Download Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means)
The objectives of this lesson are to learn:
•
the definition/purpose of independent t-Test
•
when to use the independent t-Test
•
the use of SPSS to complete an independent t-Test
•
the interpretations of results
Definition
Independent t-Test involves examination of the significant differences on one factor or
dimension (dependent variable) between means of two independent groups (e.g., male vs.
female, with disability vs. without disability) or two experimental groups (control group
vs. treatment group). For example, you might want to know whether there is a significant
difference on the level of social activity between individuals with disabilities and
individuals without disabilities.
When to Use Independent t-Test
Any analysis where:
•
There is only one dimension or factor (dependent variable)
•
There are three or more groups of the factor (independent variable)
•
One is interested in looking at mean differences across two independent groups
Steps for Independent t-Test Using SPSS
We will use a step-by-step approach to go through the steps for an Independent t-Test
using SPSS statistical analysis package. Here is the background information of the
sample data we are using here.
Number of subjects: 60
Independent variable (Factor): Gender (male = 1, female = 2).
Dependent variable: Vocational rehabilitation service cost (VRS cost)
Data: Table 1
Table 1
M
3
4
9
6
6
5
5
5
6
9
5
0
0
8
2
8
9
8
2
1
5
0
0
5
5
5
5
0
5
5
a le
9 7 5
9 8 5
7 0 0
1 0 5 0
6 2 5
9 7 5
3 5 5
8 7 5
3 2 5
3 0 0
F e m a le
3
3
3
1
1
1
2
7
8
2
2
0
6
3
1
0
3
2
5
7
3
4
5
5
5
5
5
5
5
5
5
5
6
3
9
3
6
9
6
9
5
9
6
8
0
4
5
6
5
6
8
2
5
5
0
0
5
5
0
5
0
5
5
9
9
4
8
7
9
1
1
1
1
8
7
2
2
3
2
2
4
5
3
0
5
5
5
5
5
5
0
5
5
9 9
2 4 5
3 0 5
1 0 5 0
6 5 5
9 5 0
5 3 8
2 2 2
2 8 0
Steps for Independent t-Test:
Step 1 : A statement of statistical hypothesis
H 0 : µ1 = µ 2 or means for two groups are equal
There is no significant difference between genders in receiving vocational
rehabilitation service cost
H a : µ1 ≠ µ 2 ( µ1 f µ 2 or µ1 p µ 2 )
Step 2 : Setting the α level of risk associated with the null hypothesis (or Type I
error)
The level of Type I error is .05.
Step 3 & 4: Test statistic using SPSS/ interpreting results
Analyze ⇒ Compare Means ⇒ Independent t-Test (Figure 2)
Figure 2
Group 1 = Male = 1
Group 2 = Female = 2
Alpha
level = .05
SPSS Output and Interpretation
T-Test
Group Statistics
Gender
Males
Females
VR Cost
N
31
29
Mean
552.4516
578.7586
Std. Deviation
293.25357
324.83893
Std. Error
Mean
52.66990
60.32108
Interpretation:
This table displays the number of subjects, mean value of VRS cost, standard
deviation, and standard error for the test variable(s) within categories defined by
the grouping variable (Males and Females).
Since the Independent t Test procedure compares the two group means, it is useful
to know what the mean values are (Male mean = 552.4516, Female Mean =
578.7586).
Independent Samples Test
Levene's Test for
Equality of Variances
F
VR Cost
Equal variances
assumed
Equal variances
not assumed
.707
Sig.
.404
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-.330
58
.743
-26.3070
79.80332
-186.051
133.43669
-.329
56.382
.744
-26.3070
80.07965
-186.702
134.08782
Interpretation:
The Independent t Test procedure compares means for two groups of subjects.
If the significance value for the Levene test is high (greater that 0.05), use the
results that assume equal variances for both groups. Otherwise, Use the results
that do not assume equal variances for both groups. In our case, the equal
variances are assumed (p = .404 > .05).
A significance value of .743 (greater than .05) indicates that there is no significant
difference between the two group means.
Furthermore, the confidence interval for the mean difference contains zero within
its range. This also indicates that the difference is not significant.
If the significance value is high (typically greater than .05) and the confidence
interval for the mean difference contains zero, then you cannot conclude that there
is a significant difference between the two group means.
Step 5: Conclusion
Based on the results of independent t-Test (p = .743 > .05), we failed to reject the
null hypothesis (Ho). Therefore, we concluded that there was no significant difference
between male and female in VRS cost.