In a study of college students, researchers test whether sex is associated with voting registration status (registered vs not). Which statistical test is appropriate?

In a study of college students, researchers test whether sex is associated with voting registration status (registered vs not). Which statistical test is appropriate?

• A. Chi-square test of independence with 1 degree of freedom
• B. Fisher's exact test
• C. Two-proportion z-test
• D. Paired t-test

Answer: (A)

Two categorical variables are being examined: sex and voting registration status. The goal is to see if these variables are related or operate independently. The chi-square test of independence is designed for exactly this situation: it compares the observed counts in each cell of a contingency table to the counts expected if there were no association between the variables. For a 2x2 table, the degrees of freedom are (2−1)×(2−1) = 1, so the test statistic follows a chi-square distribution with 1 degree of freedom. A small p-value indicates evidence of an association between sex and registration status; a larger p-value suggests they appear independent. Fisher's exact test is a valid alternative when cell counts are very small. A two-proportion z-test could compare the registration rate between the two sexes but is less general for testing association across all cells in a contingency table. In typical practice with adequate sample size, the chi-square test of independence is the standard choice.

Two categorical variables are being examined: sex and voting registration status. The goal is to see if these variables are related or operate independently. The chi-square test of independence is designed for exactly this situation: it compares the observed counts in each cell of a contingency table to the counts expected if there were no association between the variables. For a 2x2 table, the degrees of freedom are (2−1)×(2−1) = 1, so the test statistic follows a chi-square distribution with 1 degree of freedom. A small p-value indicates evidence of an association between sex and registration status; a larger p-value suggests they appear independent. Fisher's exact test is a valid alternative when cell counts are very small. A two-proportion z-test could compare the registration rate between the two sexes but is less general for testing association across all cells in a contingency table. In typical practice with adequate sample size, the chi-square test of independence is the standard choice.