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

DEMONSTRATION 11.2 359
STEP 2
Locate the critical region Degrees of freedom for the repeated-measures t test are
obtained by the formula
For these data, degrees of freedom equal
df = n − 1
df = 7 − 1 = 6
The t distribution table is consulted for a two-tailed test with α = .05 for df = 6. The
critical t values for the critical region are t = ±2.447.
STEP 3
Compute the test statistic Once again, we suggest that the calculation of the t statistic
be divided into a three-part process.
Variance for the D Scores The variance for the sample of D scores is
s 2 5
SS
n 2 1 5 74 6 5 12.33
Estimated Standard Error for M D
The estimated standard error for the sample mean
difference is computed as follows:
s 5Î s2
MD
n
Î 5 12.33 5 Ï1.76 5 1.33
7
The Repeated-Measures t Statistic Now we have the information required to calculate
the t statistic.
t 5 M D 2m D
s
MD
5 3 2 0
1.33 5 2.26
STEP 4
Make a decision about H 0
, and state the conclusion The obtained t value is not extreme
enough to fall in the critical region. Therefore, we fail to reject the null hypothesis. We
conclude that there is no evidence that the commercial will change people’s attitudes,
t(6) = 2.26, p > .05, two-tailed. (Note that we state that p is greater than .05 because
we failed to reject H 0
.)
DEMONSTRATION 11.2
EFFECT SIZE FOR THE REPEATED-MEASURES t
We will estimate Cohen’s d and calculate r 2 for the data in Demonstration 11.1. The data
produced a sample mean difference of M D
= 3.00 with a sample variance of s 2 = 12.33.
Based on these values, Cohen’s d is
estimated d 5
mean difference
standard deviation 5 M D
s 5 3.00
Ï12.33 5 3.00
3.51 5 0.86
The hypothesis test produced t = 2.26 with df = 6. Based on these values,
r 2 5
t2
t 2 1 df 5 s2.26d2
s2.26d 2 1 6 5 5.11 5 0.46 sor 46%d
11.11