Z-Test of the Ratio of Selection Rates

The z-test of the ratio of selection rates (or Z_IR), is a statistical test that assesses the ratio of two proportions or selection rates (e.g., the ratio of the selection rate for males to the selection rate for females).  The equation is shown below:

where ln is the natural log, 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 Pmin 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.

Morris and Lobsenz (2000) indicate that the Z_IR test has a few advantages over the Z_D test (and over the chi-square test since the Z_D and chi-square tests are mathematically equivalent when analyzing 2 X 2 contingency tables).  One advantage is that the Z_IR test uses the same effect size comparison as the four-fifths rule (i.e., a selection rate ratio) whereas Z_D compares the difference in selection rates.  Given that the four-fifths rule (or impact ratio) compares the ratio of selection rates and the Z_D compares the difference in selection rates, comparing the results is somewhat like comparing apples and oranges.  In contrast, comparing the Z_IR test to the impact ratio is a more equivalent comparison.  Another advantage of the Z_IR test is that it is slightly more powerful than the Z_D or chi-square tests, especially as the proportion of minorities is smaller.

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