If expected cell counts in a contingency table are small, which test is more appropriate than the chi-square independence test?

• A. Pearson correlation
• B. ANOVA
• C. Fisher's exact test
• D. Wilcoxon signed-rank test

Answer: (C)

When observed counts are small, the chi-square test’s usual approximation to the sampling distribution becomes unreliable. Fisher's exact test sidesteps that by calculating the exact probability of the observed arrangement under the null hypothesis of independence. For a 2x2 table, it fixes the marginal totals and uses the hypergeometric distribution to enumerate all possible tables as extreme or more extreme than what was seen, then sums their probabilities to obtain the p-value. This exact approach remains valid regardless of how small the counts are, making it the best choice in this situation. The other tests aren’t designed to assess independence in a contingency table with small counts: Pearson correlation handles continuous variables, ANOVA compares means across groups, and the Wilcoxon signed-rank test deals with paired data.