For a 2x2 table, what statistic tests independence between two categorical variables?

For a 2x2 table, what statistic tests independence between two categorical variables?

• A. Fisher's exact test
• B. McNemar's test
• C. Pearson chi-square statistic (chi-square test)
• D. Z-test for proportions

Answer: (C)

Testing independence between two categorical variables in a 2x2 table is about comparing what you observe in the four cells to what you would expect if the variables were independent. The Pearson chi-square statistic does this by using the expected counts under independence, E_ij = (row_i total × column_j total) / grand total, and summing (O_ij − E_ij)² / E_ij over all four cells. For a 2x2 table, this statistic follows a chi-square distribution with 1 degree of freedom, so a large value suggests the variables are not independent. This is the standard approach for assessing association in contingency tables when the sample size is adequate. If counts are very small, Fisher’s exact test provides an exact alternative. McNemar’s test applies to paired data, not to independence in a single contingency table, and a Z-test for proportions compares two proportions rather than the relationship between two categorical variables in a cross-tabulation.

Testing independence between two categorical variables in a 2x2 table is about comparing what you observe in the four cells to what you would expect if the variables were independent. The Pearson chi-square statistic does this by using the expected counts under independence, E_ij = (row_i total × column_j total) / grand total, and summing (O_ij − E_ij)² / E_ij over all four cells. For a 2x2 table, this statistic follows a chi-square distribution with 1 degree of freedom, so a large value suggests the variables are not independent. This is the standard approach for assessing association in contingency tables when the sample size is adequate. If counts are very small, Fisher’s exact test provides an exact alternative. McNemar’s test applies to paired data, not to independence in a single contingency table, and a Z-test for proportions compares two proportions rather than the relationship between two categorical variables in a cross-tabulation.