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The z-test of the ratio of selection rates (or Z
where SR is the majority
selection rate, _{maj}SR is the total selection rate, _{T}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
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 |