The mean square error,which forms the denominator in the F test of the relationship between the independent and dependent variables in the repeated measures case,will tend to be smaller than the mean square within forming the denominator of the F test in the between-subjects case.

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This is true because in the repeated measures case, each participant serves as their own control, which reduces individual variability and thus leads to a smaller denominator in the F test. In the between-subjects case, participants are independent of each other, which allows for more variability and thus a larger denominator in the F test.

The Mean Square Error,which Forms the Denominator in the F