via the odds ratio, this implies that the threshold odds ratio for assuming discrimination is 1.25 – the other measures of effect size are therefore:This implies that discrimination is presumed to exist if 0.4% of the variation in outcomes is explained and there is a 0.123 standard deviation difference between two groups. Both of these quantities are small enough that there are significant concerns about finding false positive instances of discrimination at an unacceptable level. A greater threshold for presuming that disparities are due to discrimination, such as an odds ratio of 2–3, is less likely to have false positives. Confounding and regression analysis A second concern of using disparate impact is that disparities may be affected by underlying variables, called confounders, which would imply that the disparity is due to underlying differences that are not predicated on group membership. For example, all of the following disparities exist: Women tend to be underrepresented among firefighters This led New York City to drop its physical-skills test for probationary firefighters Women driving for Uber tend to be paid less than men Black men account for a disproportionate share of Americans killed by police officers It is possible that all of these disparities are due to discrimination, but regression analysis allows us to account for variables that may explain differences. For example, suppose that we are attempting to investigate whether or not a pay disparity between two groups is due to discrimination. Then we may construct a multiple regression model for pay as:where the are the confounding variables, is a dichotomous variable indicating group membership, and is a normally distributed random variable. After correction for the potentially confounding variables in a regression model, we should be able to tell if there is still an impact of group membership on the quantity of interest. If we have not omitted any important confounding variables and not engaged in p-hacking, then a statistically significant suggests a very good possibility of positive or negative discrimination. Circling back to our three examples, there are plausible explanations for all of the disparities that were listed: Firefighters should be physically strong, and women tend to not to be as strong as men Among Uber drivers, a 7% pay gap between men and women was explained by three factors: Where and when rides originate from (i.e., time and location) Amount of driver experience Driving speed While differences in use of less-than-deadly