scipy.stats._hypotests:boschloo_exact

Notes

Boschloo's test is an exact test used in the analysis of contingency tables. It examines the association of two categorical variables, and is a uniformly more powerful alternative to Fisher's exact test for 2x2 contingency tables.

Boschloo's exact test uses the p-value of Fisher's exact test as a statistic, and Boschloo's p-value is the probability under the null hypothesis of observing such an extreme value of this statistic.

Let's define $X_0$ a 2x2 matrix representing the observed sample, where each column stores the binomial experiment, as in the example below. Let's also define $p_1,p_2$ the theoretical binomial probabilities for $x_{11}$ and $x_{12}$. When using Boschloo exact test, we can assert three different alternative hypotheses:

• $H_0:p_1=p_2$ versus $H_1:p_1<p_2$, with alternative = "less"

• $H_0:p_1=p_2$ versus $H_1:p_1>p_2$, with alternative = "greater"

• $H_0:p_1=p_2$ versus $H_1:p_1\ne p_2$, with alternative = "two-sided" (default)

There are multiple conventions for computing a two-sided p-value when the null distribution is asymmetric. Here, we apply the convention that the p-value of a two-sided test is twice the minimum of the p-values of the one-sided tests (clipped to 1.0). Note that fisher_exact follows a different convention, so for a given table, the statistic reported by boschloo_exact may differ from the p-value reported by fisher_exact when alternative='two-sided'.