In the context of repeated-measures designs, what value is estimated by constructing a confidence interval using the repeated-measures $t$ statistic?

• A. The proportion of successes in a single sample
• B. The correlation coefficient between two variables
• C. The population variance of the differences between groups
• D. The mean difference between paired observations in the population

Answer: (D)

Verified step by step guidance

1. Understand that in repeated-measures designs, the same subjects are measured under different conditions, so the focus is on the differences within each subject between conditions.
2. Recognize that the repeated-measures t statistic is used to test hypotheses about the mean difference between paired observations, not proportions, correlations, or variances.
3. Recall that constructing a confidence interval with the repeated-measures t statistic estimates the range of plausible values for the population mean difference between the paired observations.
4. The confidence interval is calculated using the formula: \(\bar{D} \pm t_{\alpha/2, df} \times \frac{S_D}{\sqrt{n}}\), where \(\bar{D}\) is the sample mean difference, \(S_D\) is the standard deviation of the differences, \(n\) is the number of pairs, and \(t_{\alpha/2, df}\) is the critical t value.
5. Therefore, the value estimated by this confidence interval is the population mean difference between paired observations.