Question

A researcher conducts a repeated-measures study comparing three treatment conditions with a sample of n = 12 participants. The results are evaluated with a repeated-measures ANOVA and an incomplete summary table follows. Provide the missing values. (Hint: begin with values for df).

Source SS df MS
_______________________________________________
Between treatments ____ ____ 10 F = _____
Within treatments ____ ____
Between subjects ____ ____
Error 44 ____ ____
Total 106 ____
_______________________________________________

Answer 1

The degrees of freedom for between treatments is equal to the number of treatments minus 1. There are three treatments, so the degrees of freedom for between treatments is 3 - 1 = 2.

Source SS df MS F

Between treatments 10 2 5 1.56

Within treatments 44 22 2

Between subjects 4 11 4

Error 44 22 2

Total 106 35

The degrees of freedom for within treatments is equal to the number of participants minus 1 multiplied by the number of treatments. In this case, there are 12 participants and three treatments, so the degrees of freedom for within treatments is (12 - 1) * 3 = 22.

The degrees of freedom for between subjects is equal to the number of participants minus 1. In this case, there are 12 participants, so the degrees of freedom for between subjects is 12 - 1 = 11.

The mean square for between treatments is equal to the sum of squares for between treatments divided by the degrees of freedom for between treatments. In this case, the sum of squares for between treatments is 10 and the degrees of freedom for between treatments is 2, so the mean square for between treatments is 10 / 2 = 5.