When to use Fisher's test

Fisher's exact test is designed for 2imes22 imes2 tables when sample sizes are small or expected counts are low.

It keeps the row and column totals fixed, then compares the observed table to all equally margined tables that are at least as rare.

Reading the result

If the p-value is less than or equal to your chosen significance level alphaalpha, the data provide evidence against the null hypothesis of no association.

A large p-value does not prove independence. It only means the observed table is not unusual enough, under the null model, to reject it.