366 PART 7 The Part of Tens

For example, imagine that you’ve calculated you need a sample size of 100 partici-

pants using α = 0.05 as your criterion for significance. Then your boss says you

have to apply a two-fold Bonferroni correction (see Chapter 11) and use α = 0.025

as your criterion instead. You need to increase your sample size to 100 x 1.2, or 120

participants, to have the same power at the new α level.

Adjusting for Unequal Group Sizes

When comparing means or proportions between two groups, you usually get the

best power for a given sample size — meaning it’s more efficient — if both groups

are the same size. If you don’t mind having unbalanced groups, you will need

more participants overall in order to preserve statistical power. Here’s how to

adjust the size of the two groups to keep the same statistical power:»

» ^{If you want one group twice as large as the other: Increase one group by}

50 percent, and reduce the other group by 25 percent. This increases the total

sample size by about 13 percent.»

» ^{If you want one group three times as large as the other: Reduce one}

group by a third, and double the size of the other group. This increases the

total sample size by about 33 percent.»

» ^{If you want one group four times as large as the other: Reduce one group}

by 38 percent and increase the other group by 250 percent. This increases the

total sample size by about 56 percent.

Suppose that you’re comparing two equal-sized groups, Drug A and Drug B. You’ve

calculated that you need two groups of 32, for a total of 64 participants. Now, you

decide to randomize group assignment using a 2:1 ratio for A:B. To keep the same

power, you’ll need 32

1 5

. , or 48 for Drug A, an increase of 50 percent. For B,

you’ll want 32

0 75

.

, or 24, a decrease of 25 percent, for an overall new total 72

participants in the study.

Allowing for Attrition

Sample size estimates apply to the number of participants who give you complete,

analyzable data. In reality, you have to increase this estimate to account for those

who will drop out of the study, or provide incomplete data for other reasons (called