One of the primary advantages of a repealedmeasures design, compared to an independentmeasures design, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing three treatment conditions.
a.
To test: The significance of the mean difference using independent measure ANOVA with
Given info:
The data is provided in the question.
Treatment 1  Treatment 2  Treatment 3 












Calculation:
Step 1:
The null and alternative hypotheses are:
Null hypothesis:
Where
Alternate hypothesis:
Step 2:
Compute the degrees of freedom (df) for the between treatment effects, within treatment effects and total and corresponding sum of squares (SS).
Now, it is known that, for a given sample size, the degrees of freedom (df) is:
Thus,
The number of treatments,
As within treatments degrees of freedom,
With
Step 3:
Compute Fratio.
The total sum of squares is:
The within treatment sum of squares is:
The within treatment sum of squares is:
b.
c.
To find: Why the results of analysis differ in part a and part b.
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