# Sample size for repeated-measures ANOVA

## Effect size is the difference in means between three observations of an outcome

In order to run an

A good rule of thumb is to

For example, let's say that researchers find quality evidence that people in the treatment group have an average pain score of 7.1 with a standard deviation of 1.6 at baseline, an average pain score of 4.3 with a standard deviation of 1.1, and a 6-month follow-up average score of 4.1 with a standard deviation of 1.4. Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect to detect the hypothesized treatment effect.

*a priori*sample size calculation for repeated-measures ANOVA, researcheres will need to seek out evidence that**provides the means and standard deviations of the outcome at the three different observations**. The**absolute****differences**between these three mean values and their respective variances constitutes an evidence-based measure of effect size. Find articles in the literature that are conceptually or theoretically similar to the study of interest or use similar outcomes and use those values in the sample size calculation for repeated-measures ANOVA.A good rule of thumb is to

**overestimate the variance of the effect size**. Researchers do this because it forces them to have to collect more observations of the outcome, which in turn leads to more precise and accurate measures of effect with repeated-measures ANOVA.For example, let's say that researchers find quality evidence that people in the treatment group have an average pain score of 7.1 with a standard deviation of 1.6 at baseline, an average pain score of 4.3 with a standard deviation of 1.1, and a 6-month follow-up average score of 4.1 with a standard deviation of 1.4. Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect to detect the hypothesized treatment effect.

### The steps for calculating sample size for a repeated-measures ANOVA in G*Power

1. Start up G*Power.

2. Under the

3. Under the

4. Under the Type of power analysis drop-down menu, select

5. Click the

6. Click on the

7. In the

Enter

Enter

Enter

8. Click

9. Click

10. Enter

11. In the

12. In the

13. Click

2. Under the

**Test family**drop-down menu, select**F tests**.3. Under the

**Statistical test**drop-down menu, select**ANOVA: Repeated measures, within factors**.4. Under the Type of power analysis drop-down menu, select

**A priori: Compute required sample size - given alpha, power, and effect size**.5. Click the

**Determine**button.6. Click on the

**Direct**marker to highlight the menu.7. In the

**Partial eta-squared**box, enter one of the following values:Enter

**".01"**if researchers believe there will be a**small treatment effect**.Enter

**".03"**if researchers believe there will be a**moderate treatment effect**.Enter

**".05"**if researchers believe there will be a**large treatment effect**.8. Click

**Calculate**.9. Click

**Calculate and transfer to main window**.10. Enter

**.80**into the**Power (1-beta err prob)**box, unless researchers want to change the power according to the current empirical or clinical context.11. In the

**Number of groups**box, enter**"1"**12. In the

**Number of measurements**box, enter**"3"**13. Click

**Calculate**.Based on the values and steps above, for one group being measured across three observations, an alpha of .05, and a power of .80, and

**small treatment effect of .01**, researchers would need to collect**161**observations to detect a significant treatment effect.Click on the

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