The point of this page, however, involves the problematic nature of the four-fifths rule as a measure of association. Many regard the four-fifths rule as a useful indicator of effect size (see, e.g., this explanation on the site adverseimpact.org). But not only is a rate ratio not a useful indicator of effect size, it is illogical to regard it as such. See the Illogical Premises II sub-page of the Scanlan’s Rule page (SR), which explains that it is illogical to regard a rate ratio as reflecting the same measure of association as to different baseline rates given that, if the rate ratios are the same as to one outcome, they must be different as to the opposite outcome. The point is easier to explain with regard to the mistaken perception that a factor will typically cause equal proportionate changes across a range of baseline rates, as discussed in the Subgroup Effects, Illogical Premises, and Inevitability of Interaction sub-pages of SR. See also the February 25, 2013 BMJ comment “Goodbye to the Rate Ratio.”
Table 1 below, which is an illustration akin to that in Table 1 of the 2009 Royal Statistical Society presentation, shows the various effect sizes (reflected by the EES, see Solutions sub-page of Measuring Health Disparities), consistent with a situation where the success rates of the disadvantaged group is 80 percent of the success rate of the advantaged group. The table thus shows at different overall selection rates (benchmarked by the selection rate of the advantaged group (DGSR)), a four-fifths disadvantaged to advantaged group selection rate ratio (SRR) means quite different things as to the strength of the forces causing the rates to differ.
The penultimate column (FRR for failure rate ratios) shows how the matter would be viewed in terms of ratios of experiencing the adverse outcome.
In order to provide some perspective on meaning of each EES figure, the final column (%DG>AGMean) shows the proportion of the disadvantaged group with prospects regarding whatever is at issue that is superior to the mean prospect for the advantaged group. By way of explanation, the first row reflects that fact that with a 0.1 standard deviation, 46.4% of the disadvantaged group is above the advantaged group mean, which is to say the distributions are fairly similar. The subsequent rows reflect increasingly dissimilar distributions.
For a fuller discussion of the implications of reliance on standard measures of differences between outcome rates in the employment context, see pages of 24-28 of the Harvard University Measurement Letter.
Table 1. Illustration of Differences in Level of Association Reflected by Situations Where Success Rate of Disadvantaged Group is Four-Fifths of the Success Rate of the Advantaged Group at Different Levels of Prevalence [ref b3811 a 3]