An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.For this study,the three sample means are,M₁ = 1,M₂ = 2,and M₃ = 3.For the ANOVA,what value would be obtained for SS_between? A)1 B)5 C)10 D)15

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Quizplus · Accepted Answer

The value for $SS_{between}$ in an ANOVA can be calculated using the formula $$SS_{between} = n(\bar{X}_1 - \bar{X}_G)^2 + n(\bar{X}_2 - \bar{X}_G)^2 + n(\bar{X}_3 - \bar{X}_G)^2$$, where $n$ is the number of scores in each group, $\bar{X}_1$, $\bar{X}_2$, and $\bar{X}_3$ are the group means, and $\bar{X}_G$ is the grand mean of all scores. Given $\bar{X}_1 = 1$, $\bar{X}_2 = 2$, $\bar{X}_3 = 3$, and $n = 5$, the grand mean $\bar{X}_G = (1+2+3)/3 = 2$. Substituting these values into the formula gives $SS_{between} = 5(1-2)^2 + 5(2-2)^2 + 5(3-2)^2 = 5(1) + 5(0) + 5(1) = 10$.

An Independent-Measures Research Study Compares Three Treatment Conditions Using a Sample