Independent t-Test
CJ 526 Statistical Analysis in
Criminal Justice
When to Use an Independent t-Test
Two samples
2. Interval or ratio level dependent variable
Either
Experimental and control group comparison
Or
Comparing two separate independent groups
(no overlap)
1.
Characteristics of an Independent tTest
1.
Sample means are hypothesized to be the
same. Either
1.
2.
Treatment has no effect, comparing an
experimental that received treatment and a
control group that did not receive treatment
Or, two independent groups are the same with
respect to a DV
Example of an Independent t-Test

A psychologist wants to determine
whether diversity training has an effect on
the number of complaints filed against
employees. He/she randomly assigns 20
employees to a training group, and 20
employees to a control group.
Example of an Independent t-Test -continued
1.
Number of Groups: 2
2.
Nature of Groups: independent
3.
Independent Variable: training
Dependent variable: number of
complaints
4.
Example of an Independent t-Test -continued
5. Dependent Variable and its Level of
Measurement: complaints--interval
6. Target Population: employees
7. Appropriate Inferential Statistical
Technique: t-test
8. One or two-tailed? Probably one tail
Example of an Independent t-Test -continued
9. Null Hypothesis:
1.
Mean of exp group – mean of control group = 0
10. Alternative Hypothesis:
Mean of experimental group minus mean of control
group does not equal 0
11. Decision Rule:
1.
If the p-value of the obtained test statistic is less
than .05, reject the null hypothesis
Example of an Independent t-Test -continued
12. Obtained Test Statistic: t
13. Decision: accept or reject null hypothesis
Null hypothesis—training did not affect complaints,
comparing experimental and control groups
Alternative, one tail—training reduced complaints as
compared to a control group without training
See p. 725
Results Section


The results of the Independent t-Test using
diversity training as the independent
variable and number of complaints filed
against employees were statistically
significant, t (18) = 2.35, p < .05.
D.f. degrees of freedom = n(group
1)+n(group 2) - 2
Discussion Section


It appears that employees undergoing
diversity training have fewer complaints
filed against them.
Or, if the null hypothesis was retained, the
conclusion would be that diversity training
did not affect the number of complaints
filed
SPSS Independent-Samples tTest Procedure

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
Analyze, Compare Means, IndependentSamples t-Test
Move DV over to Test Variables
Move IV over to Grouping Variable

Enter numerical values of the IV under
Define Groups
SPSS Independent-Samples t-Test
Sample Printout
T-Test
Group Statistics
Score on Drink Index
Gender of Respondent
Female
Male
N
10
10
Mean
23.80
28.70
Std. Deviation
14.816
14.833
Std. Error
Mean
4.685
4.691
Independent Samples Test
Levene's Test for
Equality of Variances
F
Score on Drink Index
Equal variances
as sumed
Equal variances
not ass umed
.086
Sig.
.773
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-.739
18
.469
-4.90
6.630
-18.828
9.028
-.739
18.000
.469
-4.90
6.630
-18.828
9.028
SPSS Independent-Samples tTest Printout

Group Statistics






DV
Levels of IV
N: Sample size
Mean
Standard Deviation
Standard Error of the Mean
SPSS Independent-Samples tTest Printout -- continued

Levene’s Test for Equality of Variances


Test for homogeneity of variance assumption
t-Test for Equality of Means

If Levene test is not significant


Equal variances assumed
If Levene test is significant

Equal variances not assumed
SPSS Independent-Samples tTest Printout -- continued

t-Test for Equality of Means



t: obtained test statistic
df: degrees of freedom
Sig: p-value


Divide by 2 to get one-tailed p-value
Mean Difference

Difference between the two sample means
SPSS Independent-Samples tTest Printout -- continued


Standard Error of the Difference
95% Confidence Interval of the Difference


Lower
Upper