Question

A repeated measures ANOVA is statistically more powerful than a randomized ANOVA. One reason is that the same subjects are used (like a paired t test). Why else? The within source of variance in a randomized ANOVA becomes ___subject______ and __error________in a repeated measures ANOVA. Only the __error_____ is used to calculate the F ratio. Because the denominator is smaller, the F ratio will be ___?____ and more likely to ______?_________ .

Hints: error, fail to reject the null hypothesis, smaller, larger, subject, reject the null hypothesis

Answer 1

A repeated measures ANOVA is statistically more powerful than a randomized ANOVA.

One reason is that the same subjects are used (like a paired t test).

Why else?

When using a repeated-measures ANOVA, individual differences across participants, the single largest factor contributing to error variance, has been removed because the same participants across conditions are used . Because error variance represents the denominator in the F-ratio, a smaller number is used in dividing and the answer results in a larger final F-ratio. This means that a repeated-measures ANOVA is more sensitive to small differences between groups than is a randomized ANOVA (Jackson, 2012).

Hence, the within source of variance in a randomized ANOVA becomes same across subjects and reduces the error variance in a repeated measures ANOVA. Only the decreased error variance is used to calculate the F ratio. Because the denominator is smaller, the F ratio will be larger and more likely to reject the null hypothesis.