Appendix

Calculating Sums of Squares for One-Way Repeated-Measures ANOVA

Calculating sums of squares for a one-way repeated-measures ANOVA is quite similar to calculating sums of squares for a between-subjects, one-way ANOVA. Here are the pre-treatment, post-treatment, and follow-up distraction scores, squared and summed just as they were in Chapter 10 for a between-subjects, one-way ANOVA:

Pre-Treatment Post-Treatment Follow-Up
X X2 X X2 X X2
Case 1 13 169 10 100 12 144
Case 2 30 900 20 400 26 676
Case 3 20 400 13 169 17 289 Grand
Case 4 26 676 17 289 20 400 X X2
Sum 89.00 2,145.00 60.00 958.00 75.00 1,509.00 224.00 4,612.00
n 4 4 4 12

Once this is done, the values can be plugged into Equations 10.2, 10.3, and 10.4. SSTotal is calculated using Equation 10.2:

image

Next, we obtain SSBetween via Equation 10.3. This is called SSTreatment for repeated-measures ANOVA.

image

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Then, using Equation 10.4, calculate SSWithin:

image

So far, all has been the same as for a between-subjects, one-way ANOVA. Now, it is time to diverge and calculate SSBetween. To do so, we need to add two new columns to the data table:

Pre-Treatment Post-Treatment Follow-Up
X X2 X X2 X X2 Case Total T2/k
Case 1 13 169 10 100 12 144 35 408.33
Case 2 30 900 20 400 26 676 76 1,925.33
Case 3 20 400 13 169 17 289 Grand 50 833.33
Case 4 26 676 17 289 20 400 X X2 63 1,323.00
Sum 89.00 2,145.00 60.00 958.00 75.00 1,509.00 224.00 4,612.00 224.00 4,490.00
n 4 4 4 12

The two new columns are on the far right. The first, labeled “Case Total,” is the sum of all the scores for each case. For case 1, this is T = 13 + 10 + 12. The next column is that case total squared and then divided by k, the number of conditions. For case 1, this is 352/3. Note that all of these values are summed. SSSubjects is calculated:

image

Finally, SSResidual is needed. SSResidual is what remains after SSSubjects is removed from SSWithin:

SSResidual = SSWithin – SSSubjects

= 325.50 – 308.67

= 16.83

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