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 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.
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 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.
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.
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