Chi-Square

The chi-square test is a statistical test that is often used for analyzing adverse impact. The chi-square test is a statistical test of the association between two qualitative variables.  A qualitative variable varies in kind (e.g., race, sex, decision outcome) as opposed to quantity (e.g., test score).  Chi-square compares the fit between observed frequencies and expected frequencies.  Observed frequencies are the obtained sample results.  Expected frequencies are what would be expected if there was no relationship between the two variables. The tables below show observed frequencies for a hypothetical sample and the resulting expected frequencies for this sample.

The expected frequency for males that pass is equal to the total percent that pass (including both male and female groups) multiplied by the total number of males (i.e., .2 X 65 = 13).  If there was no relationship between sex and outcome, 7 females would be expected to pass.  In actuality, 5 females pass.  This would suggest that there is a relationship between sex and outcome; males have a more favorable outcome and females have a less favorable outcome than what would be expected were there no relationship. 

If you enter the sample results (i.e., observed or actual frequencies) into Adverse Impact Analysis you will see that the expected frequencies are automatically computed and displayed to the right of the sample frequencies. 

The statistical test results are also automatically computed and shown in the bottom right portion of Adverse Impact Analysis.  The results show that that the p-value associated with this sample is 0.29, which is not less than the 0.05 alpha level; therefore, the results are not statistically significant.  If you based your decision solely on the chi-square test, you would conclude that there is no adverse impact in this sample.

When analyzing a 2 X 2 contingency table, the chi-square test is mathematically equivalent to the pooled two-sample z-score 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.  However, the chi-square test could be used to analyze larger contingency tables; for example, it could be used to analyze a 4 X 2 contingency table assessing the relationship between race (with four levels: Black, White, Hispanic, Asian) and outcome (promoted vs. not promoted).

Use Adverse Impact Analysis to estimate adverse impact using chi-square now.