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

248 CHAPTER 8 | Introduction to Hypothesis Testing
For this example, the researcher obtained a mean of M = 16.5 percent for the 36 participants
who were served by a waitress in a red shirt. This sample mean corresponds to a
z-score of
z 5 M 2m 16.5 2 15.8
5 5 0.7
s M
0.4 0.4 5 1.75
A z-score of z = 1.75 is in the critical region for a one-tailed test (see Figure 8.8). This
is a very unlikely outcome if H 0
is true. Therefore, we reject the null hypothesis and conclude
that the red shirt produces a significant increase in tips from male customers. In the
literature, this result would be reported as follows:
Wearing a red shirt produced a significant increase in tips, z = 1.75, p < .05, one tailed.
Note that the report clearly acknowledges that a one-tailed test was used.
■ Comparison of One-Tailed vs. Two-Tailed Tests
The general goal of hypothesis testing is to determine whether a particular treatment has
any effect on a population. The test is performed by selecting a sample, administering the
treatment to the sample, and then comparing the result with the original population. If the
treated sample is noticeably different from the original population, then we conclude that
the treatment has an effect, and we reject H 0
. On the other hand, if the treated sample is still
similar to the original population, then we conclude that there is no convincing evidence
for a treatment effect, and we fail to reject H 0
. The critical factor in this decision is the size
of the difference between the treated sample and the original population. A large difference
is evidence that the treatment worked; a small difference is not sufficient to say that the
treatment has any effect.
The major distinction between one-tailed and two-tailed tests is in the criteria they
use for rejecting H 0
. A one-tailed test allows you to reject the null hypothesis when
the difference between the sample and the population is relatively small, provided the
difference is in the specified direction. A two-tailed test, on the other hand, requires a
relatively large difference independent of direction. This point is illustrated in the following
example.
EXAMPLE 8.4
Consider again the one-tailed test in Example 8.3 evaluating the effect of waitresses wearing
red on the tips from male customers. If we had used a standard two-tailed test, the
hypotheses would be
H 0
: μ = 15.8 (The red shirt has no effect on tips.)
H 1
: μ ≠ 15.8 (The red shirt does have an effect on tips.)
For a two-tailed test with α = .05, the critical region consists of z-scores beyond ±1.96.
The data from Example 8.3 produced a sample mean of M = 16.5 percent and z = 1.75.
For the two-tailed test, this z-score is not in the critical region, and we conclude that the red
shirt does not have a significant effect.
■
With the two-tailed test in Example 8.4, the 0.7-point difference between the sample
mean and the hypothesized population mean (M = 16.5 and μ = 15.8) is not big enough
to reject the null hypothesis. However, with the one-tailed test in Example 8.3, the same
0.7-point difference is large enough to reject H 0
and conclude that the treatment had a
significant effect.