A repeated-measures study and an independent-measures study both produced a t statistic with df = 16.How many individuals participated in each study?
A)18 for repeated-measures and 17 for independent-measures
B)18 for repeated-measures and 18 for independent-measures
C)17 for repeated-measures and 17 for independent-measures
D)17 for repeated-measures and 18 for independent-measures

Question

A repeated-measures study and an independent-measures study both produced a t statistic with df = 16.How many individuals participated in each study?​
A)​18 for repeated-measures and 17 for independent-measures
B)​18 for repeated-measures and 18 for independent-measures
C)​17 for repeated-measures and 17 for independent-measures
D)​17 for repeated-measures and 18 for independent-measures

Quizplus · Accepted Answer

The t-distribution with df = 16 indicates that both studies had a small sample size. According to the formula for calculating df for independent t-tests and repeated-measures t-tests, in both cases, the sample size is equal to 2 times the df plus any constant (n = 2df + c). Assuming c is 0 (which is a reasonable assumption), the sample size for both studies is 2(16) = 32. Since the repeated-measures study uses the same individuals for both conditions, there must have been fewer individuals (n/2) than the independent-measures study, which can use different individuals for each condition. Therefore, the answer is D, with 17 individuals in the repeated-measures study and 18 individuals in the independent-measures study.

A Repeated-Measures Study and an Independent-Measures Study Both Produced a T