In a study with a 2x2 design to test the association between group and outcome, which test would assess whether there is an association?

In a study with a 2x2 design to test the association between group and outcome, which test would assess whether there is an association?

• A. 2-proportion z-test
• B. Chi-square test of independence
• C. Fisher's exact test
• D. ANOVA

Answer: (C)

Testing whether two binary variables are related in a 2x2 contingency table uses a test of independence. Fisher's exact test is the best choice here because it provides an exact p-value for the association by computing the probability of the observed table (and more extreme ones) under the assumption of fixed margins. This avoids relying on large-sample approximations. Fisher's exact test is especially advantageous when some cell counts are small (expected frequencies below 5), where the usual chi-square approximation can be inaccurate. In larger samples with all expected counts comfortably above 5, the chi-square test of independence gives very similar results and is also appropriate. Other options don’t target the same question: a 2-proportion z-test compares two proportions directly, which is not the same as assessing whether there’s an association between two categorical variables in a contingency table; ANOVA is for comparing means of a continuous outcome across groups, not for binary associations.

Testing whether two binary variables are related in a 2x2 contingency table uses a test of independence. Fisher's exact test is the best choice here because it provides an exact p-value for the association by computing the probability of the observed table (and more extreme ones) under the assumption of fixed margins. This avoids relying on large-sample approximations.

Fisher's exact test is especially advantageous when some cell counts are small (expected frequencies below 5), where the usual chi-square approximation can be inaccurate. In larger samples with all expected counts comfortably above 5, the chi-square test of independence gives very similar results and is also appropriate.

Other options don’t target the same question: a 2-proportion z-test compares two proportions directly, which is not the same as assessing whether there’s an association between two categorical variables in a contingency table; ANOVA is for comparing means of a continuous outcome across groups, not for binary associations.