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

FOCUS ON PROBLEM SOLVING 261
8. The power of a hypothesis test is defined as the
probability that the test will correctly reject the null
hypothesis.
9. To determine the power for a hypothesis test, you must
first identify the treatment and null distributions. Also,
you must specify the magnitude of the treatment effect.
Next, you locate the critical region in the null distribution.
The power of the hypothesis test is the portion
of the treatment distribution that is located beyond the
boundary (critical value) of the critical region.
10. As the size of the treatment effect increases, statistical
power increases. Also, power is influenced
by several factors that can be controlled by the
experimenter:
a. Increasing the alpha level increases power.
b. A one-tailed test has greater power than a twotailed
test.
c. A large sample results in more power than a small
sample.
KEY TERMS
hypothesis testing (225)
null hypothesis (228)
alternative hypothesis (228)
level of significance (230)
alpha level (230)
critical region (230)
test statistic (233)
Type I error (236)
Type II error (237)
beta (238)
significant (241)
directional test (246)
one-tailed test (246)
effect size (251)
Cohen’s d (251)
power (255)
SPSS ®
The statistical computer package SPSS is not structured to conduct hypothesis tests using
z-scores. In truth, the z-score test presented in this chapter is rarely used in actual research
situations. The problem with the z-score test is that it requires that you know the value of
the population standard deviation, and this information is usually not available. Researchers
rarely have detailed information about the populations that they wish to study. Instead, they
must obtain information entirely from samples. In the following chapters we introduce new
hypothesis-testing techniques that are based entirely on sample data. These new techniques are
included in SPSS.
FOCUS ON PROBLEM SOLVING
1. Hypothesis testing involves a set of logical procedures and rules that enable us to make
general statements about a population when all we have are sample data. This logic is
reflected in the four steps that have been used throughout this chapter. Hypothesis-testing
problems will become easier to tackle when you learn to follow the steps.
STEP 1
STEP 2
STEP 3
STEP 4
State the hypotheses and set the alpha level.
Locate the critical region.
Compute the test statistic (in this case, the z-score) for the sample.
Make a decision about H 0
based on the result of Step 3.
2. Students often ask, “What alpha level should I use?” Or a student may ask, “Why is an alpha
of .05 used?” as opposed to something else. There is no single correct answer to either of
these questions. Keep in mind the aim of setting an alpha level in the first place: to reduce
the risk of committing a Type I error. Therefore, the maximum acceptable value is α = .05.
However, some researchers prefer to take even less risk and use alpha levels of .01 or smaller.