Do the data meet criteria for homogeneity of variance? - Grand Canyon University

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High School ・Statistics ・MLA
  1. Does the data follow homogenous variance criteria? Provide a reason for your reply. The data fulfill homogeneity requirements for variance, because Levene statistics p = 0.455 suggest that the difference between the three groups is not important. Draw the frequency distribution of the dependent variable by hand when measuring it, working hours on work. What is the delivery form? What is the outcome of the normality test for the variable Shapiro-Wilk while using SPSS? What are the means for three groups’ hours worked on a job?The mean hours worked post-treatment for the supported employment group was 14.6 hours, treatment as usual-observational 15.20 hours and treatment as usual-randomized 26.0 hours.
  2. What are the F value and the group and error df for this data set.

The f value is 6.162 and the degree of freedom is 2 (between group) and 12 within groups.

  1. Is the F significant at α = 0.05? Specify how you arrived at your answer.
    F is significant at α = 0.05 because the p value obtained from the SPSS ANOVA (6.1) is larger that f critical obtained from the table, which is 3.4
  2. If using SPSS, what is the exact likelihood of obtaining an F 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 an F value at least as extreme as or close to the one observed is 0.14% (which is the same as the P value from ANOVA analysis multiplied with 100).
  3. Which group worked the most weekly job hours post-treatment? Provide a rationale for your answer.
    Treatment as usual-randomized group worked the most weekly job hours. Their mean work hours are 26.6 hours compared to treatment as usual-observational and supported employment group.
  4. Write your interpretation of the results as you would in an APA-formatted journal.
    A one-way ANOVA performed in the number of hours worked indicated significant differences among the three groups, F (2, 12) = 6.16, p = 0.014. Post hoc comparisons using Tukey HSD comparison test indicated that veterans with spinal injuries who received supported employment worked less hours (14.6) compared to those who received treatment as usual (26.6 hours).
  5. Is there a difference in your final interpretation when comparing the results of the LSD post hoc test versus Tukey HSD test? Provide a rationale for your answer.

    Yes, LSD is more lenient compared to Tukey HSD test.
  6. If the researcher decided to combine the two Treatment as Usual groups to represent an overall “Control” group, then there would be two groups to compare: Supported Employment versus Control. What would be the appropriate statistic to address the difference in hours worked between the two groups? Provide a rationale for your answer.

    T-test would be the most appropriate to address the difference in hours because t-test is ideal when compare the means of two groups.

Exercise 33 – SPSS Output

Descriptives

Hours worked post-treatment

 

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

Supported Employment

5

14.60

6.504

2.909

6.52

22.68

8

24

Treatment as usual-observational

5

15.20

3.701

1.655

10.60

19.80

9

18

Treatment as usual-randomized

5

26.60

7.436

3.326

17.37

35.83

15

35

Total

15

18.80

8.029

2.073

14.35

23.25

8

35

Test of Homogeneity of Variances

Hours worked post-treatment

Levene Statistic

df1

df2

Sig.

.840

2

12

.455

ANOVA

Hours worked post-treatment

 

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

457.200

2

228.600

6.162

.014

Within Groups

445.200

12

37.100

   

Total

902.400

14

     

Multiple Comparisons

Dependent Variable: Hours worked post-treatment

 

(I) Treatment Group

(J) Treatment Group

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

 

Lower Bound

Upper Bound

Tukey HSD

Supported Employment

Treatment as usual-observational

-.600

3.852

.987

-10.88

9.68

Treatment as usual-randomized

-12.000*

3.852

.023

-22.28

-1.72

Treatment as usual-observational

Supported Employment

.600

3.852

.987

-9.68

10.88

Treatment as usual-randomized

-11.400*

3.852

.030

-21.68

-1.12

Treatment as usual-randomized

Supported Employment

12.000*

3.852

.023

1.72

22.28

Treatment as usual-observational

11.400*

3.852

.030

1.12

21.68

LSD

Supported Employment

Treatment as usual-observational

-.600

3.852

.879

-8.99

7.79

Treatment as usual-randomized

-12.000*

3.852

.009

-20.39

-3.61

Treatment as usual-observational

Supported Employment

.600

3.852

.879

-7.79

8.99

Treatment as usual-randomized

-11.400*

3.852

.012

-19.79

-3.01

Treatment as usual-randomized

Supported Employment

12.000*

3.852

.009

3.61

20.39

Treatment as usual-observational

11.400*

3.852

.012

3.01

19.79

*. The mean difference is significant at the 0.05 level.

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