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

328 CHAPTER 10 | The t Test for Two Independent Samples
DEMONSTRATION 10.1
THE INDEPENDENT-MEASURES t TEST
In a study of jury behavior, two samples of participants were provided details about a trial
in which the defendant was obviously guilty. Although group 2 received the same details as
group 1, the second group was also told that some evidence had been withheld from the jury
by the judge. Later the participants were asked to recommend a jail sentence. The length of
term suggested by each participant is presented here. Is there a significant difference between
the two groups in their responses?
Group 1 Group 2
4 3
4 7
3 8 for Group 1: M = 3 and SS = 16
2 5
5 4 for Group 2: M = 6 and SS = 24
1 7
1 6
4 8
There are two separate samples in this study. Therefore, the analysis will use the independentmeasures
t test.
STEP 1
State the hypothesis, and select an alpha level
H 0
: μ 1
− μ 2
= 0 (For the population, knowing evidence has been withheld has no
effect on the suggested sentence.)
H 1
: μ 1
− μ 2
≠ 0 (For the population, knowledge of withheld evidence has an effect
on the jury’s response.)
We will set the level of significance to α = .05, two tails.
STEP 2
STEP 3
Identify the critical region For the independent-measures t statistic, degrees of freedom
are determined by
df = n 1
+ n 2
− 2
= 8 + 8 − 2
= 14
The t distribution table is consulted, for a two-tailed test with α = .05 and df = 14. The critical
t values are +2.145 and −2.145.
Compute the test statistic As usual, we recommended that the calculation of the t statistic
be separated into three stages.
Pooled Variance For these data, the pooled variance equals
s 2 5 SS 1 SS 1 2 16 1 24
5
p
df 1
1 df 2
7 1 7 5 40
14 5 2.86
Estimated Standard Error Now we can calculate the estimated standard error for mean
differences.
s 5 sM1 2M 2
d Î s2 s
p
2 p
1
n 1
n 2
5Î
2.86
8 1 2.86 5 Ï0.358 1 0.358 5 Ï0.716 5 0.85
8