Simpson’s Paradox


Exhibit 33.12 Total applicants and admissions.

B56063% 2568%
F373 6%341 7%

Exhibit 33.13 Breakdown of applicants and admissions, across departments.

Consider the widely reported example pertaining to University of California, Berkeley. (Details sourced from Wikipedia).

The university was sued for bias against women. The total admissions figures for the fall of 1973 (Exhibit 33.12) showed that men were more likely than women to be admitted, and the difference was statistically significant.

However, on examining the individual departments (Exhibit 33.13), it appeared that no department was significantly biased against women. In fact, most departments had a small but statistically significant bias in favour 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).

This case illustrates Simpson’s paradox, aka Yule–Simpson effect or amalgamation paradox. The paradox occurs when a trend appears in several different groups of data but disappears or reverses when these groups are combined.

The Simpson’s paradox occasionally surfaces in market research. In retail tracking studies for instance, sometimes it is observed that a brand is gaining share in all channels (supermarkets, minimarkets, provision stores etc.), but losing share at the total market level. This occurs when the brand’s share is low in a relatively important (big) channel that is growing faster than the rest of the market.

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