© John Wiley & Sons, Inc.

FIGURE 3-3: The power of a statistical test increases as the effect size increases.

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.