A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.How many individuals participated in each study?
A)11 for repeated, and 11 for matched
B)11 for repeated, and 12 for matched
C)11 for repeated, and 22 for matched
D)12 for repeated, and 12 for matched

Question

A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.How many individuals participated in each study?​
A)​11 for repeated, and 11 for matched
B)​11 for repeated, and 12 for matched
C)​11 for repeated, and 22 for matched
D)​12 for repeated, and 12 for matched

Quizplus · Accepted Answer

For a repeated-measures experiment or a paired t-test, the degrees of freedom are calculated as df = n - 1, where n is the number of pairs. Therefore, for a t statistic with df = 10, we can solve for n:
n - 1 = 10
n = 11
For a matched-subjects experiment or an independent t-test, the degrees of freedom are calculated as df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared. Since this problem only gives us one df value, we can assume that both groups have the same sample size, denoted as n. Therefore, for a t statistic with df = 10, we can solve for n:
2n - 2 = 10
2n = 12
n = 6
So the only answer choice that fits both calculations is C, with 11 participants in the repeated-measures experiment and 22 participants (11 pairs) in the matched-subjects experiment.

A Repeated-Measures Experiment and a Matched-Subjects Experiment Each Produce a T