An independent-measures research study computes three treatment conditions with a sample of n=10 in each conditions. The sample means are M1=2, m2=3, and m3=7.
a. Compute SS for the set of 3 treatment means. (Use the three means as a set of n=3) scores and compute SS.)
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To compute SS (Sum of Squares) for the set of 3 treatment means, you need to follow these steps:
Step 1: Find the grand mean (M).
The grand mean is the mean of all the treatment means. To find it, you need to add up all the means and divide by the total number of means (n=3) in this case:
M = (M1 + M2 + M3) / 3
M = (2 + 3 + 7) / 3
M = 4
Step 2: Calculate the SS.
SS is the sum of the squared deviations of each treatment mean from the grand mean. To compute it, you can use the following formula:
SS = Σ (X - M)^2
Where X is each treatment mean (M1, M2, M3), and M is the grand mean you calculated in Step 1.
For our example, we compute the squared deviations for each mean:
M1: (2 - 4)^2 = 4
M2: (3 - 4)^2 = 1
M3: (7 - 4)^2 = 9
Now sum up these squared deviations:
SS = 4 + 1 + 9
SS = 14
Therefore, the SS for the set of 3 treatment means is 14.