6. The following data represent the results from an independent-measures study c

Question

6. The following data represent the results from an independent-measures study comparing three
treatments.
a. Compute SS for the set of 3 treatment means. (Use the three means as a set of n = 3 scores and
compute SS.)
b. Using the result from part a, compute n(SSmeans). Note that this value is equal to SSbetween (see
Equation 13.6).
c. Now, compute SSbetween with the computational formula using the T values (Equation 13.7). You
should obtain the same result as in part b.
Treatment
I           II   III
n = 10 n = 10  n = 10
M = 2 M = 3 M = 7
T = 20 T = 30 T = 70

Explanation / Answer

(a) Average of the means (Grand mean) = (2 + 3 + 7)/3 = 4 Sum of squares = (2 - 4)^2 + (3 - 4)^2 + (7 - 4)^2 = 4 + 1 + 9 = 14 ---------------------------------------------------------------------------------------- (b) SS(between) = 10 * 14 = 140 ---------------------------------------------------------------------------------------- (c) Correction factor = (20 + 30 + 70)^2 / (10 * 3) = 480 Total sum of squares = 10 * 2^2 + 10 * 3^2 + 10 * 7^2 - 480 = 140 SS(between) = (20^2 /10) + (30^2 /10) + (70^2 /10) - 480 = 140

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