Pooled Two-Sample Z-Score Test

The pooled two-sample z-score test is the statistical test recommended by the Office of Federal Contract Compliance Programs (see p. 383).  It is also referred to as the Z-test of the difference in selection rates (or Z_D) or the two standard deviation test (or 2-SD).  The Z_D test is a statistical test that assesses the difference between two proportions or selection rates (e.g., the difference between the selection rate for males and the selection rate for females.  The equation is shown below:

where SR_min is the minority selection rate, SR_maj is the majority selection rate, SR_T is the total selection rate, N is the total number of applicants, and P_min is the proportion of minorities (Morris, 2001).  If the absolute value of the resulting z-value is greater than 1.96 (i.e., if Z < -1.96 or Z > 1.96), then the z-test is significant at an alpha level of .05.

When analyzing a 2 X 2 contingency table, the pooled two-sample z-score test is mathematically equivalent to the chi-square test (Moore & McCabe, 1993).  A 2 X 2 contingency table is an analysis of two qualitative variables, each of which has two levels.  For example, the two variables may be sex (with two levels: male vs. female) and outcome (with two levels: hired vs. not hired). Analyses of adverse impact typically analyze 2 X 2 contingency tables. 

Use Adverse Impact Analysis to estimate adverse impact using the Z_D test now.