Sample size for Wilcoxon test
Effect size is the difference in means or medians between two observations of the outcome
Most ordinal outcomes are reported as medians and interquartile ranges, and those are the correct statistics for purposes of reporting in a publication. However, when it comes to sample size calculations, researchers may be required to make an informed hypothesis based on the means and standard deviations that are reported in a published article. A good rule of thumb is to overestimate the variance of the effect size. Researchers do this because it forces them 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 people in the control group have 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) in this instance. Researchers could enter these values into G*Power and know exactly how many observations of the outcome They would need to detect the 2.8 treatment effect.
The steps for calculating sample size for a Wilcoxon test in G*Power
2. Under the Test family drop-down menu, select t tests.
3. Under the Statistical test drop-down menu, select Means: Wilcoxon signed-rank test (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. Under the Parent distribution drop-down menu, select Normal, unless researchers want to change the distribution according to the current empirical or clinical context.
8. Click the Determine button.
9. Enter the mean for the first observation into the Mean group 1 box. Example: "7.1"
10. Enter the mean for the second observation into the Mean group 2 box. Example: "4.3"
11. Enter the standard deviation associated with the mean of the first observation into the SD insert group 1 box. Example: "1.6"
12. Enter the standard deviation associated with the mean of the second observation into the SD insert group 2 box. Example: "1.1"
13. Click Calculate.
14. Click Calculate and transfer to main window.
15. Leave the alpha value at 0.05, unless researchers want to change the alpha value according to the current empirical or clinical context.
16. 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.
17. Click Calculate.
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