Which test is preferred for nominal data with very small sample sizes where expected counts are less than 5?

Which test is preferred for nominal data with very small sample sizes where expected counts are less than 5?

• A. Mann-Whitney U test
• B. Fisher exact test
• C. Chi-square test
• D. Mantel-Haenszel

Answer: (B)

When you’re dealing with nominal data in a 2x2 table and the sample is very small (with expected counts less than 5), you need an exact test rather than a large-sample approximation. The Fisher exact test computes the exact probability of the observed arrangement under the null hypothesis of no association between the variables, using the hypergeometric distribution. This gives a precise p-value that remains valid regardless of how small the counts are. The chi-square test relies on an approximation that becomes unreliable with small expected counts. The other options aren’t suited for this scenario: Mann-Whitney U compares a continuous or ordinal outcome between two groups, not categorical data; Mantel-Haenszel is for stratified analyses to adjust or pool across layers. So the exact approach for this situation is Fisher exact test.

When you’re dealing with nominal data in a 2x2 table and the sample is very small (with expected counts less than 5), you need an exact test rather than a large-sample approximation. The Fisher exact test computes the exact probability of the observed arrangement under the null hypothesis of no association between the variables, using the hypergeometric distribution. This gives a precise p-value that remains valid regardless of how small the counts are. The chi-square test relies on an approximation that becomes unreliable with small expected counts. The other options aren’t suited for this scenario: Mann-Whitney U compares a continuous or ordinal outcome between two groups, not categorical data; Mantel-Haenszel is for stratified analyses to adjust or pool across layers. So the exact approach for this situation is Fisher exact test.