Which statistical test is used to evaluate the size and significance of the difference between two means?

Which statistical test is used to evaluate the size and significance of the difference between two means?

• A. t-test
• B. ANOVA
• C. Pearson's r
• D. Regression analysis

Answer: (A)

To determine if two group means differ in a way unlikely by chance, you use a t-test. The t-test compares the observed difference between the two sample means to the amount of difference you’d expect if the true means were the same, taking into account the variability and sample sizes. This yields a p-value that indicates whether the difference is statistically significant. At the same time, you can assess the size of the difference with an effect size such as Cohen’s d, which helps you understand practical importance beyond the p-value. If there were more than two groups, you’d use ANOVA to test differences across all group means, though with only two groups the t-test is the direct, efficient approach. Pearson’s r measures how two variables co-vary (a correlation), not a difference between means, and regression analyzes how one variable predicts another, not a simple mean difference.

To determine if two group means differ in a way unlikely by chance, you use a t-test. The t-test compares the observed difference between the two sample means to the amount of difference you’d expect if the true means were the same, taking into account the variability and sample sizes. This yields a p-value that indicates whether the difference is statistically significant. At the same time, you can assess the size of the difference with an effect size such as Cohen’s d, which helps you understand practical importance beyond the p-value.

If there were more than two groups, you’d use ANOVA to test differences across all group means, though with only two groups the t-test is the direct, efficient approach. Pearson’s r measures how two variables co-vary (a correlation), not a difference between means, and regression analyzes how one variable predicts another, not a simple mean difference.