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

SECTION 10.4 | Effect Size and Confidence Intervals for the Independent-Measures t 321
results of a t test. Now we use the APA format to report the results of Example 10.2, an
independent-measures t test. A concise statement might read as follows:
The students who were tested in a dimly lit room reported higher performance scores
(M = 12, SD = 2.93) than the students who were tested in the well-lit room (M = 8,
SD = 3.07). The mean difference was significant, t(14) = 2.67, p < .05, d = 1.33.
You should note that standard deviation is not a step in the computations for the independent-measures
t test, yet it is useful when providing descriptive statistics for each
treatment group. It is easily computed when doing the t test because you need SS and df
for both groups to determine the pooled variance. Note that the format for reporting t is
exactly the same as that described in Chapter 9 (page 287) and that the measure of effect
size is reported immediately after the results of the hypothesis test.
Also, as we noted in Chapter 9, if an exact probability is available from a computer
analysis, it should be reported. For the data in Example 10.2, the computer analysis
reports a probability value of p = .018 for t = 2.67 with df = 14. In the research report,
this value would be included as follows:
The difference was significant, t(14) = 2.67, p = .018, d = 1.33.
Finally, if a confidence interval is reported to describe effect size, it appears immediately
after the results from the hypothesis test. For the cheating behavior examples
(Example 10.2 and Example 10.7) the report would be as follows:
The difference was significant, t(14) = 2.67, p = .018, 95% CI [0.782, 7.218].
LEARNING CHECK
1. An independent-measures study with n = 8 in each treatment produces M = 86 for
the first treatment and M = 82 for the second treatment with a pooled variance of
16. What is Cohen’s d for these data?
a. 0.25
b. 0.50
c. 1.00
d. 2.00
2. An independent-measures study with n = 12 in each treatment produces M = 34
with SS = 44 for the first treatment and M = 42 with SS = 66 for the second treatment.
If the data are used to construct a 95% confidence interval for the population
mean difference, then what value will be at the center of the interval?
a. 0
b. 2.074
c. 8
d. 22
3. An independent-measures study with n = 10 in each treatment produces M = 35
for the first treatment and M = 30 for the second treatment. If the data are evaluated
with a hypothesis test and the decision is to reject the null hypothesis with
α = .05, then what value cannot be inside the 95% confidence interval for the
population mean difference?
a. 0
b. 2.101
c. 5
d. Impossible to determine without more information.