CAIQS User's Guide
Contents
1. txt to the file name that you specify Thus with Wordpad if you specify the name of the input file as MINPUT the file will in fact be saved as and this is the name that you have to use in the command to run the present programs Here is a sample input file for the caiqs program 4 2 1 1 1 3 4 000 6 000 2 000 1 000 0 170 0 000 0 100 0 290 0 160 0 170 1 000 0 120 0 160 0 300 0 260 0 000 0 120 1 000 0 470 0 120 0 200 0 100 0 160 0 470 1 000 0 240 0 250 0 290 0 300 0 120 0 240 1 000 0 170 0 160 0 260 0 200 0 250 0 170 1 000 1 000 0 090 0 090 0 200 0 450 0 000 0 075 0 250 0 320 6 Running the Program Suppose you copied the executable source of the program to the d publik directory on your machine In that case the input file must also be saved in the d publik CAIQS program v 1 28 02 03 5 directory Next to run the program you have to open an MS DOS Command window The way to do this varies from one operating system i e Windows 95 98 NT to the other and you should use your local HELP button when in doubt about this feature In the MS DOS Command window you type d followed by RETURN or ENTER and your computer will return the D gt command prompt Next you type cd publik after the D gt command prompt again followed by RETURN or ENTER and your computer will respond with the D publik gt command prompt Now you can execute the program by typing caiqs lt mi2. For example suppose that the difference between the average score on predictor 2 of the majority and the minority population expressed relative to the common standard deviation of the predictor in both populations is 0 450 then the second element of DIFP DIFP 2 is set equal to 0 450 CAIQS program v 1 28 02 03 4 7 Optional only required when NC 0 DIFC I with ranging from 1 to NC 10f7 3 The element DIFC I specifies the effect size of the Ith predictor As the program presumes that the average score of the predictors is zero in the majority applicant population the elements of the vector DIFC also have typically a negative value 8 Optional only required when NRSR 4 0 RSR I with ranging from 1 to NRSR 10f7 3 The elements of RSR specify the selection ratios for which the user wants the cal culation of the adverse impact and the average quality in addition to the selection ratios that are analyzed by default 5 Sample Input File Important in preparing the input file use a simple text editor such as Notepad Wordpad or any other standard ASCII producing editor DO NOT USE TEXT PRO CESSING PROGRAMS SUCH AS MS WORD or WORDPERFECT Also when saving the input file in Notepad use the option All Files in the Save as type box When saving in Wordpad use the Text Document MS DOS Format option in the Save as type box and be aware that Wordpad has the nasty habit of adding the exten sion
3. group respectively assuming that both applicant groups have the same composite criterion predictor variance 1 see below and given that the total applicant group consists of a proportion pa of majority group candidates and a proportion p of minority group applicants the average score on the composite criterion predictor of the majority and TOE 59 the minority group selected is according to the first metric expressed as and s _ a respectively In the above expressions Pihi and 1 papid where d denotes the effect size of the composite criterion predictor In the second metric only the values and ue are reported In addition to these average scores s _ 5 s Ha and ue the corresponding differences are presented as well These differences represent the effect size expressed in the metric of and a respectively of the criterion predictor composite in the selected subgroup and these measures can therefore be used to gauge the effect of prior selection on the subgroup differences found in the selected group cf the paper by Roth et al 2001 The option to consider selections where the selection ratio refers to a given proportion of the majority applicant group was added to provide results that cover those computed by Bartram 1995 Also in that case only the second metric is used to report the average qualities of the majorit
4. v 1 SR SRA SM SMA 0 010 0 012 1 326 1 331 0 050 0 059 1 030 1 037 0 100 0 117 0 879 0 888 0 150 0 173 0 779 0 791 0 200 0 229 0 703 0 715 0 250 0 284 0 639 0 653 0 300 0 339 0 583 0 599 0 350 0 393 0 533 0 551 0 400 0 446 0 487 0 506 0 450 0 498 0 444 0 465 0 500 0 549 0 403 0 426 0 550 0 600 0 364 0 389 0 600 0 650 0 326 0 354 0 650 0 699 0 289 0 319 0 700 0 748 0 252 0 286 0 750 0 795 0 215 0 252 0 800 0 840 0 178 0 219 0 850 0 885 28 02 03 SRI AI SMI SDIF 002 0 156 1 1 212 0 119 014 0 232 0 0 907 0 131 033 0 285 0 149 0 139 057 0 327 0 645 0 146 083 0 363 0 563 0 152 113 0 396 0 495 0 159 145 0 428 0 0 434 0 165 180 0 459 0 379 0 171 218 0 489 0 328 0 178 259 0 519 0 280 0 185 302 0 550 0 234 0 193 349 0 581 0 188 0 201 399 0 613 0 144 0 210 452 0 647 0 100 0 220 510 0 682 0 055 0 231 571 0 719 0 009 0 243 638 0 759 0 039 0 258 711 0 804 262 962 809 708 631 566 510 459 412 368 327 287 249 211 174 137 099 060 MA 267 969 818 720 644 581 526 477 492 390 351 318 277 242 208 174 141 107 MI 147 837 678 572 489 420 359 303 251 202 155 110 065 020 02
5. 6 072 121 173 DIF 120 132 141 148 154 161 167 174 181 188 195 204 213 223 234 247 262 280 CAIQS program v 1 28 02 03 8 0 140 0 186 0 090 0 276 0 900 0 927 0 792 0 854 0 019 0 073 0 230 0 303 0 099 0 152 0 147 0 299 0 950 0 967 0 883 0 914 0 025 0 037 0 299 0 336 0 056 0 117 0 214 0 332 1 000 1 000 1 000 1 000 0 081 0 000 0 407 0 407 0 000 0 080 0 321 0 401 Details for minimum possible overall SR without AI 0 846 0 881 0 705 0 800 0 063 0 110 0 168 0 278 0 145 0 188 0 086 0 274 Details for requested overall selection ratios 0 075 0 088 0 023 0 261 0 875 0 883 0 746 0 137 0 944 0 952 0 817 0 135 0 250 0 284 0 113 0 396 0 566 0 581 0 420 0 161 0 659 0 653 0 495 0 159 0 320 0 360 0 159 0 440 0 489 0 506 0 336 0 170 0 563 0 579 0 412 0 168 8 Description of Output The output is largely self explanatory Suffice it to restate that the average qualities labeled as SM SMA SMI and the difference SDIF refer to the solution values that cor respond to the earlier discussed metric of global standardization whereas the quantities M MA MI and DIF represent the average scores and the difference as obtained for the standardization with respect to the majority applicant group 9 Dependencies and Acknowledgment The present program is written in Fortran77 It was compiled to an executable code for WIN32 PCs ie Windows 95 98 ME or NT 2000 with th
6. CAIQS program v 1 28 02 03 1 CAIQS User s Guide The program computes the adverse impact and the average quality of a single 1 Description stage large sample selection using a weighted predictor combination for either a given set of overall selection ratios or a given set of majority group related selection ratios By default the calculation of the adverse impact and the average quality is performed for the following selection ratios 01 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 and 1 00 For each selection ratio the average quality corresponds to the average score of the selected applicants on either the predictor composite or a weighted combination of criterion dimensions The average quality is computed for a all the selected applicants b the selected applicants from the majority group and c the selected applicants from the minority group When the computations refer to the selection of a given overall selection ratio then the results are reported using two different metrics a results standardized with respect to the distribution metric of the total applicant population and b results standardized with respect to the distribution metric of the majority group population More specifically using 0 and p for the average composite criterion or predictor score in the majority group and the average composite criterion or predictor score in the minority
7. al to 1 NCR when NCR is set equal to 1 then the computed average qualities pertain to the criterion composite whereas for NCR equal to 0 the average qualities refer to the predictor composite NRSR the number of additional selection ratios for which the user requests the computation of adverse impact and average quality e 2 Optional only required when NVERH 1 VERH 7 3 VERH indicates the ratio between the size of the majority applicant group and that of the minority applicant group 3 Optional only required when NREG 0 WEP I with 1 NP 10f7 3 The element WEP I indicates the weight with which the Ith predictor is used in the predictor composite 4 Optional only required when NC 4 0 WEC I with 1 NC 10f7 3 The element WEC I indicates the weight with which the Ith criterion dimension is used in the criterion composite 5 and following CORIN I J with both and J ranging from 1 to NP NC 77 3 CORIN specifies the full correlation matrix between the predictors first NP rows and columns of the matrix and the criterion dimensions final NC rows and columns of the matrix 6 DIFP I with ranging from 1 to NP 10f7 3 The element DIFP I specifies the effect size of the Ith predictor As the program presumes that the average score of the predictors is zero in the majority applicant population the elements of the vector DIFP have typically a negative value
8. and the criterion dimensions is standard multivariate normal in the majority applicant population The method is appropriate for large sample selections The results are exact when the number of applicants both in the majority and the minority applicant group tends to infinity For small er samples of applicants the average quality results are only approximate and typically overestimate the real expected values 3 Technical Aspects At present the program is limited to situations where the total number of predic tors and criterion dimensions is not greater than 10 The limitation is easily removed however To safely run the compiled program a PC running under MS Windows 95 98 NT or 2000 and with at least 64 MB RAM memory is required 4 Input 1 NP NC NVERH NREG NCR NRSR 613 with NP the number of predictors NC the number of criterion dimensions NVERH when NVERH is set equal to 1 the calculations are performed for overall selection ratios whereas for NVERH 0 the calculations pertain to selection ratios for the majority applicant group CAIQS program v 1 28 02 03 3 NREG when NREG is equal to 0 the weights with which the predictors are combined to the predictor composite is specified by the user When NREG 1 the program computes the regression based weights for the predictors with respect to the criterion composite Observe that the latter option is only feasible when NC is at least equ
9. e GNU Fortran G77 com piler cf http www geocities com Athens Olympus 5564 The program uses routines from the SLATEC program library cf Fong et a 1993 http www geocities com Athens Olympus 5564 and a couple of algorithms from StatLib http lib stat cmu edu apstat When the user reports results obtained by the present program due ref erence should be made to De Corte 2003 and De Corte amp Lievens 2003 11 References De Corte W 2003 Caiqs User s Guide http allserv rug ac be wdecorte software html CAIQS program v 1 28 02 03 9 De Corte W amp Lievens F 2003 A practical procedure to estimate the quality and the adverse impact of single stage selection decisions International Journal of Selection and Assessment 11 89 97 Bartram D 1995 Predicting adverse impact in selection testing nternational Journal of Selection and Assessment 3 52 61 Fong K W Jefferson T H Suyehiro amp Walton L 1993 Guide to the SLATEC common mathematical library http www netlib org slatec Roth P L Bobko P Switzer F 5 1 amp Dean M A 2001 Prior selection causes biased estimates of standardized ethnic group differences simulation and analysis Personnel Psychology 54 591 617
10. inority and the majority group of the criteria 0 450 0 000 Correlation matrix of the predictors first 4 rows and columns and the criteria final 2 rows and columns Row 1 1 000 0 170 0 000 0 100 0 290 0 160 Row 2 0 170 1 000 0 120 0 160 0 300 0 260 Row 3 0 000 0 120 1 000 0 470 0 120 0 200 Row 4 0 100 0 160 0 470 1 000 0 240 0 250 Row 5 0 290 0 300 0 120 0 240 1 000 0 170 Row 6 0 160 0 260 0 200 0 250 0 170 1 000 Correlation between weighted predictor and weighted criterion combinations 0 487 Squared correlation 0 237 Effect size predictor composite 0 643 Effect size criterion composite 0 407 Minimum overall selection ratio without AI 4 5th rule is 0 846 with selection ratio majority and minority group equal to 0 881 0 705 respectively For each overall selection ratio SR the majority group SR SRA the minority group SR SRI the adverse impact AI the overall average quality of the selected individuals with respect to the majority group distribution wrtmgd M the average quality of the majority group selected wrtmgd MA and the minority group selected again wrtmgd MI and the difference between MA and MI On the second line the globally standardized gs overall average quality of the selected individuals SM the gs average quality of the majority selected individuals SMA the gs average quality of the minority selected SMI and the difference between SMA and SMI SDIF CAIQS program
11. nput gt moutput where minput is the name of the input file and moutput is the name of the output file At the end of the execution the PC will return the command prompt D publik gt You can then inspect the output by editing the output file with either Notepad Wordpad or any other simple editor program 7 Sample Output Computing adverse impact and average quality of the selected subjects with respect to either a criterion or a predictor composite of a selection using a weighted predictor combination for a given overall or majority group related selection ratio Program written by Anonymous The program uses routines from the Slatec library see http www geocities com Athens Olympus 5564 and a couple of algorithms from StatLib see http lib stat cmu edu apstat Problem specification Number of predictors 4 Number of criteria 2 Computation for overall selection ratio Yes Use regression based weights Yes Expected scores on composite criterion Yes Ratio number of majority vs number of minority applicants 4 000 Predictor weights from predictor one to the last 0 244 0 270 0 039 0 206 Regression based weights Criterion weights from criterion one to the last CAIQS program v 1 28 02 03 6 6 000 2 000 Effect sizes i e standardized difference between the minority and the majority group of the predictors 1 000 0 090 0 090 0 200 Effect sizes i e standardized difference between the m
12. y and the minority selected candidates as well as the difference between the two quantities Apart from performing the calculations for the given set of selection ratios the CAIQS program v 1 28 02 03 2 program also determines the minimum value of the overall or majority group related selection ratio for which the adverse impact ratio of the selection is no less than 800 cf the so called four fifths rule and reports the average qualities total majority and minority group selected and the above documented effect sizes In addition the user can complete the calculations for a limited number of still other overall or majority group related selection ratios Finally when the program is used to focus on a criterion composite the user can a pre specify the weights with which the predictors are combined to the predictor composite or b let the program compute the regression based weights of the predictors with respect to criterion composite Obviously when the user focuses on the predictor composite then only option a is available 2 Assumptional Basis The calculations are based on the assumption that the predictor and eventually the criterion dimensions have a joint multivariate normal distribution with the same vari ance covariance matrix but a different mean vector in the two applicant populations Given this assumption it is without further restrictions understood that the joint dis tribution of the predictors
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