Z-Test of the Ratio of Selection Rates
The z-test of the ratio of selection rates (or ZIR), 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, SRmin is the minority selection rate, SRmaj is the majority selection rate, SRT 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 ZIR test has a few advantages over the ZD test (and over the chi-square test since the ZD and chi-square tests are mathematically equivalent when analyzing 2 X 2 contingency tables). One advantage is that the ZIR test uses the same effect size comparison as the four-fifths rule (i.e., a selection rate ratio) whereas ZD compares the difference in selection rates. Given that the four-fifths rule (or impact ratio) compares the ratio of selection rates and the ZD compares the difference in selection rates, comparing the results is somewhat like comparing apples and oranges. In contrast, comparing the ZIR test to the impact ratio is a more equivalent comparison. Another advantage of the ZIR test is that it is slightly more powerful than the ZD or chi-square tests, especially as the proportion of minorities is smaller.
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