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

342 CHAPTER 11 | The t Test for Two Related Samples
error, the first step is to compute the variance (or the standard deviation) for the sample of
D scores.
s 2 5
SS
n 2 1 5 SS or s
df
5Î SS
df
The estimated standard error is then computed using the sample variance (or sample standard
deviation) and the sample size, n.
s
MD
5Î
s2
n
or s
MD
5
s
Ïn
(11.3)
The following example is an opportunity to test your understanding of variance and
estimated standard error for the repeated-measures t statistic.
EXAMPLE 11.1
A repeated-measures study with a sample of n = 8 participants produces a mean difference
of M D
= 5.5 points with SS = 224 for the difference scores. For these data, find the variance
for the difference scores and the estimated standard error for the sample mean. You
should obtain a variance of 32 and an estimated standard error of 2.
■
Notice that all of the calculations are done using the difference scores (the D scores) and
that there is only one D score for each subject. With a sample of n participants, the number
of D scores is n, and the t statistic has df = n − 1. Remember that n refers to the number
of D scores, not the number of X scores in the original data.
You should also note that the repeated-measures t statistic is conceptually similar to the
t statistics we have previously examined:
sample statistic 2 population parameter
t 5
estimated standard error
In this case, the sample data are represented by the sample mean of the difference scores
(M D
), the population parameter is the value predicted by H 0
(μ D
= 0), and the amount of
sampling error is measured by the standard error of the sample mean (s
MD
).
LEARNING CHECK
1. For the following data from a repeated-measures study, what is the sum of the
squared deviations (SS) for the difference scores? I II
a. 54
4 8
b. 18
9 3
c. 12
6 7
d. 0
8 9
2. For a repeated-measures hypothesis test, which of the following is the correct statement
of the alternative hypothesis (H 1
)?
a. For the individuals in the entire population there is no consistent difference
between the two treatments.
b. For the individuals in the entire population there is a consistent difference
between the two treatments.