The office of student life wants to know if there is a significant difference between the three fraternities on campus?

The office of student life wants to know if there is a significant difference between the three fraternities on campus?

• A. Paired t-test
• B. Chi-square test
• C. One-way ANOVA (independent samples)
• D. Mann-Whitney U test

Answer: (C)

When you want to know if three independent groups have different averages, use a one-way ANOVA for independent samples. In this scenario, the three fraternities form separate groups, and you’re testing whether their mean outcome differs across groups. ANOVA compares the variability between groups to the variability within groups with an F statistic to determine if at least one group mean is different from the others. If you find a significant result, you’d typically follow up with post hoc tests to identify exactly which fraternities differ. This approach relies on a few assumptions: the observations are independent, the outcome is approximately normally distributed within each fraternity, and the variances are similar across groups. Other tests don’t fit as well here: a paired t-test is for two related samples, the chi-square test is for categorical data, and the Mann-Whitney U test covers two independent groups (and is nonparametric), not three.

When you want to know if three independent groups have different averages, use a one-way ANOVA for independent samples. In this scenario, the three fraternities form separate groups, and you’re testing whether their mean outcome differs across groups. ANOVA compares the variability between groups to the variability within groups with an F statistic to determine if at least one group mean is different from the others. If you find a significant result, you’d typically follow up with post hoc tests to identify exactly which fraternities differ.

This approach relies on a few assumptions: the observations are independent, the outcome is approximately normally distributed within each fraternity, and the variances are similar across groups. Other tests don’t fit as well here: a paired t-test is for two related samples, the chi-square test is for categorical data, and the Mann-Whitney U test covers two independent groups (and is nonparametric), not three.