Chapter 13, Problem 1P

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

# How does the denominator of the F-ratio (the error term) differ for a repeated-measures ANOVA compared to an independent-measures ANOVA?

To determine

To explain: The way the denominator of the F-ratio differs for a repeated-measures ANOVA compared to an independent-measures ANOVA.

Explanation

The denominator of the F-ratio of an ANOVA measures the error. The denominator is obtained by removing the treatment effects or ‘between-treatment variability’ and ‘individual effects’ from the total variability in the study.

In independent-measures design, each individual is assigned to one treatment only. As a result, individual effects do not exist. Thus, the denominator of independent-measures ANOVA is obtained by subtracting the between-treatment variability from the total variability.

In repeated measure ANOVA, each individual receives all the available treatments. Thus, the individual effects must be eliminated, along with the treatment effect, to get the measure of error. Thus, the denominator of repeated-measures ANOVA is obtained by subtracting the between-treatment variability and the individual effect from the total variability.

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