Independent and Paired Samples T-Test: Assumptions, Means, and Interpretation

Statistics
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22nd August 2018
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Exercise 31
1. Do the example data meet the assumptions for the independent samples t -test? Provide a
rationale for your answer.
Answer
The flowing assumptions were all met:
a. Normal distribution of the datasets.
b. Dependent variable measured on ratio or interval level.
c. Homogeneity of variance in the two groups, that is, the two groups need to have
equal variance.
d. The groups should be independent of each other.
e. A large sample size
2. If calculating by hand, draw the frequency distributions of the dependent variable, wages
earned. What is the shape of the distribution? If using SPSS, what is the result of the
Shapiro-Wilk test of normality for the dependent variable?
Answer
The shape of the distribution is bell-shaped, the results of the Shapiro-Wilk test are
shown in the table below. As can be seen, the p-value is .194 (a value greater than 5%
level of significance) which means that the null hypothesis of normality is not rejected
hence the data is normally distributed or follows a normal distribution.
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Support .155 20 .200* .935 20 .194
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
3. What are the means for two group’s wages earned?
Answer
The table for the comparison of the means of the two groups is given below. As can be
seen, the mean for the experimental group is $232.70 while that for the control group is
$128.40.
Group Statistics
Group N Mean
Std.
Deviation
Std. Error
Mean
Support 1 10 232.70 65.325 20.658
2 10 128.40 43.025 13.606
4. What is the independent samples t -test value?
Answer
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The value of the t-test is given as 4.217.
5. Is the t -test significant at a = 0.05? Specify how you arrived at your answer.
Answer
Yes based on the given t-value, the test is statistically significant at 55 level of
significance; this because the p-value for the test is 0.001 (a value less than 5% level of
significance).
Independent Samples Test
Levene's Test
for Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence Interval of
the Difference
Lower Upper
Support Equal variances assumed 2.477 .133 4.217 18 .001 104.300 24.736 52.332 156.268
Equal variances not assumed 4.217 15.572 .001 104.300 24.736 51.745 156.855
6. If using SPSS, what is the exact likelihood of obtaining a t -test value at least as extreme
or as close to the one that was actually observed, assuming that the null hypothesis is
true?
Answer
The given p-value is equivalent to the likelihood of making a type 1 error. The p-value
was 0.001, implying that there is a 0.1% likelihood that the null hypothesis is true.
7. Which group earned the most money post-treatment?
Answer
The group that earned the most money post-treatment is those with the assistance
program.
8. Write your interpretation of the results as you would in an APA-formatted journal.
Answer
An independent samples t-test was performed to test whether there is significant
difference in the earnings of the Veterans with disabilities for those who participated in a
work assistance program and those who did not participate in work assistance program.
Results showed that Veterans with disabilities who participated in a work assistance
program (M = $232.70, SD = $65.32, n = 10) earned significantly more money than those
veterans with disability who did not receive work assistance (M = $128.40, SD = $43.02,
n = 10), t(18) = 4.22, p = 0.001.
9. What do the results indicate regarding the impact of the supported employment
vocational rehabilitation on wages earned?
Answer
Results showed that supported employment vocational rehabilitation has a positive effect
on the wages earned by disabled veterans. Veteran with disabilities and participate in a
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