the 'six largest departments' table above). Notably, the numbers of biased departments were not the basis for the conclusion, but rather it was the gender admissions pooled across all departments, while weighing by each department's rejection rate across all of its applicants. Whether the data show a definite women-favoring bias or just a minority-favoring bias (or a combination thereof) could be a different aspect for analysis: the data possibly show a bias in favor of the minority gender, as is visible in occurrence of 'more applicants' (orange) in the exact opposite gender than the 'more successful applicants' (green), and women were the minority in the entire population of applicants (see totals), thus are more probable to be the minority in a greater number of departments (would only not be so if men excess of 856 from the totals was accumulated in the top men departments, which is not the case). The paper does not explore this detail however (although it does recognize "drive to recruit minority group members" as explanation for some women-only data phenomena). Kidney stone treatment Another example comes from a real-life medical study comparing the success rates of two treatments for kidney stones. The table below shows the success rates (the term success rate here actually means the success proportion) and numbers of treatments for treatments involving both small and large kidney stones, where Treatment A includes open surgical procedures and Treatment B includes closed surgical procedures. The numbers in parentheses indicate the number of success cases over the total size of the group. The paradoxical conclusion is that treatment A is more effective when used on small stones, and also when used on large stones, yet treatment B appears to be more effective when considering both sizes at the same time. In this example, the "lurking" variable (or confounding variable) causing the paradox is the size of the stones, which was not previously known to researchers to be important until its effects were included. Which treatment is considered better is determined by which success ratio (successes/total) is larger. The reversal of the inequality between the two ratios when considering the combined data, which creates Simpson's paradox, happens because two effects occur together: The sizes of the groups, which are combined when the lurking variable is ignored, are very different. Doctors tend to give cases with large stones the better treatment A, and the cases with small