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

246 CHAPTER 8 | Introduction to Hypothesis Testing
Usually a researcher begins an experiment with a specific prediction about the direction
of the treatment effect. For example, a special training program is expected to increase
student performance, or alcohol consumption is expected to slow reaction times. In these
situations, it is possible to state the statistical hypotheses in a manner that incorporates the
directional prediction into the statement of H 0
and H 1
. The result is a directional test, or
what commonly is called a one-tailed test.
DEFINITION
In a directional hypothesis test, or a one-tailed test, the statistical hypotheses
(H 0
and H 1
) specify either an increase or a decrease in the population mean. That
is, they make a statement about the direction of the effect.
The following example demonstrates the elements of a one-tailed hypothesis test.
EXAMPLE 8.3
Earlier, in Example 8.1, we discussed a research study that examined the effect of waitresses
wearing red on the tips given by male customers. In the study, each participant in a sample
of n = 36 was served by a waitress wearing a red shirt and the size of the tip was recorded.
For the general population of male customers (with waitresses wearing a white shirt), the
distribution of tips was roughly normal with a mean of μ = 15.8 percent and a standard
deviation of σ = 2.4 percentage points. For this example, the expected effect is that the
color red will increase tips. If the researcher obtains a sample mean of M = 16.5 percent
for the n = 36 participants, is the result sufficient to conclude that the red shirt really
increases tips?
■
■ The Hypotheses for a Directional Test
Because a specific direction is expected for the treatment effect, it is possible for the
researcher to perform a directional test. The first step (and the most critical step) is to state
the statistical hypotheses. Remember that the null hypothesis states that there is no treatment
effect and that the alternative hypothesis says that there is an effect. For this example,
the predicted effect is that the red shirt will increase tips. Thus, the two hypotheses
would state:
H 0
: Tips are not increased. (The treatment does not work.)
H 1
: Tips are increased. (The treatment works as predicted.)
To express directional hypotheses in symbols, it usually is easier to begin with the alternative
hypothesis (H 1
). Again, we know that the general population has an average of μ =
15.8, and H 1
states that this value will be increased with the red shirt. Therefore, expressed
in symbols, H 1
states,
H 1
: μ >15.8 (With the red shirt, the average tip is greater than 15.8 percent.)
The null hypothesis states that the red shirt does not increase tips. In symbols,
H 0
: μ ≤ 15.8 (With the red shirt, the average tip is not greater than 15.8.)
Note again that the two hypotheses are mutually exclusive and cover all of the possibilities.
Also note that the two hypotheses concern the general population of male customers, not
just the 36 men in the study. We are asking what would happen if all male customers were
served by a waitress wearing a red shirt.