Grand Canyon University: Workbook Exercises 31 & 32 (Statistics Project Sample)

Workbook Exercises 31 & 32
Name
Grand Canyon University
1
Exercise 31
1 Do the example data meet the assumptions for the independent samples t-test? Provide a rationale for your answer.The data meet the assumption for the independent samples t-test because the participants the first group are different from those in the second group. Take, for instance, the participants in the treatment group runs from 1 to 10 with no number repeated with the participants in the control group run from 11 to 20, again with no number repeated. This makes the two data from the two groups to be statistically different.
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? (Instructor’s note: Use SPSS for this question.)
The Shapiro-Wilk p-Value for the weekly wages was 0.194. The p-Value indicates that the frequency distribution did not significantly deviate from normality.
3 What are the means for two group’s wages earned?
The mean for the weekly wages earned for the treatment group was 232.7 while the mean for the weekly wages earned for the control group was 128.4. However, the combined mean of the two group was 180.55
4 What is the independent samples t-test value?The independent sample t-test value for the weekly wages earned by the treatment group is t = 4.217.
5 Is the t-test significant at a = 0.05? Specify how you arrived at your answer.
At a = 0.05, the t-values is statistically significance. We arrived at this answer by comparing the t-value of 4.217 with the lower limit of 52.33 and upper limit of 156.27. the value 4.217 lies outside the two limits.
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? (Instructor’s note: Use SPSS for this question.)
Using the SPSS, we find that there is a 95% chance of obtaining a t-test value at least as an extreme or close to the one observed.
7 Which group earned the most money post-treatment?The total weekly wage earned by treatment group was $2,327 while the total weekly wage earned by control group was 1,284. It therefore, follows that the treatment group earned the most money post treatment
8 Write your interpretation of the results as you would in an APA-formatted journal.With a sample of size n = 20 for the treatment group, a = 0.05 > t = 4.217, the result indicated statistical significance for the t-test. It, therefore, follows that there is no difference between participants’ number and weekly wages earned.
9 What do the results indicate regarding the impact of the supported employment vocational rehabilitation on wages earned?
The results indicate that supported vocational rehabilitation has significant impacts on wages earned for both the treatment and control groups.
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 determine the difference between the two groups. This is because our analysis gave us a level of significance at alpha = 0.05.
Exercise 32
1 Do the example data meet the assumptions for the paired samples t-test? Provide a rationale for your answer.
Yes, the data sample meet the criteria for “paired sample t-test. This is because the sample variables have been collected from a single group of participants with similar characteristics for baseline and post-treatment probing.
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? (Instructor’s note: Use SPSS for this question.)
The Shapiro-Wilk p-Value for the weekly wages was 0.716. The p-Value indicates that the frequency distribution did not significantly deviate from normality.
3 What are the means for the baseline and posttreatment affective distress scores, respectively?The mean for the baseline affective distress was 3.030 while the mean for the Post Treatment Distress was 2.040.
4 What is the paired samples t-test value? The paired samples t-test value is 2.865.
5 Is the t-test significant at α = 0.05? Specify how you arrived at your answer.At α = 0.05, the t-test is significant. We arrived at this answer by using the calculated p-Value of 0.019, which is less than the α = 0.05.
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? (Instructor’s note: Use SPSS for this question.)the exact likelihood of obtaining a t-test value at least as an extreme as or as close to the one that was actually observed if we assume that the null hypothesis is true will be more than 0.099% but less than 0.1%.
7 On average, did the affective distress scores improve or deteriorate over time? Provide a rationale for your answer.
On average, the affective scores deteriorated overtime but finally became constant. The constant value in affective distress are represented by a constant Q-Q line for the baseline and post-treatment affective distress.
8 Write your interpretation of the results as you would in an APA-formatted journal.The paired sample t-test calculated from baseline affective distress and post-treatment affective distress revealed deteriorating of distress scores over time, t(9) = 2.865, p >0.001; mean = 3.03 and 2.04 for the two tests. Therefore, the mode of treatment is effective for affective distress.
9 What do the results indicate regarding the impact of the rehabilitation on emotional distress levels?The results indicate that rehabilitation lowers emotional distress levels among patients.
10 What are the weaknesses of the design in this example?
It may be hard to determine whether or not the changes in one sample have been caused by the intervention program. The design does not take into consideration other factors that may have contributed towards the changes.
Exercise 31 – SPSS Output
Case Processing Summary


Group

Cases



Valid

Missing

Total



N

Percent

N

Percent

N

Percent

WeeklyWage


20

100.0%

0

0.0%

20

100.0%

Tests of Normality


Group

Kolmogorov-Smirnova

Shapiro-Wilk



Statistic

df

Sig.

Statistic

df

Sig.

WeeklyWage


.155

20

.200*

.935

20

.194

*. This is a lower bound of the true significance.

a. Lilliefors Significance Correction

WeeklyWage Stem-and-Leaf Plot for
Group=
Frequency Stem & Leaf
3.00 0 . 777
4.00 1 . 2344
5.00 1 . 55667
4.00 2 . 0012
2.00 2 . 59
2.00 3 . 33
Stem width: 100.00
Each leaf: 1 case(s)
Descriptive Statistics


N

Minimum

Maximum

Mean

Std. Deviation

WeeklyWage

20

70.00

330.00

180.5500

75.90123

Valid N (listwise)

20





Group Statistics


Group

N

Mean

Std. Deviation

Std. Error Mean

WeeklyWage

Participant#TreatmentGroup

10

232.7000

65.32491

20.65755


Participant#ControlGroup

10

128.4000

43.02506

13.60572

Independent Samples Test

Levene’s Test for Equality of Variances

t-test for Equality of Means



F

Sig.

t

df,

Sig.(2-tailed)

Mean Diff.

STD. Error Difference

95% Confidence Interval of the Difference










Lower

Upper

Weekly Wage

Equal Variance assumed
Equal variance not assumed

2.4
77

.133

4.217
4.217

18
15.572

.001
.001

104.30000
104.30000

24.73560
24.73560

52.33243
51.74540

156.26757
156.85460

Exercise 32 – SPSS Output
Descriptive Statistics


N

Minimum

Maximum

Mean

Std. Deviation

BaselineAffectiveDistressScores

10

.3

5.2

3.030

1.6640

PostTreatmentAffectiveDistress

10

.7

3.7

2.040

.9834

Valid N (listwise)

10





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