On page 48 of the July 2013 Federal Contract Compliance Manual (FCCM) the OFCCP describes its methodology for calculating the impact ratio and how the compliance officers (CO) are supposed to use the results of the impact ratio analyses:
Even though the OFCCP in the above description suggests that the adverse results from an impact ratio analysis by itself should be interpreted as a definite proof of the discrimination, the OFCCP instructs the compliance officers to use the results of the impact ratio analysis in deciding whether or not to audit a contractor. Therefore, it is important to review the foundation and the origins of the impact ratio analysis and discuss the conditions under which the impact ratio test may produce false positives, i.e., the situation in which the result from an impact ratio analysis triggers the compliance officer to conduct an audit when there was no need for one.
The statistical term for impact ratio is relative risk (RR).^{i} Relative risk is the ratio of the probability or chance of an event occurring for one group versus the probability or chance of the same event occurring for another, otherwise similar, group. If the chance of the event occurring for the first group is lower than the chance of the event occurring for the second group, then the ratio of the two probabilities (probability of first group on the top and probability of second group in the bottom) will be less than 100%. For example, if the ratio of two probabilities was 70% this means that the probability of event for the first group was 70% of the probability of the event for the second group.
Suppose in a hiring event a contractor reviews 200 applications from a group of applicants who are very similar to each other in terms of their work history and other qualifications. Suppose further that there are 100 men and 100 women among the applicants. All applicants are applying to get into a single specific job, i.e., there is no variation among the applicants with respect to their preferences for different jobs, which means any of the applicants, if offered the job, will accept the offer. The contractor eventually hires 40 candidates among the 200 candidates; 10 of the hires go to women, and 30 of the hires go to men.
Given the above scenario the chance or the probability of hire for women is 10% (10/100 = 10%) and for men is 30% (30/100 = 30%). Therefore, the relative risk or the impact ratio for this hiring event is 33% (10%/30% = 33%). This means the women’s chance of securing this job with this contractor is 33% of the men’s chance of securing the same job. In this specific situation using the result of the impact ratio analysis the OFCCP is justified in conducting an additional investigation to find out why the female candidates’ selection rate or probability of hire is so much lower than the selection rate or the probability of hire for men.
The above example actually describes the same example that the OFCCP has used on page 49 of its July 2013 Federal Contract Compliance Manual. The FCCM describes the calculation of the impact ratio for the above example and, after calculating the impact ratio of 33% for women, concludes:
AN ALTERNATIVE METHODOLOGY: Adjusted Impact Ratio Analysis (AIRA)
The OFCCP’s method for “identifying the personnel activity that should be investigated further on site,” described in the above paragraphs, assumes that all 100 women and all 100 men applied to a single job or jobs that were substantially similar. What if the applicants had applied to a job group within which there were two or more different jobs (or departments) that were substantially different from each other in terms of both the work environment and also the nature of the tasks?
Let’s assume that within a given job group women and men applied to two different departments, department A and department B. Let’s further assume that women favored the job in department B and men favored the job in department A. Out of 100 women, 4 applied to department A and 96 applied to department B. Out of 100 men, 56 applied to department A and 44 applied to department B. Out of a total of 40 hires into this job group, 28 applicants were hired into department A and 12 applicants were hired into department B. In department A, out of 28 hires, 2 were women and 26 were men. Similarly, in department B, out of 12 hires, 8 were women and 4 were men.
Therefore, based on the percentages of the applicants who applied to two departments, it appears that men had a slight preference to go to department A, and women had a strong preference to go to department B. Given this additional information on the flow of the applications to different departments and also the preferences of men and women for different jobs and departments and the number of hires for each department, should the procedure outlined in the OFCCP methodology be modified in any way? The answer is: YES.
In the Federal Contract Compliance Manual’s procedure for calculating Impact Ratio, the OFCCP’s implicit assumption is that all 100 women and 100 men had equal chance of being selected for the 40 available opportunities. However, given the above additional information it appears that the chance of being selected to department A was higher than the chance of being selected to department B. Department A had offered 28 opportunities for the selection, whereas department B had offered only 12 opportunities for selection. This means the applicants’ decisions regarding which department they want to apply directly to affect their chances of being selected. Therefore, in calculating the impact ratio of the employers’ selection decisions, the applicants’ decisions to apply to a certain department were important and should have been taken into account.
Now that we know department was an important factor in the selection process, we need to incorporate the department-related information in our calculation of the relative risk or impact ratio analysis. Therefore, in the steps outlined below I have used the OFCCP’s instructions to calculate the crude or unadjusted impact ratio and modified it to take into account the different rates of men and women applying to each department. It turns out that there is a well known statistical procedure which can be used to adjust the crude impact ratio or relative risk for the fact that not all applicants were applying to the same department/job.^{ii} The resulting adjusted impact ratio takes into account the information regarding the departments. In the procedure outlined below IR represents the OFCCP’s crude and unadjusted impact ratio and AIR represents the Adjusted Impact Ratio after the department-related information is incorporated in the calculation.
OFCCP’s instruction on page 49 of the FCCM modified to incorporate the department information:
Step 1: Calculate the rate of selection for each group in each department (round off to two decimal places).
Step 2: Observe which group has the highest selection rate.
Men are the most favored group because they have the highest selection rate
(30% men is a higher rate than 10% women).
Step 3: Calculate the crude or unadjusted impact ratio for the two groups. Since this is a positive action, the most favored group’s rate (in this case men) is in the denominator position.
Step 4: Observe whether the impact ratio in Step 3 is less than 80%.
Step 5: Observe that department is one of the factors that has to be taken into account for calculating any impact ratio. Therefore, to calculate the Adjusted Impact Ratio (AIR), perform the calculation in step 6 below.
Step 6: Adjust the number of selections of men and women in each department by multiplying the selection of women / men in each department by the percent of other group in the same department. Sum the women’s adjusted selections across departments and divide the sum by the sum of the adjusted men’s selections across departments:
The Adjusted Impact Ratio (AIR) of 98% indicates that overall selection rate of women across two departments, when properly adjusted, is almost the same as the selection rate of the men across two departments. Since the selection rate for women is more than 80% of that for men, the compliance officer should consider the impact ratio analysis (IRA) not adverse.
The above example shows that the OFCCP’s impact ratio analysis assumes complete homogeneity of the applicants. If the assumption about the homogeneity of the applicants is not correct then the crude impact ratio analysis may produce a misleading result. The adjusted impact ratio takes into account the differences among applicants and produces a more reliable measure.
^{i. Relative risk is used extensively in statistical and epidemiological studies. For example, to determine the efficacy of a certain drug/treatment, scientists compare the risk or probability of developing disease after the exposure of a group of subjects to a drug/treatment with the risk or probability of developing disease among an otherwise similar group that has not been exposed to the drug/treatment. ↩}
^{ii. Adjusted relative risk is called Mantel–Haenszel Relative Risk in the statistical literature. See: Tarone, R. E., “On Summary Estimators of Relative Risk,” Journal of Chronic Disease, 34, 463-468. ↩}