are described in the section about graph types 7 For rose diagrams the Frequency Shown As box lets you choose between the two methods for producing the rose diagram sections see the section about rose diagramsl 7A for more details If one of the linear histogram types is chosen then you can use the Linear Width option to set the extent of the X axis The Options page lets you change a variety of settings that affect how the data are displayed Main Statistics f Options None Select g vector Mean Axes Colors Lines amp Patterns Weighted r Mean vectors only Symbols Subgroup means Titles Rayleigh critical value Fonts Print Frequency table OK Cancel Help You can choose to have the mean and confidence intervals displayed on the graphs The mean can be depicted either as a line to the edge of the circle or as a vector the length of which reflects the r value If you have vector data that consist of both an angle and a length or distance and you have defined the two variables as a vector pair in Data Define Vector Pairh then you can choose to have a Weighted r Mean plotted on the
163. s how we expect the data to be imported so we can press the OK button The data will be imported and the Status Window will be opened You can use the Data Edit Data command to open the editor and confirm that the data have been imported properly 6 This example data file has two pages of data We can choose to import data from the other pages These pages are accessed by clicking on the tabs just below the date preview spreadsheet To preview the second page click on the tab named Intensive 7 This time the desired column label Arrival does not appear in the shaded area This is because the file has two extra blank lines at the top of the sheet Import statistics Columns 1 Rows 256 Arrival 11 00 00 04 00 00 11 05 00 22 00 00 18 45 00 23 00 00 8 To fix this problem change the Names at row option to 3 then press Update Preview This tells Oriana to look at row 3 of the worksheet for the column labels You should now see the Arrival label in the shaded area and the data will now be imported properly Tutorial oa Note that if you hadn t changed the row for the column labels Oriana would still have imported this file However it would have treated the whole column as text rather than times and the variable type in the imported file would have been Label Cut and Paste An alternative method for importing data into Oriana is to use the Windows clipboard to transfer data directly between two programs To do this
164. s lets you enter the exact boundaries for each segment So if you enter a 15 in this option as the first boundary and a 30 as the second then all values from 0 15 will be in the first segment all values greater than 15 and up to 30 are in the second segments To build up your list of boundaries tick the Manual option then enter the first boundary into the Boundary box and click the Add button This will add the value to the box below Continue doing this for all boundaries If you need to remove a boundary you can select it in the list and click the Remove button If your second variable consists of discrete values e g just the numbers 1 2 3 and 4 and you want a separate segment for each you can use the Segment for each unique value option The Select page is also slightly different from the Graphs Histogram 33 dialog box Two Variable Histograms Main Variable Subgrouping i Direction Options month gt None f Sled O Time 2 Use variable Axes Col Summarize Dates As one Wo Summar Lines amp i Patterns aoe Variable aa earn Direction symbok Speed Month of the Year Month SE pee eee Titles Time Week of Year numeric Fonts Day of Year numeric OK Cancel Help The Variable box now only allows one variable to be selected There is also a second box labeled Second Variable which allows for selection of the second variable 6 5 4 Graphs C
165. s will have sequential numbers appended to your chosen file name to distinguish them All result pages will be exported to a single file Different types of windows have their contents saved in different formats some may have a choice of formats for saving See the descriptions of the window typesl 5 for more details Changing variable type You may occasionally find that you need to change the type of a variable Most often this is when you are creating a new data file in expert mode In this mode a blank data editor window is displayed with all the variables set to be of the type Angle You will then need to change the variable types to suit your purpose You may also decide later after entering some data that another data type might be more appropriate The simplest way is to use the drop down boxes at the top of each column Just click on the small downward pointing arrow and select the new type from the list B D E Angles Date z Direction Time Date 56 0000 09 20 01 01 2001 55 0000 19 20 02 01 2001 210 0000 Month of year 04 52 03 01 2001 170 0000 Week of year 08 00 04 01 2001 220 0000 08 40 05 01 2001 240 0000 00 44 06 01 2001 35 0000 10 40 07 01 2001 07 20 08 01 2001 02 24 09 01 2001 10 01 2001 15 0000 55 0000 You can also use the Data Change Variable Typeli0 menu item This will display a dialog box with all possible data types It will also let you change the grouping statel 20 of the circul
166. sed but the compression method is lossy which means it throws away some information in order to compress the image This method is better suited for photographic images for line drawings such as produced by Oriana this compression can cause some of the lines to become fuzzy and artifacts to appear in areas of solid color as demonstrated in the two pictures below magnified five times I I I 1 220 Windows Bitmap s JPEG Results If the topmost window is the Results window then this command will export the results on the current page to a text file or Excel workbook You can use the Files of type drop 6 1 11 6 1 12 6 1 13 down list at the bottom of the dialog to choose whether you want the results in Excel a tab delimited text file with tab characters between the columns or comma delimited text file with commas between the columns By default just the currently visible results page is exported but if you tick the Export all pages option then all pages will be exported They will all be output to the same file In Excel each page will become a separate sheet in the workbook whereas in text files a page break will be used to separate the results pages Notes The contents of the Notepad can also be exported to a plain text file with this command File Merge Files This option allows you to combine two or more Oriana files into a single one When the dialog box is displayed you can use th
167. st U 207 6 239 2 254 4 236 5 y Statistics The contents of this window can be saved using the File Export menu item when the window is the active window The results are written to the file in a tab delimited plain text i e ASCII format that can be read into any other program The columns will be separated by tabs so that the alignment will be preserved in any program that can interpret these tabs to form a table 2 2 1 5 Graph windows The graph window displays all the graphs so far produced one on each page When you first create a graphl 47 you can change various settings that determine how the graph is drawn You can then modify the appearance of the graph by choosing the Graph Edit graphli4 menu item or by right clicking on the graph and choosing Edit Graph The size of the graph can be changed by resizing the window Some of the graphs have a fixed length width ratio but the shape of others can be adjusted by changing the shape of the window f Oriana Graphs BAX Y 2 var Rose 15 35 Direction and Speed W 1 d D 1 ti Wind Speed 7 Rose 15 36 14 In Irec ion Zero values 35 11 Direction D v Raw Data 15 36 3 nell 4 8 400 a E 12 Cade aac eee E 12 16 Direction Month Time gt 16 22720022 AD 200 si0 400 90 100 Tse 299 2777 soo gage 77 7 400 180 Th
168. t Insert Row Column or Insert Row Column from the context menu To insert two or more rows or columns select two or more existing ones If Insert Row Column is chosen when there are not any whole rows or columns selected a dialog box will appear This lets you specify exactly what to insert Deleting columns and rows To completely remove rows or columns from the spreadsheet select a whole row or column then choose Edit Delete Row Column or Delete Row Column from the context menu To delete two or more rows or columns select two or more existing ones Note pressing the Del key while columns or rows are selected will not remove them but instead will delete their contents If Delete Row Column is chosen when there are not any whole rows or columns selected a dialog box will appear This lets you specify exactly what to delete Reversing editing changes The Oriana data editor keeps track of all changes you have made Changes can be undone in the reverse order that they were performed by choosing Edit Undo from the menu or pressing Ctrl Z The menu item and the hint on the status bar at the bottom of the window will tell you exactly what change will be undone next To reinstate a change that you have undone choose the Edit Redo menu item The list of editing changes is only maintained while the data editor is open If you close the data editor and reopen it you will not be able to undo previous changes Entering freq
169. t list can be displayed by using the drop down box that appears in every cell of a Subgroup variable You can use this drop down box to enter new data into empty cells or to change that in existing ones 2 3 3 Data Structure Data within Oriana can be structured in several different ways Raw Data The first is the one that was the sole method in version 1 of Oriana Here each column in the data editor represents an independent collection of measurements If all your data are repeated observations of a single type of object or event then you would have just a single column of data Examples might include e Directions that pigeons fly after release Orientation of tool marks in sedimentary rocks e Direction of wind at a single station e Time of arrival of patients at the emergency ward of a hospital You might also want to divide the data up into different groups so that you can compare the groups and look for similarities or differences For example e Directions that pigeons fly from different release points e Orientation of tool marks in different strata of rock e Direction of wind in different months or seasons e Time of arrival of emergency patients on different days of the week In these cases you would have a separate column for data from each release point strata month or day Here is an example of data of wind directions from each month Notice that each column can have different numbers of observations
170. th word wrap E3 Notepad oog Watson Williams test all samples gives p 0 0104 so we can accept the alternative hypothesis that the samples do not all have the same mean Pairwise tests give p lt 0 05 for Set1 amp Set5 Set and Set10 Set5 amp Setl4 Set6 amp Set10 amp Set10 amp Set14 7 Comparing these results alongside the basic stats we can see that there appear to be two groups of samples some with means around 172 174 and some with means from 177 181 Test this with multisample tests of the two groups TF Test on just Set5 Set8 and Set10 gives p 0 8329 2 3 2 3 1 You can open and close the window through the Window Show Notepad menu option The text in the window is retained even if you close it so it reappears when you reopen the window note however that it is cleared when a new data file is loaded or created The text is saved to the desktop file so that it can be reinstated later when you reload the desktop The text in the Notepad can be printed through File Print or copied to the clipboard Edit Copy for transfer to another Windows program You can also export the results to a text file using File Export for importing to other programs Oriana Concepts The following section describes some of the basic concepts behind Oriana s data handling Circular Data Oriana is designed to analyze circular data The fact that circular data are measured on a closed c
171. the Stacked and Stepped 851 ones can also be produced from two separate variables where one is circular and the other is a set of associated data Examples would be wind direction and speed or the direction and distance of travel of an animal This graph is formed by dividing up the second variable into frequency classes and using those as the segments of the graph Direction a 0 Zero values 35 11 0 2 74 6 gt 5 8 gt 8 00 In the above graph zero values for the wind speed are left out of 5 8 the graph as is common in meteorological studies where the direction measured during becalmed periods could be misleading This is an option on the Graphs Two Var Histograms 134 dialog box Also on this dialog box is the Subgroup means option which specifies that separate means are displayed for each class of the second variable Circular linear Plot This graph type like the two variable histogram also plots two variables one circular and one linear However in this case the second variable is depicted not as frequencies in segments of the histogram but as individual points Each observation or row in the data matrix is depicted as a point arrow bar or wedge The first type the scatterplot has each observation represented by a point The position around the circular axis represents the circular variable while the position on the concentric grid represents the linear value Here is an example
172. the distribution plots 8 compare a single sample against a theoretical distribution They are produced by first centering the data on their medians so that any differences in the medians do not affect the graphs and then sorting them into ascending order These are then plotted against each other If the two samples have different numbers of observations the number of points plotted is the lower of the two Observations to be plotted from the larger of the samples are chosen to be evenly distributed throughout the range If the two distributions are similar then the points will lie close to the 45 angle reference line In the following graph the points make a distinct departure from the reference line and thus it appears that the two distributions are different This is confirmed by significance levels far below 0 05 for the Mardia Watson Wheeler 73 and the Watson s U2 74 test SELAG ISOETES 6 Menus This section describes the menu structure of Oriana 6 1 File The File menu contains the commands for opening and saving data and desktop files as well as the printer related functions All of the save and print functions act on the currently active window 6 1 1 File New This option allows you to set up a new data file You can specify the initial size of the data file and the types of data 1A When you choose the File New command one of two New Data dialog boxes will be displayed depending on which yo
173. the two samples using Moore s modified Rayleigh test The null hypothesis is that there is no difference between the two samples A probability less than your chosen significance level usually 0 05 indicates that the pairs differ between the samples As with Hotelling s this test is for use with paired sample experimental designs and that it is assumed that each row in the matrix is for an individual case Correlations Oriana provides two different correlation procedures for comparing variables one between two circular variables and one between a circular and a linear one These correlations assume that the data are entered in a pairwise fashion that is each row in the data matrix contains data related to the same observation or sample For example a data set may contain two variables one the direction of travel of an insect and the other the direction to a light source Each row would represent the observation of these two directions at a single point in time These correlations are described briefly in the next sections See the section on the Analyses Correlations 125 command for details on how to run these analyses Circular circular correlation The circular circular correlation coefficient Fisher 1993 p 151 Mardia amp Jupp 2000 p 250 Zar 1999 p 649 calculates the correlation between two circular variables This uses the Fisher amp Lee 1983 method which is analogous to the Pearson product moment correlation
174. ting Each segment will represent that proportion of the total range of the second variable For example if the second variable ranges from 0 to 100 choosing 5 segments means that the first one will represent the number of observations between 0 and 20 the second from 20 40 and so on 3 19 Tutorial Segments Automatic Number of Segments sit 1 Log scale Segment for each unique value Manual 8 Ifyou prefer you can set the boundaries between each segment manually using the Manual option above This lets you enter the exact boundaries for each segment So in the above example of a variable ranging from 0 100 if you enter a 15 in this option as the first boundary and a 30 as the second then all values from 0 15 will be in the first segment all values greater than 15 and up to 30 are in the second segments and so on To build up your list of boundaries tick the Manual option then enter the first boundary into the Boundary box and click the Add button This will add the boundary to the box below Continue doing this for all boundaries If you need to remove a boundary you can select it in the list and click the Remove button If your second variable consists of discrete values e g just the numbers 1 2 3 and 4 and you want a separate segment for each you can use the Segment for each unique value option Circular linear plots The process of producing circular linear plots 87 Vis similar to that described in the
175. tion A probability less than your chosen significance level usually 0 05 indicates that there is a common mean direction to the population It is assumed that the data are not grouped and that they conform to the bivariate normal distribution Note that the test is particularly sensitive to departures due to skewness Moore s Modified Rayleigh Test Zar 1999 p 639 641 isa nonparametric analogue of the Rayleigh test for testing if angles are uniformly distributed around the circle The null hypothesis is that the data are uniformly distributed If the p value is less than the chosen significance level usually 0 05 then the alternative hypothesis that the data are not uniformly distributed is accepted 4 1 2 One Sample Tests BASIC STATISTICS Data file F StatData Oriana Ori2 Test Data wWind2002 ori Hourly wind data garden weather station Jun Dec 2002 Analysis begun 21 October 2005 15 26 34 Variable Direction Data Type Angles Number of Observations 4495 Data Grouped No Group Width amp Number of Groups Rayleigh Test 2 363 8757 Rayleigh Test p lt 1E 12 Rao s Spacing Test U 331 8087 Rao s Spacing Test p lt 0 01 Watson s U Test Uniform U 23 5836 Watson s U Test p lt 0 005 Kuiper s Test Uniform Y 15 7294 Kuiper s Test p lt 0 01 Chi Squared Test Uniform 2 ws Chi Squared Test p me V Test V expected mean 225 00 0 2844 Y Test u 26 9647 Y Test p lt 1E 12 een Bo Hes Hat 3 resa C
176. tor itself If your data are in this format then you can enter them into Oriana as four sets of linear data for the X Y coordinates then convert them to angles and lengths using the Data Convert X Y to circular 14 command 2 3 4 2 3 5 Grouped Circular Data Often circular data can be considered as grouped This should not be confused with grouping data into different subgroups such as arrival times on different days or wind direction in different months Grouped circular data means that the observations have been recorded approximately to the nearest interval rather than exactly For example e Arough approximation might be made as to direction of travel 0 45 90 135 180 etc e The direction might be recorded to the nearest 10 rather than a more exact measure e g 20 rather than 21 25 or time to the closest hour e The data might be collated into a frequency table based on intervals such as 10 observations between 0 and 30 12 between 30 and 60 etc e Many of the Oriana circular data types are inherently grouped Day of Week has seven intervals one for each day Month of Year has 12 intervals and Compass Direction can have four eight or 16 This can simplify data collection but it can also cause problems in data analysis It can introduce a bias into the results or indeed can completely invalidate the statistical procedure Where possible Oriana will attempt to correct fo
177. u used last By default the New File Wizard is displayed This takes you step by step through declaring what type of data you are going to enter and how many columns there are and giving labels to each variable and the whole file At the end after pressing the Finish button the status window will be displayed and an empty spreadsheet will be opened ready for you to enter data You can also switch to Expert Mode by pressing the appropriate button In this mode you simply enter the number of columns you wish to have in your file and press OK Once the data editor is displayed you can then declare the type of each variable with the Data Change Variable Typel10 option or by using the drop down boxes in the first row of each column 6 1 2 File Open This command lets you open an existing data file If another data file is already open it will be closed after asking if you want to save any changes or results When you choose the File Open command the Open File dialog box will be displayed This is similar to the standard file dialogs used in many Windows programs but with some additions Open data file Look in Ori2 Test Data ly gt 2 amp fe pe Syeeta tester data BP FisherB21testCI k B o 179 ori S Deviations ori Bcroupeddatat C My Recent Bass ori Bexamporit Ori BE intensive ori Documents Balizeros ori B FisherB3 ori BE LinearLogScaleT 9 B arrival ori
178. u want to restore it choose the Edit Undo option The data editor is the only window that allows the user to delete data so this option is disabled when any other window is activated 6 2 7 6 2 8 Edit Select All This command will allow you to select all of the text or data in the currently active window in preparation for copying it to the clipboard or deleting it This command is disabled when graph windows are active because the editing commands always work on the whole graph window Edit Insert Row Column When the data editor is active this command can be used to insert new rows or columns into the spreadsheet The exact function of this command varies depending on how the cells in the spreadsheet are currently selected 3 If a single cell is selected the dialog box below will be displayed allowing you to specify what you want inserted You can choose to insert either rows or columns and you can specify whether they should be inserted at the end of the spreadsheet or the current location Insert Rows Columns Insert Where Number to Add 1 If you have selected 32 whole rows or whole columns then the dialog will not be displayed Instead if a whole row is selected Oriana will insert a new row at that point Likewise if a whole column is selected a new column will be inserted there If you want to insert more than one row or column then just select the appropriate number of rows
179. uency data In most cases you will be entering raw data the individual measurements collected in your study However in some cases you may be provided with data that are in the form of a frequency table where the number of measurements of each Tutorial unique data value are recorded e g 25 observations of the angle 45 Data in this format can also be entered directly in Oriana by creating two variables one for your circular data and one of the Linear type that is used for entering the frequencies You can set up such a data file using Files New Using the New File Wizard first choose your data type then on the next page where different data file layouts are described choose the Frequency option Following through the rest of the wizard will result in a file similar to that below where you can enter your data in the left hand column and the frequencies in the right eee Data Editor KJ 4 B a Type Angles _ Linear xl Name Direction Frequency 2 15 000 25 000 3 30 000 35 000 4 45 000 45 000 5 60 000 35 000 6 75 000 25 000 v 90 000 15 000 8 180 000 15 000 9 195 000 25 000 10 210 000 35 000 11 225 000 45 000 12 240 000 35 000 13 255 000 25 000 gt When analyzing and graphing these data you will need to choose the Frequency option rather than the Raw option on the Select page of the analysis or graph dialog box See the end of the tutorial about Calculating Statisticsl 4 for more details Not
180. ular linear correlation 76 You can switch between having the data in the old Oriana 1 format and the new paired format with the Data Change Data Structure 109 command See that section for more details and restrictions Also when opening a file created with the old Oriana version 1 you will be asked if you wish to convert it to the paired format Note with paired data it is most suitable to describe each column in the data editor as a variable However with the original Oriana version 1 method of structuring the data each column is better thought of as a set of observations Throughout the program and this document the term variable is usually used for each column but in data sets using the latter method of structuring the term set of observations can be substituted Frequency Data Often data are collected or provided in the form of a frequency table where the number of times a particular direction was Getting Started observed is recorded as the frequency for example ovedion aa Oriana has two ways of dealing with data like this 1 The first is a special data editing mode called Frequency Editing which allows you to enter and edit data in this fashion To enter data in this method you would first create a new data file 29 as normal then select a cell in the appropriate column of the data editor and choose the Data Edit Frequencies menu command This will open a dialog box with a frequency table like the one above
181. value Fonts Print Frequency table Exclude 0 0 values OK Cancel Help The Exclude 0 0 values option excludes any cases where the second variable is 0 This is useful in meteorological graphs With diagrams depicting wind speed it is customary to not include data when the wind speed is zero the associated direction could be unreliable as the wind vane could be pointing in any direction in becalmed situations Instead the legend box will give the percentage of the zero values in the data set The Segments section allows you to specify the number of frequency classes and thus segments on each bar to be used for the second variable When Automatic is selected you can choose to have Oriana automatically divide each wedge of the rose diagram into a certain number of segments specified by the Number of Segments setting Each segment will represent that proportion of the total range of the second variable For example if the second variable ranges from 0 to 100 choosing 5 segments means that the first one will represent the number of observations between 0 and 20 the second from 20 40 and so on If your second variable is better expressed on a logarithmic scale with many very large values as well as small ones you can tick the Log scale scale option to base the divisions on a log scale e g 0 10 10 100 and 100 1000 If you prefer you can set the boundaries between each segment manually using the Manual option above Thi
182. ves some background about the statistical analyses and graphs The first section entitled Getting Started explains the structure of the program while the second is a tutorial To get the most out of the program you should work through the samples in the tutorial Throughout the text you will encounter symbols like this 35 These symbols are page references They point you towards the section of the manual that gives you more information about the term or concept that you have just read We hope that you find Oriana useful Suggested Citation If you have used Oriana in study that you are publishing the following is a suggested format for the citation Kovach W L 2011 Oriana Circular Statistics for Windows ver 4 Kovach Computing Services Pentraeth Wales U K We are always interested to see how Oriana is being used We would appreciate receiving reprints of any papers you have published in which Oriana was used for data analysis Thank you Address for Correspondence Kovach Computing Services 85 Nant y Felin Pentraeth Anglesey LL75 8UY Wales U K E mail sales kovcomp com Web http www kovcomp com Tel UK 01248 450414 Intl 44 1248 450414 Fax UK 020 8020 0287 Intl 44 20 8020 0287 Note Please see the technical support section of this manual before contacting us for technical support We also maintain a mailing list for notifying customers of new programs and other items of interest
183. way The difference may be in the distribution mean direction or other parameter further investigation will be needed to determine what the difference is between the two samples As with the single sample test the two sample Watson s test cannot be performed on grouped 26 data Hotellings Paired Test Hotelling s Paired Test Zar 1999 p 645 compares two samples of paired data using Hotelling s procedure This tests whether the paired observations differ between the two samples The null hypothesis is that there is no difference between the two samples A probability less than your chosen significance level usually 0 05 indicates that the pairs differ between the samples It is assumed that the data are not grouped and that they conform to the bivariate normal distribution Note that the test is particularly sensitive to departures due to skewness Note that this test is for use with paired sample experimental designs and that it is assumed that each row in the matrix is for an individual case for example each row contains data for an individual organism before and after treatment or in two different situations If one sample has more cases than the other all the extra cases will be treated as missing data and will be ignored Moore s Paired Test Moore s Paired Test Zar 1999 p 647 is a nonparametric alternative to Hotelling s Paired Test This also tests whether 4 3 4 3 1 the paired observations differ between
184. way that you did with the colors Axes Stats lines Style Solid iv Style Solid iv width 1 v width 2 v Grid Style Dot v Outline around bars SS y width 1 r Draw Grid Set Series Pattern HE Solid Plot Series Patterns Series 1 Solid Series 2 Clear Series 3 Horizontal Series 4 Vertical Series 5 Diagonal Right Series 6 Diagonal Left Series 7 Cross Series 8 DiagCross 3 16 3 17 10 This page also lets you customize the lines used in the graph axes and grid Use the drop down box labeled Axes Style to change between solid and dashed or dotted lines for the axes and Axes Width for the width of the solid lines Note that the standard Windows line drawing routines do not allow a width to be specified for the dashed and dotted lines so if you specify a width greater than 1 it will always be drawn as solid 11 Also on this page you can specify if outlines should be drawn around the bars and symbols of the graph Saving the desktop Oriana follows a desktop metaphor 44 in which several windows relating to a single data file can be displayed at once You can save the position and contents of all these windows to a file then reload it later This lets you pick up working where you left off To explicitly save your desktop simply choose the File Save Desktop command You can save several desktops under different names You can then restore any of them usin
185. xisting data Overuriting old data with new Make the cell active click with the mouse or move to that cell with the cursor keys type the new value and press the Enter key Modifying data within a cell Make the cell active and press F2 or double click on the cell with the mouse This will cause the contents of the cell to be selected Clicking again or press the right or left arrow keys will cause a caret vertical line to appear You can move this back and forth with the cursor keys Any new letters or numbers typed will appear at the position of the cursor With labels and the portion of numeric data to the left of the decimal the new characters will be inserted With the fractional part of numeric data the typed digits will replace those at the caret which will be shown as a triangle under the digit Some variable types such as Day of Week have a fixed list of possible data values This list can be seen by clicking on the down arrow button to the right of each cell see below The Tutorial entry for that cell can then be selected from the list You can also just start typing while the cell is active the data editor will automatically insert the data value that matches what you have typed so far ui lueSsuoy ry Cevuoy 0 Wednesday gt March 0 Thursday April 0 Friday y May Cmtiveleans l lona With time and date variables the separators between elements of the data value are automatically included there
186. y of automatically generated data You can generate identical data for all rows or an incrementing series of data You can also fill the variable with random data or data drawn randomly from a von Mises distribution Menus 117 Fill Variable With Data Variable Direction v ol Cancel Start Row 1 2 Number of Rows 100 Help Value 90 Fill Type Date Fill ec Identical Incrementing Random es Von Mises Random Date The Variable option above lets you select the variable to fill and the Start Row and Number of Rows options let you define what part of the column to fill If you have a block of cells selected in the data editor when this command is chosen then these two values will match the selected cells The two boxes below these change labels and function depending on the Fill Type chosen The Fill Types are Identical This fills the variable with identical data Enter the value to place in the variable in the Value box The data will be checked for its validity when you press the OK button and an error message will be displayed if the value is not valid for the data type of the selected variable The program can cope with partial data so entering Mon in a Day of Week variable will fill it with Monday and entering 01 01 in a Date variable will fill it with the date 01 01 2009 if the current year is 2009 Incrementing This fills the variable with incrementi
187. yclical scale means that most of the more common types of statistical analyses are unsuitable Oriana performs analyses designed specifically for circular data Many different types of data are circular in nature Directional or orientation data measured as angles in degrees are the most common type In this case the circular scale ranges from 0 to just less than 360 degrees Directional data can be of two types unidirectional or bidirectional These are also known as vectorial and axial respectively Vectorial data consist of a directed line such as direction of travel or the direction someone is facing Axial data on the other hand consist of an undirected line either end of the line could be taken as the direction For instance a horizontal fracture in a piece of glass could be interpreted as being oriented as either 90 degrees or 270 degrees The way these two types of data are represented on a graph varies so that they can be distinguished When axial data are analyzed they are first converted to vectors by doubling each data value and reducing any greater than 360 using modulo arithmetic The results will be converted back so that they will be in the range of 0 180 degrees 2 3 2 Getting Started There are other types of cyclical or circular data Time of day is another common type with values measured on a closed scale from 00 00 hours to 23 59 hours Other variations on chronological data can also be analyzed as circula
188. year as having 52 weeks some can actually have a 53rd week The dates 27 Dec 2004 to 2 Jan 2005 were week 53 of the year 2004 If the data you enter into a WOY variable range from 1 52 then each week represents 6 9231 and Week 1 is 3 4615 If any week numbers of 53 are included then each week is 6 7924 wide and Week 1 is 3 3962 Lunar This data type is designed for people working with data that might be related to the phases of the moon e g laying of eggs by turtles The data are entered as dates see the entry below for the Date variable type for comments about the format However when circular statistics are calculated or circular graphs produced these dates are converted into angular data by Getting Started calculating the length of the lunar month and the day of the lunar cycle For example a date of 3 April 2011 will be plotted on a circular histogram at the top in the 0 position since that is the date of anew moon and 18 April 2011 a full moon day will be at the 180 position Note that all dates are based on the Gregorian calendar in accordance with ISO standard 8601 60 This is the calendar that was adopted in 1582 by the Vatican and many Catholic countries 1752 by the British Empire 1918 in Russia and numerous other dates in other countries around the world If you are working with dates that were recorded under the Julian calendar before these years they will need to be converted to the Gregorian cal

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