Fisherpvalues

Fisherpvalues are p-values obtained from Fisher's exact test, a statistical significance test used for the analysis of 2x2 contingency tables. Named after Ronald A. Fisher, they are particularly appropriate when sample sizes are small or when expected frequencies in any cell are low, making chi-square approximations unreliable.

The p-value in this context is exact under the null hypothesis of independence between the two binary variables. It is computed from the hypergeometric distribution by summing the probabilities of all contingency tables that are as or more extreme than the observed one, given the fixed margins of the table.

In practice, two definitions of "extreme" are used (one-tailed and two-tailed tests); some software reports a mid-p value to balance conservativeness. The interpretation of Fisherpvalues is that, assuming the margins are fixed, the observed association is unlikely under the null hypothesis. They do not measure effect size themselves, but they are often reported alongside or in conjunction with odds ratios.

Fisherpvalues are widely available in statistical software packages, such as R's fisher.test and Python's scipy.stats.fisher_exact; the test is exact but can be computationally intensive for larger tables. Limitations include sensitivity to the exact margins chosen and the fact that p-values do not convey the magnitude of association, which may lead researchers to report both p-values and effect estimates.

Fisherpvalues are a common alternative to chi-square tests in small-sample epidemiology, genetics, and other fields where precise significance testing is important.