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

SECTION 8.2 | Uncertainty and Errors in Hypothesis Testing 239
FIGURE 8.6
The locations of the critical
region boundaries for three
different levels of significance:
α = .05, α = .01,
and α = .001.
23.30
21.96
22.58
0
m from H 0
a 5 .05
a 5 .01
a 5 .001
1.96
2.58
3.30
z
treatment does have an effect, the sample data must be in the critical region. If the treatment
really has an effect, it should cause the sample to be different from the original population;
essentially, the treatment should push the sample into the critical region. However, as the
alpha level is lowered, the boundaries for the critical region move farther out and become
more difficult to reach. Figure 8.6 shows how the boundaries for the critical region move
farther into the tails as the alpha level decreases. Notice that z = 0, in the center of the distribution,
corresponds to the value of μ specified in the null hypothesis. The boundaries for
the critical region determine how much distance between the sample mean and μ is needed
to reject the null hypothesis. As the alpha level gets smaller, this distance gets larger.
Thus, an extremely small alpha level, such as .000001 (one in a million), would mean
almost no risk of a Type I error but would push the critical region so far out that it would
become essentially impossible to ever reject the null hypothesis; that is, it would require
an enormous treatment effect before the sample data would reach the critical boundaries.
In general, researchers try to maintain a balance between the risk of a Type I error
and the demands of the hypothesis test. Alpha levels of .05, .01, and .001 are considered
reasonably good values because they provide a low risk of error without placing excessive
demands on the research results.
LEARNING CHECK
1. When does a researcher risk a Type I error?
a. anytime H 0
is rejected
b. anytime H 1
is rejected
c. anytime the decision is “fail to reject H 0
”
d. All of the other options are correct.
2. Which of the following defines a Type II error?
a. rejecting a false null hypothesis
b. rejecting a true null hypothesis
c. failing to reject a false null hypothesis
d. failing to reject a true null hypothesis