An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three sample totals are, t1 = 5, t2 = 10, and t3 = 15, and Sum of X squared= 75 for the entire set of scores. What value would be obtained for ss ?
To find the value for ss (sum of squares), we need to calculate the sum of squared deviations from the mean for each treatment condition. Follow these steps to get the answer:
1. Calculate the mean for each treatment condition. Divide each total (t1, t2, and t3) by the sample size (n = 5).
Mean for t1 = t1 / n = 5 / 5 = 1
Mean for t2 = t2 / n = 10 / 5 = 2
Mean for t3 = t3 / n = 15 / 5 = 3
2. Next, calculate the sum of squares for each treatment condition. The formula for sum of squares (SS) is the sum of squared deviations from the mean.
SS for t1 = (t1 - mean for t1)^2
= (5 - 1)^2
= 16
SS for t2 = (t2 - mean for t2)^2
= (10 - 2)^2
= 64
SS for t3 = (t3 - mean for t3)^2
= (15 - 3)^2
= 144
3. Finally, calculate the overall sum of squares (ss) by summing up the individual sum of squares for each treatment condition.
ss = SS for t1 + SS for t2 + SS for t3
= 16 + 64 + 144
= 224
Therefore, the value obtained for ss is 224.