Here we introduce the Fisher’s Exact (FE) test, a simple but very useful statistical measure in situations involving binary (*e.g.*, Yes/No, Win/Lose, Hired/Not Hired) outcomes affecting two distinct classes. Unlike most other common statistical measures such as the chi-squared test or regression, FE is particularly adept at dealing with small (*n* < 20) sample sizes. The general FE layout is depicted below:

Note that we calculate totals for each row and column, as well as a grand total in the lower right cell. The FE null hypothesis states that the outcomes {*A*,*B*,*C*,*D*}, individually and collectively, are all due to random chance.

Stated somewhat differently, FE is based on the idea that the probability of obtaining {*A*,*B*,*C*,*D*} in that exact quantity and that exact order is determined by the hypergeometric distribution:

where *N* is the population size: *A*+*B*+*C*+*D,*

*m*/

*N*is the non-biased probability of a favorable outcome,

*n* is the number of chance occurrences (*e.g.*, coin flips, football games, hiring decisions, *etc*.), and

*k* is the observed number of favorable outcomes.

In the context of labor and employment law, the two classes are invariably some protected category (based on race, age, gender, *etc*.) and another class that includes everyone else.

For example, assume a firm is undertaking a necessary headcount reduction within a large department, and further assume that the displacements fell in accordance with the distribution set forth below:

Assuming these numerical data are positioned in cells B2:D4, the FE argument would be this:

=COMBIN(B2+C2,B2)*COMBIN(B3+C3,B3)/COMBIN(D4,B2+B3)

Note that the returned *p*-value is approximately 0.38.

By convention, the FE threshold for statistical significance is *p* </= 0.05. Consequently, we cannot reject the null hypothesis that this hypothetical displacement distribution was the result of random chance.

Obviously, unlike regression, FE cannot account for the effect of category-neutral variables like seniority, or subjective variables like performance. And while neither DOL nor OFCCP currently endorse the use of FE as a statistical indicator, it nevertheless provides a very good first-level screen for the presence of a pattern that may warrant further investigation.