# Factors Affecting Power: Size of the Difference between Population Means
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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, µ

_{diff} , 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 µ

_{diff} 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, µ

_{diff} would be a positive number. The larger
the effect of the drug, the larger the value of µ

_{diff}.

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 μ

_{diff }(0,
10, 20, and 30) are shown on the next page. As you will see, the farther
the value of μ

_{diff }is from zero,
the smaller the

Type II error rate (β)
and therefore the larger the power.