Kruskal Wallis Test Samplesituation Hypothesis

 

Student Name: Christian A. Taghoy 

Semester/Year:

Course:

Submitted To: Dr. Edsel Inocian, Ph.D.

EDUC 602 – Inferential Statistics

Summer 2018

Kruskal-Wallis Test 

Situation:

Does physical exercise alleviate depression? We find some depressed people and check that they are all equivalently depressed to begin with. Then we allocate each person randomly to one of three groups: no exercise; 20 minutes of jogging per day; or 60 minutes of jogging per day. At the end of a month, we ask each participant to rate how depressed they now feel, on a Likert scale that runs from 1 ("totally miserable") through to 100 (ecstatically happy").   24 Persons Rating

No exercise

Jogging for 20 minutes 23 26 51 49 58 37 29 44

mean rating (SD):

39.63 (12.85)

Jogging for 60 minutes 22 27 39 29 46 48 49 65

40.63 (14.23)

59 66 38 49 56 60 56 62 55.75 (8.73)

Step 1: State the Problem

Is there a difference in the rating of depression between the 3 groups of people: no exercise, 20 minutes daily jogging, and 60 minutes daily jogging? 

Step 2: State the Hypothesis

H0 = There is no significant difference in the rating of depression between the 3 groups of people . Ha = There is significant difference in the rating of depression between the 3 groups of people.  

Step 3: Identify the Test statistic to be used & select a Level of Significance

Kruskal-Wallis Test; 

 = 0.05



 

  Step 4: Compute the Test Statistic

Using SPSS: 

Ranks  Condition Rating

N

Mean Rank

No Exercise

8

9.56

Jogging for 20 Minutes

8

9.94

Jogging for 60 Minutes

8

18.00

Total

24

Test Statisticsa,b  Rating Kruskal-Wallis H

7.290

df

2

 Asymp. Sig. a. Kruskal Wallis Test

.026

b. Grouping Variable: Condition

Descriptive Statistics  N

Mean

Std. Deviation

Minimum

Maximum

Rating

24

45.3333

13.85222

22.00

66.00

Condition

24

2.00

.834

1

3

Step 5: Formulate the Decision Rule, Critical Regions and state the Findings Decision Rule: Accept or fail to reject H0 if computed p-value (Sig.) is greater than 0.05 or reject the null

hypothesis H0 if p-value ≤ 0.05;  Finding: Sig. at 0.026 is lesser than  0.05

Step 6: Make a Decision

Reject the null hypothesis H0 

 

 

Step 7: Interpret the test results

There is significant difference in the rating of depression between the 3 groups of people.  

Step 8: Conclusion

At 0.05 level of significance, there is enough evidence to conclude that there is significant difference in

the rating of depression between the 3 groups of people: 1 st group - no exercise, 2nd group - 20 minutes daily jogging, and 3rd group - 60 minutes daily jogging.  Based on the mean rating between the groups, the 3rd group recorded the highest rating at 55 out of 100. The 1st and 2nd group does not seem to differ with their rating of depression at 39 and 40 respectively. 

Step 9: Implications

Jogging even for just an hour daily seems to improve our mood and makes us happier. happier. As a form of an exercise, jogging keeps your weight in check, makes you stronger, and keeps you feeling youthful and staying active into old age. So next time you’re feeling depressed, try a hard workout — you’ll feel happier for days on end.