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1. Do the example data meet the assumptions for the independent
samples t -test? Provide a rationale for your answer.
The
assumptions being the variable measured on a continuous or ordinal scale, the
sample is random, the sample size is big enough, normal distribution is seen
when the data is plotted, and there is homogeneity of variance.
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?
The
shape of the distribution is a standard shape; the results of the Shapiro-Wilk
test is shown below. The Shapiro-Wilk
significance is .194 shows that it is above the 0.05 alpha level of the null
hypothesis that the distribution is normal.
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?
The
means for the two group are $232.70 for the experimental, and $128.40 for the
control.
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?
The t-test value is 4.217.
5.
Is the t -test significant at a = 0.05? Specify how you arrived at your answer.
The
t-test is significant at the ?= 0.05, with a t-value of 4.217 and 18 degrees of
freedom, a value chart with show that it is significant to the p = 0.001
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?
The
probability of making a type 1 error would be the p- value gotten. This was
0.001, which means there is a 0.1% possibility that the null hypothesis is
true.
7.
Which group earned the most money post-treatment?
The
group with assistance program earned the most money post treatment.
8.
Write your interpretation of the results as you would in an APA-formatted
journal.
Veterans
with disabilities (n = 10) who participated in a work assistance program earned
significantly more money (M = $232.70, SD = $65.32) than those veterans (n =
10) with disability who did not receive work assistance (M = $128.40, SD =
$43.02, t(18) = 4.217, p = 0.001).
9.
What do the results indicate regarding the impact of the supported employment
vocational rehabilitation on wages earned?
An
independent samples t-test demonstrated that employment occupational
rehabilitation positively affects the wages earned by impaired veterans. This
program might be advantageous for a few and further research is justified.
10.
Was the sample size adequate to detect significant differences between the two
groups in this example? Provide a rationale for your answer.
The
sample size was adequate to detect significant differences between these two
groups. This can be found in the glaring
difference between the mean measure of cash earned, the p value, t value, and
the confidence interval between groups.
Exercise
32
1. Do the example data meet the
assumptions for the paired samples t -test? Provide a rationale for your
answer.
Yes, data measured is from only one
group of individuals with a normal distribution of scores. The dependent
variable is measured at an interval level. The only difference between the
groups is that the paired scores are independent.
2. If calculating by hand, draw the
frequency distributions of the two variables. What are the shapes of the
distributions? If using SPSS, what are the results of the Shapiro-Wilk tests of
normality for the two variables?
The shape of the distribution
between the two groups is leptokurtic.
Tests
of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
PDbaseline
.286
10
.020
.885
10
.149
PDposttx
.224
10
.168
.911
10
.287
3. What are the means for the
baseline and posttreatment affective distress scores, respectively?
The baseline mean is 5.3 and the post
treatment mean is 3.3
Paired
Samples Statistics
Mean
N
Std.
Deviation
Std.
Error Mean
Pair 1
PDbaseline
5.2000
10
.91894
.29059
PDposttx
3.3000
10
.94868
.30000
4. What is the paired samples t
-test value?
The paired samples for the t test value is
10.59.
Paired
Samples Test
Paired
Differences
t
df
Sig.
(2-tailed)
Mean
Std.
Deviation
Std.
Error Mean
95%
Confidence Interval of the Difference
Lower
Upper
Pair 1
PDbaseline – PDposttx
1.90000
.56765
.17951
1.49393
2.30607
10.585
9
.000
5. Is the t -test signi?cant at ? =
0.05? Specify how you arrived at your answer.
Yes, at the point when the alpha is
resolved it relies upon how extreme the reactions are. The lower the alpha, the
more serious the consequences are so you need as precise an investigation as
could be expected under the circumstances. On the off chance that the alpha is
a higher number the less consequences the side effects. The study is conducted
on peridontitis which has side effects of a low severity level. Therefore, an
alpha of 0.05 is appropriate.
6. If using SPSS, what is the exact
likelihood of obtaining a t- test value at least as extreme as or as close to
the one that was actually observed, assuming that the null hypothesis is true?
Assuming a true null hypothesis, P< 0.001 would be the likelihood of such a t-test being obtained. 7. On average, did the affective distress scores improve or deteriorate over time? Provide a rationale for your answer. Overall the scores got worse as time progressed. There were only two individuals that improved. Only 20% of the individuals were better. 8. Write your interpretation of the results as you would in an APA-formatted journal. After performing t tests for both groups the study concluded that the group treated for peridontitis had a lower probing depth from baseline to post-treatment. The t value was 10.59 and P was <0.001. 9. What do the results indicate regarding the impact of the rehabilitation on emotional distress levels? There is a significant decrease in distress after treatment, indicating the treatment is effective. The t value is 2.89 and P is < 0.05 indicating that the null hypothesis can be rejected. 10. What are the weaknesses of the design in this example? Appears to be a pilot study with a low sample size. Although it will help in the creation of further, larger studies, the results of this study can only be interpreted with caution and are certainly not generalizable.