25 The value of the standard error of estimate of the multiple regression equation is entered here.
26 Click Transform, Compute Variable, select CDF & NoncentralCDF under Function Group, select cdfnorm under Functions and Special Variables. Transfer into Numeric Expression Window. Enter name of standardized criterion cut off [Zyk].
27 Assuming a selection ratio of 0,80.
34.2. Click Range, LOWEST through value, enter the value of P80, enter under New Value in the box Value a code value for PERFD that would indicate that applicants in the validation sample were not selected [0] and click Add.
34.3 Click Range, value through HIGHEST, enter a value one measurement unit bigger than P80,
enter under New Value in the box Value a code value for PERFD that would indicate that applicants in the validation sample were selected [1] and click Add.
34.4 Click Continue, click Paste
34.5 Highlight the appropriate syntax and execute/run 35. Click Analyze, Descriptive Statistics, Crosstabs
35.1 Transfer the group membership variable [GROEP] into the Row(s) window and transfer the dichotomized predicted criterion performance variable [PERFD] into the Column(s) window, click Statistics.
35.2 Tick Chi-square, click Continue.
35.3 Click Cells, tick under Percentages Row, Column, Total, click Continue, click Paste 35.4 Highlight the appropriate syntax and execute/run
Steps 31 – 35 calculates the selection ratios for the various levels of the group variable. Adverse impact ratios can be calculated from the row percentages for the various levels of the group variable [a single ratio if the group variable is a dichotomous dummy [i.e., 0,1] variable.
36 Click Analyze, Compare Means, Independent Sample T-Test
36.1 Transfer the composite criterion variable [PERFORM] to the Test Variable(s) window.
36.2 Transfer the group variable [GROEP] to the Grouping Variable(s) window 36.3 Click Define Groups
36.4 Enter the codes for Groups 1 and 2 [0 and 1].
36.5 Click Continue 36.6 Click Paste
36.7 Highlight the appropriate syntax and execute/run
Step 36 compares the mean criterion performance of Groups 1 and 2. If a significant difference exists between the criterion means adverse impact would most likely be unavoidable even if criterion performance would be predicted fairly [in the Cleary sense of the term]. One could repeat step 36 with the unstandardized predicted criterion scores [PRE_4] as the dependent variable in the T-Test analysis. If the actual criterion distributions do not differ significantly in terms of distribution and/or location across groups but the predicted criterion scores do, it would suggest that the criterion inferences derived from the predictor contain systematic group-related error. It would therefore suggest that the selection decision-making based on E[Y|X] constitutes unfair discrimination.
EVALUATION OF THE FAIRNESS OF THE PREDICTION/INFERENCE-RULE,
CALCULATION OF THE ADVERSE IMPACT
RATIO FOR THE REVISED PREDICTION
RULE CALCULATION OF E[Y|X; D] AND
P[Y<Y k |X; D] [assuming a battery of predictors]
37. Open SPSS
38. Click: File, Open, Data TELKOM.SAV
39. Click Graphs, Legacy Dialogs, Scatter/Dot, Simple Scatter, Define.
39.1 Transfer the composite criterion [PERFORM] to the Y-Axis window and the unstandardized predicted values obtained from the multiple regression model [PRE_4] to the X-axis window.
39.2 Transfer the group variable [GROEP] to the Set markers by window 39.3 Click Paste
39.4 Highlight the appropriate syntax and execute/run 40. Double click on scatter plot in output file
40.1. Click Elements, click Fit Line at Sub-groups, Click Close 40.2 Close Chart Editor
41. Click Graphs, Legacy Dialogs, Scatter/Dot, Simple Scatter, Define.
41.1 Transfer the standardized residuals obtained from the multiple regression model [ZRESID_2] to the Y-Axis window and the unstandardized predicted values obtained from the multiple regression model [PRE_4] to the X-axis window.
41.2 Transfer the group variable [GROEP] to the Set markers by window 41.3 Click Paste
41.4 Highlight the appropriate syntax and execute/run 42. Double click on scatter plot in output file
42.1. Click Options, click Y-axis Reference Line, type in Y-axis reference line position as 0, click Apply, click Close
42.2 Close Chart Editor
43. Click Analyze, Compare Means, Independent Sample T-Test
43.1 Transfer the standardized residual variable obtained from the multiple regression model [ZRESID_2] to the Test Variable(s) window.
43.2 Transfer the group variable [GROEP] to the Grouping Variable(s) window 43.3 Click Define Groups
43.4 Enter the codes for Groups 1 and 2 [0 and 1].
43.5 Click Continue 43.6 Click Paste
43.7 Highlight the appropriate syntax and execute/run OR
43. Click Analyze, Compare Means, Oneway ANOVA
43.1 Transfer the standardized residual variable obtained from the multiple regression model [ZRESID_2] to the Dependent List window
43.2 Transfer the group variable [GROEP] to the Factor window 43.3 Click Options, tick Descriptive and click Continue
43.4 Click Paste
43.5 Highlight the appropriate syntax and execute/run
44. Click Data, click Split File, tick Compare Groups, transfer the group variable [GROEP] into the Groups based on window.
44.1 Click Paste
44.2 Highlight the appropriate syntax and execute/run 45. Click Analyze, Regression, Linear
50.1 Transfer PERFORM into the Dependent variable window
50.2 Transfer the unstandardized predicted values obtained from the multiple regression model [PRE_4] into the Independent[s] variable window
50.3 Click Continue and Paste
50.4 Highlight the appropriate syntax and execute/run
46. Click Data, click Split File, transfer the group variable [GROEP] back into the variable list and tick Analyze all cases, do not create groups.
46.1 Click Paste
46.2 Highlight the appropriate syntax and execute/run
Test the assumption of equal error variances across groups 1 and 2 by testing the following null hypothesis:
H01: ²[Y|X; 1] = ²[Y|X; 2]
Ha1: ²[Y|X; 1] ²[Y|X; 2]
H01 is tested by calculating the following test statistic [assuming S²[Y|X; 1] > S²[Y|X; 2]]:
F = S²[Y|X; 1]/S²[Y|X; 2]
F F[n1-2; n2-2]
47. Click Transform, click Compute.
48. Enter name of the variable that would represent the group*predictor interaction effect [INTT] the Target Variable window and enter the expression GROEP*PRE_4 in the Numerical Expression window.
49. Click Paste, click OK
50. Highlight the appropriate syntax and execute/run 51. Click Analyze, General Linear Model, Univariate
51.1 Transfer PERFORM into the Dependent variable window
51.2 Transfer PRE-4, GROEP and INT into the Covariate(s) variable window 51.3 Click Paste
52. Click Analyze, General Linear Model, Univariate
52.1 Transfer PERFORM into the Dependent variable window
52.2 Transfer PRE_4 and GROEP into the Covariate(s) variable window
52.3 Click Paste
53. Click Analyze, General Linear Model, Univariate
53.1 Transfer PERFORM into the Dependent variable window 53.2 Transfer PRE_4 and INT into the Covariate(s) variable window 53.3 Click Paste
54. Click Analyze, General Linear Model, Univariate
54.1 Transfer PERFORM into the Dependent variable window 54.2 Transfer PRE_4 into the Covariate(s) variable window 54.3 Click Paste
55. Highlight the syntax for all three GLM analyses and execute/run
Test the following null hypotheses by using the GLM output:
H02: 2 = 3 = 0| 1 0 Ha2: 2 3 0| 1 0 if H02 is rejected the following null hypothesis is tested:
H03: 3 = 0| 1 0; 2 0 Ha3: 3 0| 1 0; 2 0 If H03 is not rejected the following null hypothesis could be tested:
H04: 2 = 0| 1 0; 3 = 0 Ha4: 2 0| 1 0; 3 = 0 If H03 is rejected the following null hypothesis is tested
H05: 2 = 0| 1 0; 3 0 Ha5: 2 0| 1 0; 3 0
56. Click Analyze, Regression, Linear
56.1 Transfer PERFORM into the Dependent variable window
56.2 Transfer PRE_4 and GROEP and/or INT [depending on the outcome of the fairness analysis] into the Independent[s] variable window
56.3 Click Statistics, tick Casewise diagnostics, click Continue
56.4 Click Plots, tick Normal Probability plot, transfer ZPRED into X window and ZRESID into Y window, Click Continue
56.5 Click Save, tick Unstandardized Predicted Values, tick Standardized Residuals, tick under Distances Mahalanobis, Cooks, Leverage values, under Influence Statistics Standardized DfBeta(s), Standarized DfFit under Predicted Values Unstandardized, click Continue
56.6 Click Paste
56.7 Highlight the appropriate syntax and execute/run 57. Click Analyze, Regression, Linear
57.1 Transfer PERFORM into the Dependent variable window
57.2 Transfer the original predictors included in the selection battery/multiple regression model [SATIK, PAB, BMV] and GROEP and/or INT into the Independent[s] variable window INT [depending on the outcome of the fairness analysis]
57.3 Click Statistics, tick Casewise diagnostics, click Continue
57.4 Click Plots, tick Normal Probability plot, transfer ZPRED into X window and ZRESID into Y window, Click Continue
57.5 Click Save, tick Unstandardized Predicted Values, tick Standardized Residuals, tick under Distances Mahalanobis, Cooks, Leverage values, under Influence Statistics Standardized DfBeta(s), Standarized DfFit under Predicted Values Unstandardized, click Continue
57.6 Click Paste
57.7 Highlight the appropriate syntax and execute/run 58. Click Graphs, Legacy Dialogs, Scatter/Dot, Simple Scatter, Define28.
58.1 Transfer the standardized residuals obtained from the fair regression model [ZRESID_3] to the Y-Axis window and the unstandardized predicted variable obtained fro the fair regression model [PRE_5] to the X-axis window.
58.2 Transfer the group variable [GROEP] to the Set markers by window 58.3 Click Paste
58.4 Highlight the appropriate syntax and execute/run 59. Double click on scatter plot in output file
59.1. Click Options, click Y-axis Reference Line, type in Y-axis reference line position as 0, click Apply, click Close
59.2 Close Chart Editor
60. Click Analyze, Compare Means, Independent Sample T-Test
60.1 Transfer the standardized residual variable [ZRESID_3] to the Test Variable(s) window.
60.2 Transfer the group variable [GROEP] to the Grouping Variable(s) window 60.3 Click Define Groups
60.4 Enter the codes for Groups 1 and 2 [0 and 1].
60.5 Click Continue 60.6 Click Paste
60.7 Highlight the appropriate syntax and execute/run
Steps 37 - 60 examines the fairness of the criterion inferences derived from the actuarial multiple regression prediction model derived via steps 9 – 11. It therefore also examines the fairness of the use of the criterion referenced inferences derived via steps 12 – 35. It therefore examines whether the use of the actuarial prediction rule or the use of the criterion referenced norm table would constitute unfair discrimination.
Depending on the nature of the findings it modifies the original prediction rule by returning an actuarial
28 The standardized residuals and unstandardized predicted values from either one of the immediately preceding