systolic blood pressure (SBP). You might set the effect size of 10 mmHg. You also know from prior

studies that the SD of the SBP change is known to be 20 mmHg. Then the equation is

, or

0.5, and you need

, or 64 participants in each group (128 total).

Comparing Means among Three, Four, or Five

Groups

Applies to: One-way Analysis of Variance (ANOVA) or Kruskal-Wallis test.

Effect size (E): The difference between the largest and smallest means among the groups divided

by the within-group SD.

Rule: You need

participants in each group.

Continuing the example from the preceding section, if you’re comparing three hypertension drugs —

Drug A, Drug B, and Drug C — and if any mean difference of 10 mmHg in SBP between any pair of

drug groups is important, then E is still

, or 0.5, but you now need

, or 80 participants

in each group (240 total).

Comparing Paired Values

Applies to: Paired Student t test or Wilcoxon Signed-Ranks test.

Effect size (E): The average of the paired differences divided by the SD of the paired differences.

Rule: You need

participants (pairs of values).

Imagine that you’re studying test scores in struggling students before and after tutoring. You determine

a six-point improvement in grade points is the effect size of importance, and the SD of the changes is

ten points. Then

, or 0.6, and you need

, or about 22 students, each of whom

provides a before score and an after score.

Comparing Proportions between Two Groups

Applies to: Chi-square test of association or Fisher Exact test.

Effect size (D): The difference between the two proportions (

and

) that you’re comparing.

You also have to calculate the average of the two proportions:

.

Rule: You need

participants in each group.

For example, if a disease has a 60 percent mortality rate, but you think your drug can cut this rate in

half to 30 percent, then

, or 0.45, and

, or 0.3. You need

, or 44 participants in each group (88 total).