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

358 CHAPTER 11 | The t Test for Two Related Samples
Chapter 15). The final table, which is split into two sections in Figure 11.5, shows the
results of the hypothesis test, including the mean and standard deviation for the difference
scores, the standard error for the mean, a 95% confidence interval for the mean difference,
and the values for t, df, and the level of significance (the p value for the test).
FOCUS ON PROBLEM SOLVING
1. Once data have been collected, we must then select the appropriate statistical analysis.
How can you tell whether the data call for a repeated-measures t test? Look at the
experiment carefully. Is there only one sample of subjects? Are the same subjects tested a
second time? If your answers are yes to both of these questions, then a repeated-measures
t test should be done. There is only one situation in which the repeated-measures t can be
used for data from two samples, and that is for matched-subjects studies (p. 337).
2. The repeated-measures t test is based on difference scores. In finding difference scores, be
sure you are consistent with your method. That is, you may use either X 2
– X 1
or X 1
– X 2
to
find D scores, but you must use the same method for all subjects.
DEMONSTRATION 11.1
A REPEATED-MEASURES t TEST
A major oil company would like to improve its tarnished image following a large oil spill.
Its marketing department develops a short television commercial and tests it on a sample
of n = 7 participants. People’s attitudes about the company are measured with a short
questionnaire, both before and after viewing the commercial. The data are as follows:
Person X 1
(Before) X 2
(After) D (Difference)
A 15 15 0
B 11 13 +2 ∑D = 21
C 10 18 +8
D 11 12 +1 M D
= 21/7 = 3.00
E 14 16 +2
F 10 10 0 SS = 74
G 11 19 +8
Was there a significant change? Note that participants are being tested twice—once
before and once after viewing the commercial. Therefore, we have a repeated-measures
design.
STEP 1
State the hypotheses, and select an alpha level The null hypothesis states that the
commercial has no effect on people’s attitude, or in symbols,
H 0
: μ D
= 0
(The mean difference is zero.)
The alternative hypothesis states that the commercial does alter attitudes about the
company, or
H 1
: μ D
≠ 0
(There is a mean change in attitudes.)
For this demonstration, we will use an alpha level of .05 for a two-tailed test.