ANOVA statistics question

Question

An independent-measures research study compares three treatment conditions with a sample of n = 10 in each condition. The sample means are M1 = 2, M2 = 3, and M3 = 7. a. Compute SS for the set of 3 treatment means.

 

(I am stuck on how to find SS given only the means for this question. I know how to find SS given sets of data, but not with just the mean. I need to use the formula EX²-G²/N.

Answer 1

Hi Michelle,

 

Since SS_total = SS_error + SS_treatment, you'll need two out of the three parts of the decomposition in order to find the third. Without more information you can only compute SS_treatment. The overall mean is the weighted average of the treatment means, and since the group sizes are the same this is (2+3+7)/3 = 4.

 

SS_treatment

 = ∑_i n_i×(mean of i^th treatment group - overall mean)

= 10×(2-4)² + 10×(3-4)² + 10×(7-4)²

= 140