Choose Your Own Comparator: The Importance of Race Coding Strategy in Compensation Equity Analyses

In the regression model, we would predict salary by including Time-in-Job, Black Dcode, Hispanic Dcode, and White Dcode[4]. If the regression coefficient associated with a particular dummy code is statistically significant, then there is support that the average salary for that particular race category is significantly different from the Asian category, after accounting for the influence of Time-in-Job on salary. The sign in front of the statistically significant regression coefficient indicates whether the average salary for the group is higher or lower than the Asian group, after accounting for the influence of Time-in-Job on salary. The table below presents the different results and interpretations of the regression coefficients associated with the dummy codes.

Note, there is no statistical test of whether the average salary for the Black category differs from that of the Hispanic category or that of the White category, after accounting for Time-in-Job. Similarly, there is no statistical test of whether the average salary for the Hispanic category differs from that of the White category, after accounting for Time-in-Job.

To illustrate the issue further, we conducted actual regression analyses using the data provided in the first table. We conducted analyses under the first theory of discrimination (all groups are underpaid compared to the White category, after accounting for Time-in-Job). We also conducted analyses under the second theory of discrimination (all groups are underpaid compared to the Asian category, after accounting for Time-in-Job). The results from each analysis are below.

*Statistically significant at p < .05

As is evident from the regression results, the dummy coding scheme does matter. In the first example, one would conclude that the Asian group has a significantly higher salary than the White group, after accounting for Time-in-Job. In the second example, one would conclude that the Black, Hispanic, and White groups ALL have significantly lower salaries than the Asian group, after accounting for Time-in-Job. Moreover, it is clear from the comparison of the R2 values that the two models are exactly the same in terms of how much overall variance is accounted for as well as the contribution of Time-in-Job. This is not a surprise, as exactly the same variables are included in each model: Time-in-Job and a set of dummy codes fully representing race. The models only differ in terms of which races are being compared to one another.

We present a slightly different data set and new regression results to highlight a different scenario in which under one theory of discrimination, there are no statistical flags, but under an alternative theory of discrimination, there are statistical flags. The presented results are based on the small data set below.

See the summary table below for average salary and Time-in-Job (expressed as years) for each racial/ethnic group.

Using the theory of discrimination presented in the first example, we hypothesize that at least one race category is potentially underpaid compared to the White category. The dummy coding scheme would follow that presented earlier for Example 1. The results presented in the “Example 3” row found in the table below highlight that the average salaries for the Black, Hispanic, and Asian groups are not significantly different than the average salaries for the White group, after accounting for the influence of Time-in-Job.

Alternatively, suppose our theory of discrimination is consistent with that used in the second example, in which we hypothesize that at least one race category is potentially underpaid compared to the Asian category (i.e., the Race group with the highest average salary, merit variables notwithstanding). Again, our dummy coding scheme would follow that presented for the second example. The results presented in the “Example 4” row found in the table below indicate that the average salary for the White group is not significantly different from the average salary for the Asian group, after accounting for Time-in-Job. Conversely, however, the results indicate that the average salary for the Black and Hispanic groups are significantly lower than the average salary for the Asian group, after accounting for Time-in-Job.