362 PART 7 The Part of Tens

that’s less than 0.05 when you run the test if a true difference of your effect size

does indeed exist. In other words, we are setting the parameters 80 percent power

at α = 0.05, because they are widely used in biological research. The remaining

four sections tell you how to modify your estimate for other power or α values, and

how to adjust your estimate for unequal group size and dropouts from the study.

Comparing Means between Two Groups»

» ^{Applies to: Unpaired Student t test, Mann-Whitney U test, and Wilcoxon}

Sum-of-Ranks test.»

» ^{Effect size (E): The difference between the means of two groups divided by}

the standard deviation (SD) of the values within a group.»

» ^{Rule: You need 16}

2

/E participants in each group, or 32

2

/E participants

altogether.

For example, say you’re comparing two hypertension drugs  — Drug A and

Drug B — on lowering 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 E

10 20

/

, or 0.5, and you need

16

0 5 ²

/

.

, 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 20}

2

/E 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

10 20

/

, or 0.5, but you now need 20

0 5 ²

/

.

, or 80 participants in each group (240

total).