46 PART 1 Getting Started with Biostatistics

For very large effect sizes, the power approaches 100 percent. For very small

effect sizes, you may think the power of the test would approach zero, but you

can see from Figure 3-3 that it doesn’t go down all the way to zero. It actually

approaches the α level of the test. (Keep in mind that the α level of the test is

the probability of the test producing a significant result when no effect is

truly present.)»

» ^{Sample size versus effect size, for various values of power: For all}

statistical tests, sample size and effect size are inversely related, if other variables

including α level and power are held constant. Small effects can be detected

only with large samples, and large effects can often be detected with small

samples. This relationship is illustrated in Figure 3-4.

FIGURE 3-3:

The power of a

statistical test

increases as the

effect size

increases.

© John Wiley & Sons, Inc.

FIGURE 3-4:

Smaller effects

need larger

samples.

© John Wiley & Sons, Inc.