Factors Affecting Power: Size of the Difference between Population Means (1 of 3)
The size of the difference between population means is an important factor in determining power. Naturally, the more the means differ from each other, the easier it is to detect the difference. In the example, the difference between means, µdiff , is the population mean difference score. It represents the size of the drug effect. For instance, if there were no difference between the drug and the placebo, then µdiff would be zero and there would be no effect of the drug. If the drug slows people down and, as a result, increases reaction time, µdiff would be a positive number. The larger the effect of the drug, the larger the value of µdiff.
Assume that the standard deviation and sample size are: σ = 50 and N = 25. (Also assume the experimenter knew the value of σ in order to make the calculations easier. The same principles would apply if the standard deviation had to be estimated.) The null hypothesis would then be rejected at the 0.05 level if M were larger than 19.6 or less than -19.6. (Click here for calculations.) The sampling distribution of M for four values of μdiff (0, 10, 20, and 30) are shown on the next page. As you will see, the farther the value of μdiff is from zero, the smaller the Type II error rate (β) and therefore the larger the power.