adverse impact analyses, disparate impact, mantel-haenszel, chi-square, fisher exact, Breslow-day, OFCCP analyses

ai toolkit online > selection rate comparison

Adverse Impact Toolkit Online - Selection Rate Comparison

This part of the Program is designed to compare the passing rates of each gender and ethnic group on a single practice, procedure, or test. It may also be used to compare group passing rates on an overall selection or promotion process, although an event-by-event analysis should be the primary comparison in most circumstances [the 1991 Civil Rights Act requires that a “particular employment practice” needs to be identified as the source of adverse impact for a plaintiff to establish a disparate impact case, unless the results are not capable for separation for analysis—see Section 2000e-2(k)(1)(A)(i)]. This type of analysis can be regarded as the “most typical” type of adverse impact analysis, and is specifically explained in the Uniform Guidelines as a “rates comparison” (see Section 4D) that compares the passing rates between two groups (e.g., men and women) on a practice, procedure, or test. This Program can also be used to analyze the outcome of layoffs, demotions, or other similar personnel transactions where there are only two possible outcomes (e.g., promoted / not promoted; hired / not hired, etc.).
Totals (for Reference Only)
Men Women White Black Hispanic Asian Native Amer. Total Min. Gender
# % # % # % # % # % # % # % # %
80% Test (1) Red = 80% Rule Violation
Stat. Test-EXACT (2) Red = Statistical Significance
Stat. Test-Estimated(2) Red = Statistical Significance

Interpretation of EXACT Statistical Test (3)
Likelihood (One Chance In):
Probability as Std. Deviations::

Interpretation of ESTIMATED Statistical Test (3)
Likelihood (One Chance In):
Probability as Std. Deviations:


(1) 80% Test: This test compares the passing rate percentage of women (to men) and each ethnic group (to whites). It is referred to as a "rule of thumb" type of analysis in the Uniform Guidelines. Adverse impact can exist with or without a violation of the 80% Test. Because the 80% Test is easily influenced by small numbers (when data sets are small) and it does not consider the probability distribution related to the data set, a greater consideration should be given to the Statistical Tests.

(2) Stat. Test: There are two Statistical Tests in this sheet. For both versions, values less than .05 (in red) are "statistically significant"; values between .05 and .10 (in orange) are "close" to significance. The "Exact" Test uses the (two-tail) Fisher Exact procedure to assess whether the difference in selection rates between two groups (e.g., men vs. women) is extreme enough to be considered "beyond chance." The "Calculate Exact Test" button must be clicked for the Exact Test to calculate. The Lancaster (1961, Significance tests in discrete distributions. J. Amer. Statist. Assoc. 56 223-234) correction has been included as a sensible compromise that mitigates the effects of conservatism of exact methods while continuing to use the exact probabilities from the small-sample distribution being analyzed. The "Estimated" Stat. Test uses the (two-tail) Hypergeometric Variance Estimator formula to estimate the Exact Test, and should only be used for mid- to large-sample sizes (at least >30).

(3) Interpretation of Statistical Test: These outputs describe the degree of the Statistical Test findings. For example, if the output shows the likelihood of the statistical test value is "1 in 20," this means that the difference in passing rates between groups (e.g., men vs. women) is so extreme that the odds of it occurring by chance is only 1 in 20, or about 5%. In other words, this result indicates that chance can be "ruled out" as this reason for this difference. The "Probability as Std. Deviations" describes the probability value (from the Statistical Test) in terms of standard deviations units, which are sometimes easier to interpret than small probability values. A standard deviation of 1.96 corresponds with a probability value of .05, and a likelihood of 1 chance in 20.