When should you use Fisher's exact test instead of the chi-square test?

When should you use Fisher's exact test instead of the chi-square test?

• A. When sample sizes are large and expected counts are well above 5.
• B. When data are normally distributed.
• C. When there are more than two categories.
• D. When sample sizes are small and expected counts are below 5.

Answer: (D)

When counts in your contingency table are small, rely on Fisher's exact test because it gives an exact p-value rather than depending on an approximation. The chi-square test uses a theoretical distribution to approximate the likelihood of the observed association, and that approximation becomes unreliable when expected counts are very low (typically below 5). Fisher's exact test fixes the margins of the table and computes the exact probability of the observed data (and more extreme possibilities) under the null hypothesis, so its results are accurate even with sparse data. If you have a larger sample and all expected counts are comfortably above 5, the chi-square test is appropriate and easier to compute. Extensions of Fisher's exact test can handle larger tables, but the core idea is the same: use Fisher's when the data are too sparse for a trustworthy chi-square approximation.

When counts in your contingency table are small, rely on Fisher's exact test because it gives an exact p-value rather than depending on an approximation. The chi-square test uses a theoretical distribution to approximate the likelihood of the observed association, and that approximation becomes unreliable when expected counts are very low (typically below 5). Fisher's exact test fixes the margins of the table and computes the exact probability of the observed data (and more extreme possibilities) under the null hypothesis, so its results are accurate even with sparse data.

If you have a larger sample and all expected counts are comfortably above 5, the chi-square test is appropriate and easier to compute. Extensions of Fisher's exact test can handle larger tables, but the core idea is the same: use Fisher's when the data are too sparse for a trustworthy chi-square approximation.