A psychologist studies whether a therapy program changes average anxiety scores. Patients are measured before and after treatment. Which test is appropriate?

A psychologist studies whether a therapy program changes average anxiety scores. Patients are measured before and after treatment. Which test is appropriate?

• A. Matched Pairs t-test
• B. 2-sample t-test
• C. 2-proportion z-test
• D. Chi-square test

Answer: (A)

The key idea is comparing two related measurements to see if a treatment changes the outcome. Measuring anxiety scores on the same patients before and after therapy creates paired data, because each person has two linked observations. To test whether the average change is different from zero, you summarize the change for each person (the difference between post and pre scores) and use a test that assesses whether the mean of those differences is zero. That’s the matched-pairs (dependent-samples) t-test. It accounts for the pairing and focuses on the average change across individuals, which is exactly what you want when evaluating a treatment’s effect on a continuous outcome like anxiety. If the differences aren’t roughly normal or the sample is very small, a Wilcoxon signed-rank test could be a nonparametric alternative, but with normally distributed differences, the paired t-test is the standard choice. The other tests don’t fit: a 2-sample t-test compares two independent groups, which isn’t appropriate since the scores come from the same people; a 2-proportion z-test analyzes proportions in categorical data; a chi-square test is for categorical data in contingency tables or categorical fit, not for comparing means of continuous scores.

The key idea is comparing two related measurements to see if a treatment changes the outcome. Measuring anxiety scores on the same patients before and after therapy creates paired data, because each person has two linked observations. To test whether the average change is different from zero, you summarize the change for each person (the difference between post and pre scores) and use a test that assesses whether the mean of those differences is zero. That’s the matched-pairs (dependent-samples) t-test. It accounts for the pairing and focuses on the average change across individuals, which is exactly what you want when evaluating a treatment’s effect on a continuous outcome like anxiety.

If the differences aren’t roughly normal or the sample is very small, a Wilcoxon signed-rank test could be a nonparametric alternative, but with normally distributed differences, the paired t-test is the standard choice.

The other tests don’t fit: a 2-sample t-test compares two independent groups, which isn’t appropriate since the scores come from the same people; a 2-proportion z-test analyzes proportions in categorical data; a chi-square test is for categorical data in contingency tables or categorical fit, not for comparing means of continuous scores.