Sample size for ANOVA
Effect size is the difference in means between three groups on the outcome
In order to run an a priori sample size calculation in a between-subjects design using a continuous outcome with three or more independent groups or levels, researchers will need to seek out evidence that provides the means and standard deviations of the outcome in the independent groups or levels. The differences between the three mean values and their respective variances constitute the evidence-based measure of effect size.
A good rule of thumb is to overestimate the standard deviation of the effect size among the three groups. 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 a) people in a medication treatment group sleep an average of 7.5 hours a night with a standard deviation of 2.2, b) people in a diet group sleep an average of 6.7 hours a night with a standard deviation of 2.1, and c) the control group sleeps an average of 7.1 hours with a standard deviation of 1.9. The groups were equally sized with 30 participants in each group. Rsearchers 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 among the groups.
A good rule of thumb is to overestimate the standard deviation of the effect size among the three groups. 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 a) people in a medication treatment group sleep an average of 7.5 hours a night with a standard deviation of 2.2, b) people in a diet group sleep an average of 6.7 hours a night with a standard deviation of 2.1, and c) the control group sleeps an average of 7.1 hours with a standard deviation of 1.9. The groups were equally sized with 30 participants in each group. Rsearchers 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 among the groups.
The steps for calculating sample size for an ANOVA in G*Power
1. Start up G*Power.
2. Under the Test family drop-down menu, select F tests.
3. Under the Statistical test drop-down menu, select ANOVA: Fixed effects, omnibus, one-way.
4. Under the Type of power analysis drop-down menu, select A priori: Compute required sample size - given alpha, power, and effect size.
5. In the Number of groups box, enter the number of independent groups or levels being compared. Example: "3"
6. Click the Determine button.
7. In the SD within each group box, enter the standard deviation researchers expect there to be within the independent groups. Example: "2.1"
8. Enter the mean for the first group into the Mean box for Group 1. Example: "7.5"
9. Enter the group size (n) for the first group into the Size box for Group 1. Example: "30"
10. Enter the mean for the second group into the Mean box for Group 2. Example: "6.7"
11. Enter the group size (n) for the second group into the Size box for Group 2. Example: "30"
12. Enter the mean for the third group into the Mean box for Group 3. Example: "7.1"
13. Enter the group size (n) for the third group into the Size box for Group 3. Example: "30"
14. Click Calculate.
15. Click Calculate and transfer to main window.
16. Leave the alpha value at 0.05, unless researchers want to change the alpha value according to the current empirical or clinical context.
17. 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.
18. Click Calculate.
2. Under the Test family drop-down menu, select F tests.
3. Under the Statistical test drop-down menu, select ANOVA: Fixed effects, omnibus, one-way.
4. Under the Type of power analysis drop-down menu, select A priori: Compute required sample size - given alpha, power, and effect size.
5. In the Number of groups box, enter the number of independent groups or levels being compared. Example: "3"
6. Click the Determine button.
7. In the SD within each group box, enter the standard deviation researchers expect there to be within the independent groups. Example: "2.1"
8. Enter the mean for the first group into the Mean box for Group 1. Example: "7.5"
9. Enter the group size (n) for the first group into the Size box for Group 1. Example: "30"
10. Enter the mean for the second group into the Mean box for Group 2. Example: "6.7"
11. Enter the group size (n) for the second group into the Size box for Group 2. Example: "30"
12. Enter the mean for the third group into the Mean box for Group 3. Example: "7.1"
13. Enter the group size (n) for the third group into the Size box for Group 3. Example: "30"
14. Click Calculate.
15. Click Calculate and transfer to main window.
16. Leave the alpha value at 0.05, unless researchers want to change the alpha value according to the current empirical or clinical context.
17. 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.
18. Click Calculate.
Based on the values from the example and the steps above, an alpha of .05 and power of .80 with three equally sized groups yields a total sample size of 402 to have adequate statistical power.
Click on the Statistics button to continue.
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