CHAPTER 25 Ten Easy Ways to Estimate How Many Participants You Need 365

Scaling from 80 Percent to

Some Other Power

Here’s how you take a sample-size estimate that provides 80 percent power from

one of the preceding rules and scale it up or down to provide some other power:»

» ^{For 50 percent power: Use only half as many participants — multiply the}

estimate by 0.5.»

» ^{For 90 percent power: Increase the sample size by 33 percent — multiply the}

estimate by 1.33.»

» ^{For 95 percent power: Increase the sample size by 66 percent — multiply the}

estimate by 1.66.

For example, if you know from doing a prior sample size calculation that a study

with 70 participants provides 80 percent power to test its primary objective,

then a study that has 1 33

70

.

, or 93 participants will have about 90 percent

power to test the same objective. The reason to consider power of levels other than

80 percent is because of limited sample. If you know that 70 participants provides

80 percent power, but you will only have access to 40, you can estimate maximum

power you are able to achieve.

Scaling from 0.05 to Some

Other Alpha Level

Here’s how you take a sample-size estimate that was based on testing at the

α = 0.05 level, and scale it up or down to correspond to testing at some other

α level:»

» ^{For α = 0.10: Decrease the sample size by 20 percent — multiply the}

estimate by 0.8.»

» ^{For α = 0.025: Increase the sample size by 20 percent — multiply}

the estimate by 1.2.»

» ^{For α = 0.01: Increase the sample size by 50 percent — multiply the}

estimate by 1.5.