Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 8.6 | Statistical Power 259
to determine the probability that their research will successfully reject the null hypothesis.
If the probability (power) is too small, they always have the option of increasing sample
size to increase power.
Alpha Level Reducing the alpha level for a hypothesis test also reduces the power of
the test. For example, lowering α from .05 to .01 lowers the power of the hypothesis test.
The effect of reducing the alpha level can be seen by looking at Figure 8.11. In this figure,
the boundaries for the critical region are drawn using α = .05. Specifically, the critical
region on the right-hand side begins at z = 1.96. If a were changed to .01, the boundary
would be moved farther to the right, out to z = 2.58. It should be clear that moving the
critical boundary to the right means that a smaller portion of the treatment distribution
(the distribution on the right-hand side) will be in the critical region. Thus, there would
be a lower probability of rejecting the null hypothesis and a lower value for the power
of the test.
One-Tailed vs. Two-Tailed Tests If the treatment effect is in the predicted direction,
then changing from a regular two-tailed test to a one-tailed test increases the power of
the hypothesis test. Again, this effect can be seen by referring to Figure 8.11. The figure
shows the boundaries for the critical region using a two-tailed test with α = .05 so that
the critical region on the right-hand side begins at z = 1.96. Changing to a one-tailed test
would move the critical boundary to the left to a value of z = 1.65. Moving the boundary
to the left would cause a larger proportion of the treatment distribution to be in the critical
region and, therefore, would increase the power of the test.
LEARNING CHECK
1. Which of the following defines the power of a hypothesis test?
a. The probability of rejecting a true null hypothesis
b. The probability of supporting true null hypothesis
c. The probability of rejecting a false null hypothesis
d. The probability of supporting a false null hypothesis
2. How does increasing the sample size influence the likelihood of rejecting the null
hypothesis and the power of the hypothesis test?
a. The likelihood of rejecting H 0
and the power of the test both increase.
b. The likelihood of rejecting H 0
and the power of the test both decrease.
c. The likelihood of rejecting H 0
increases but the power of the test is unchanged.
d. The likelihood of rejecting H 0
decreases but the power of the test is unchanged.
3. How does an increase in the value of σ influence the likelihood of rejecting the null
hypothesis and the power of the hypothesis test?
a. The likelihood of rejecting H 0
and the power of the test both increase.
b. The likelihood of rejecting H 0
and the power of the test both decrease.
c. The likelihood of rejecting H 0
increases but the power of the test is unchanged.
d. The likelihood of rejecting H 0
decreases but the power of the test is unchanged.
ANSWERS
1. C, 2. A, 3. B