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

SECTION 8.4 | Directional (One-Tailed) Hypothesis Tests 249
All researchers agree that one-tailed tests are different from two-tailed tests. However,
there are several ways to interpret the difference. One group of researchers contends that
a two-tailed test is more rigorous and, therefore, more convincing than a one-tailed test.
Remember that the two-tailed test demands more evidence to reject H 0
and thus provides a
stronger demonstration that a treatment effect has occurred.
Other researchers feel that one-tailed tests are preferable because they are more sensitive.
That is, a relatively small treatment effect may be significant with a one-tailed test
but fail to reach significance with a two-tailed test. Also, there is the argument that onetailed
tests are more precise because they test hypotheses about a specific directional effect
instead of an indefinite hypothesis about a general effect.
In general, two-tailed tests should be used in research situations when there is no strong
directional expectation or when there are two competing predictions. For example, a twotailed
test would be appropriate for a study in which one theory predicts an increase in
scores but another theory predicts a decrease. One-tailed tests should be used only in situations
when the directional prediction is made before the research is conducted and there
is a strong justification for making the directional prediction. In particular, if a two-tailed
test fails to reach significance, you should never follow up with a one-tailed test as a second
attempt to salvage a significant result for the same data.
LEARNING CHECK
1. A researcher is predicting that a treatment will increase scores. If this treatment
is evaluated using a directional hypothesis test, then the critical region for the
test ______.
a. would be entirely in the right-hand tail of the distribution
b. would be entirely in the left-hand tail of the distribution
c. would be divided equally between the two tails of the distribution
d. cannot answer without knowing the value of the alpha level
2. A sample is selected from a population with a mean of µ = 45 and a treatment
is administered to the sample. If the treatment is expected to produce a
decrease in the scores, then what would be the null hypothesis for a directional
hypothesis test?
a. µ ≥ 45
b. µ ≤ 45
c. M ≤ 45
d. M ≥ 45
3. A researcher expects a treatment to produce an increase in the population mean.
The treatment is evaluated using a one-tailed hypothesis test, and the test produces
z = –1.85. Based on this result, what is the correct statistical decision?
a. The researcher should reject the null hypothesis with α = .05 but not with
α = .01.
b. The researcher should reject the null hypothesis with either α = .05 or α = .01.
c. The researcher should fail to reject H 0
with either α = .05 or α = .01.
d. Cannot answer without additional information
ANSWERS
1. A, 2. A, 3. C