A small 2x2 table where chi-square's expected-count rule fails. What exact means here, why it is not merely a fallback, and how to report it in APA 7.
Fisher's exact test evaluates a 2×2 table by computing the probability directly rather than approximating it. It fixes the row and column totals and enumerates every table that could have produced them, then counts how many are as extreme as yours.
Chi-square, by contrast, compares its statistic against a theoretical distribution that the real data only approaches as the sample grows. In a small or sparse table the approximation drifts, and the p value it returns is usually too small.
So exact is a literal description of the method, and it is why Fisher's test remains valid where chi-square is not. It is also why it is computationally heavier, which mattered in 1935 and does not on an Apple silicon Mac.
Any expected count below 5 in a 2×2 table. At that point chi-square's p value should not be reported and Fisher's should.
Small total samples, roughly under 20 to 40 cases depending on how the counts fall, even where no single expectation quite breaches the rule.
Rare outcomes. A study of an uncommon event will produce a sparse row no matter how many participants you recruit.
It is not only a fallback. Because it is exact rather than approximate, Fisher's test is defensible at any sample size in a 2×2 table. The reason chi-square remains conventional is habit and computational history, not superiority.
For paired data, neither test applies. If the same people are counted twice, before and after, use McNemar.
Lay the data out one row per person, with a column for each of the two binary variables. Quanta builds the 2×2 table from the raw responses.
Upload categories as text rather than numeric codes, so the variables are typed as categories rather than quantities.
Configure the two variables in the Setup panel on the right and the result appears in the center panel.
Note whether the p value is one- or two-tailed. Fisher's test has a one-tailed form, and reporting a one-tailed p as though it were two-tailed halves your apparent p value. Two-tailed is the default expectation unless your hypothesis was directional and stated in advance.
Fisher's exact test produces no test statistic to report, only a p value. Give the p value, the sample size, the cell counts, and an effect size.
Fisher's exact test showed that adverse events were more common in the control condition (6 of 14) than in the treatment condition (1 of 15), p = .035 (two-tailed).
Report the actual counts, not only percentages. In a small table, 6 of 14 is honest where 43% invites a reader to imagine a larger study.
State that the test was two-tailed, or justify a one-tailed test with a hypothesis registered in advance.
Give an odds ratio or risk difference with a confidence interval. In a small sample the interval will be wide, and that width is the most useful thing you can tell a reader.
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Chi-square test of independence for larger samples · McNemar for paired categorical data · Chi-square goodness of fit one variable against expected proportions · the complete list on the analyses page.