# Sample size for repeated-measures t-test

## Effect size is the difference in means between two observations of the 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 and an average pain score of 4.3 with a standard deviation of 1.1. There is an evidenced-based measure of effect of 2.8 (7.1 - 4.3 = 2.8). Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect in order to detect the treatment effect.

*a priori*sample size calculation for a repeated-measures t-test, researchers will need to seek out evidence that**provides the means and standard deviations of the outcome at two different observations**. The**absolute****difference**between the two mean values and their respective variances dictates the evidence-based measure of effect size. Find research articles in the respective body of literature that are similar to the study of interest and use those values in sample size calculations for repeated-measures t-tests.A good rule of thumb is to

**overestimate the variance of the effect size**. Researchers do this because it forces you to have to collect more observations of the outcome, which in turn leads to more precise and accurate measures of effect.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 and an average pain score of 4.3 with a standard deviation of 1.1. There is an evidenced-based measure of effect of 2.8 (7.1 - 4.3 = 2.8). Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect in order to detect the treatment effect.

### The steps for calculating sample size for a repeated-measures t-test 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. If there is a

6. If there is a

7. Click the

8. Enter the

9. Enter the

10. Enter the

11. Enter the

12. Click

13. Click

14. Leave the alpha value at

15. Enter

16. Click

2. Under the

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

**Statistical test**drop-down menu, select**Means: Difference between two dependent means (matched pairs)**.4. Under the Type of power analysis drop-down menu, select

**A priori: Compute required sample size - given alpha, power, and effect size**.5. If there is a

**directional hypothesis**, under the**Tail(s)**drop-down menu, select**One**.6. If there is a

**non-directional hypothesis**, under the**Tail(s)**drop-down menu, select**Two**.7. Click the

**Determine**button.8. Enter the

**mean**for the first observation into the**Mean group 1**box. Example:**"7.1"**9. Enter the

**mean**for the second observation into the**Mean group 2**box. Example:**"4.3"**10. Enter the

**standard deviation**associated with the mean of the first observation into the**SD insert group 1**box. Example:**"1.6"**11. Enter the

**standard deviation**associated with the mean of the second observation into the**SD insert group 2**box. Example:**"1.1"**12. Click

**Calculate**.13. Click

**Calculate and transfer to main window**.14. Leave the alpha value at

**0.05**, unless researchers want to change the alpha value according to the current empirical or clinical context.15. 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.16. Click

**Calculate**.Based on the values above in the example and the 16 steps above, a two-tailed 2.8 point effect with an alpha of .05 and a power of .80 yields a needed sample size of only

**5**to detect that effect.Click on the

**Statistics**button to continue.## Hire A Statistician

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D., PStat** **will provide the following statistical consulting services for undergraduate and graduate students at $100/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics