For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,the participant totals (the P values)are 3,6,9,and 6.What is the value for $S S _ { \text {between } }$ subjects?
A)2
B)3
C)6
D)10

Question

Quizplus · Accepted Answer

The value for $SS_{\text{between subjects}}$ is calculated using the formula $SS_{\text{between}} = \sum (\bar{X}_G - \bar{X}_T)^2 \times n$, where $\bar{X}_G$ is the grand mean of all scores, $\bar{X}_T$ is the mean of each treatment, and $n$ is the number of scores per treatment. Here, the grand mean is $\frac{3+6+9+6}{4} = 6$, and since each participant's total is their treatment mean, we calculate $SS_{\text{between}} = (3-6)^2 + (6-6)^2 + (9-6)^2 + (6-6)^2 = 9 + 0 + 9 + 0 = 18$. However, this calculation seems to misunderstand the question's intent, which is to find $SS_{\text{between subjects}}$, not between treatments. The correct approach for $SS_{\text{between subjects}}$ involves comparing each subject's score to the grand mean, but the provided information and calculation method do not align with standard procedures for $SS_{\text{between subjects}}$. Given the options and typical methodology, a recalculation or reconsideration of the formula and the given data is necessary. The correct calculation involves the variance among the participant totals (P values) in relation to the overall mean, which is not directly shown in the provided explanation. The correct answer, based on the options and typical analysis in repeated-measures designs, should involve calculating the variance among subjects' scores, but the provided calculation and explanation mistakenly focus on treatment differences. Without the exact formula and steps used to arrive at the choices, there's a misunderstanding in the explanation provided. The correct approach to find $SS_{\text{between subjects}}$ typically involves analyzing the variance among the subjects' total scores from the grand mean, which requires a different calculation than what's been described.

For a Repeated-Measures Study Comparing Three Treatment Conditions with a Sample