Statistical proof of discrimination often entails comparisons of the demographics of an employer’s work force with that of the relevant labor force. The statistical study yields a “p-value,” and if the p-value is below some pre-specified level, the disparity is deemed “statistically significant.” The p-value is often interpreted as the probability that the observed disparity was obtained by chance, but equating the p-value with the likelihood that chance caused the disparity is an example of the “transposition fallacy.” Recognizing this fallacy, some commentators have suggested the use of Bayesian methods, under which the probability of discrimination is estimated by incorporating base rates of discrimination into the analysis, thereby avoiding the transposition fallacy.
Although avoiding the transposition fallacy, incorporation of base rates of discrimination creates its own problems. First, knowledge of the relevant base rate for the particular kind of discrimination is generally unknown (and, as a practical matter, unknowable). Second, reliance on base rates of discrimination conflicts with the policy of Rule 404 of the Federal Rules of Evidence, which bars introduction of evidence of character and prior acts to establish the propensity of an actor to act in a particular way. Base-rate evidence is of that sort, because it is introduced to establish the extent of the propensity of employers to discriminate, with the implication that the defendant employer has acted in accordance with that propensity. Thus, even if the technical problems with Bayesian analysis could be overcome, it should still not be admissible in litigation.
Browne, Kingsley R.
"No Bayesian Solution to the Transposition Fallacy: More Reason to Be Skeptical of Statistical Proof of Discrimination,"
Hofstra Labor & Employment Law Journal: Vol. 35
, Article 3.
Available at: https://scholarlycommons.law.hofstra.edu/hlelj/vol35/iss2/3