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

310 CHAPTER 10 | The t Test for Two Independent Samples
10.3 Hypothesis Tests with the Independent-Measures t Statistic
LEARNING OBJECTIVES
6. Use the data from two samples to conduct an independent-measures t test
evaluating the significance of the difference between two population means.
7. Conduct a directional (one-tailed) hypothesis test using the independent-measures
t statistic.
8. Describe the basic assumptions underlying the independent-measures t hypothesis
test, especially the homogeneity of variance assumption, and explain how the
homogeneity assumption can be tested.
The independent-measures t statistic uses the data from two separate samples to help
decide whether there is a significant mean difference between two populations or between
two treatment conditions. A complete example of a hypothesis test with two independent
samples follows.
EXAMPLE 10.2
Research has shown that people are more likely to show dishonest and self-interested
behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010). In one
experiment, participants were given a set of 20 puzzles and were paid $0.50 for each one
solved in a 5-minute period. However, the participants reported their own performance and
there was no obvious method for checking their honesty. Thus, the task provided a clear
opportunity to cheat and receive undeserved money. One group of participants was tested
in a room with dimmed lighting and a second group was tested in a well-lit room. The
reported number of solved puzzles was recorded for each individual. The following data
represent results similar to those obtained in the study.
Number of Solved Puzzles
Well-Lit Room
Dimly Lit Room
11 6 7 9
9 7 13 11
4 12 14 15
5 10 16 11
n = 8 n = 8
M = 8 M = 12
SS = 60 SS = 66
STEP 1
STEP 2
State the hypotheses and select the alpha level.
H 0
: μ 1
− μ 2
= 0
H 1
: μ 1
− μ 2
≠ 0
(No difference.)
(There is a difference.)
We will set α = .05.
Directional hypotheses could be used and would specify whether the students who were
tested in a dimly lit room should have higher or lower scores.
This is an independent-measures design. The t statistic for these data has degrees
of freedom determined by
df = df 1
+ df 2
= (n 1
− 1) + (n 2
− 1)
= 7 + 7
= 14