To the extent that the mean square within is larger than the mean square error,a larger F ratio and a greater likelihood of rejecting the null hypothesis should result in a between-subjects analysis of variance as opposed to a repeated measures analysis of variance.

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In ANOVA, a larger F ratio results from a larger mean square between (not within) relative to the mean square error, indicating a greater likelihood of rejecting the null hypothesis.

To the Extent That the Mean Square Within Is Larger