# 5.4: More Notes on Repeated Measures ANOVA

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Repeated Measures ANOVAs have some special properties that are worth knowing about. The main special property is that the error term used to for the $$F$$-value (the MS in the denominator) will always be smaller than the error term used for the $$F$$-value the ANOVA for a between-subjects design. We discussed this earlier. It is smaller, because we subtract out the error associated with the subject means.

This can have the consequence of generally making $$F$$-values in repeated measures designs larger than $$F$$-values in between-subjects designs. When the number in the bottom of the $$F$$ formula is generally smaller, it will generally make the resulting ratio a larger number. That’s what happens when you make the number in the bottom smaller.

Because big $$F$$ values usually let us reject the idea that differences in our means are due to chance, the repeated-measures ANOVA becomes a more sensitive test of the differences (its $$F$$-values are usually larger). This is a major advantage of using repeated-measures ANOVA, and within-subjects designs. The other advantage we have already mentioned before is that within-subjects design requires a smaller sample size.

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