In probability and statistics, Simpson’s paradox (or the Yule–Simpson effect) is a paradox in which a correlation present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and it occurs when frequency data are hastily given causal interpretations. Simpson’s Paradox disappears when causal relations are brought into consideration (see Implications to decision making).
One of the best known real life examples of Simpson’s paradox occurred when the University of California, Berkeley was sued for bias against women who had applied for admission to graduate schoolsthere. The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.
But when examining the individual departments, it appeared that no department was significantly biased against women. In fact, most departments had a “small but statistically significant bias in favor of women.”
The research paper by Bickel, et al. concluded that women tended to apply to competitive departments with low rates of admission even among qualified applicants (such as in the English Department), whereas men tended to apply to less-competitive departments with high rates of admission among the qualified applicants (such as in engineering and chemistry). The conditions under which the admissions’ frequency data from specific departments constitute a proper defense against charges of discrimination are formulated in the book Causality by Pearl.