Practice exam #4

You want to know whether there is some difference in the amount of sporting events attended for 3 different groups of people: (a) psychology majors, (b) physical education majors, and (c) business majors. In order to test this hypothesis, you randomly select members of each group and find out how many sporting events they each have attended in the past year. You assume an alpha level of p < .01. Here are the scores:

number of sporting events attended in past year:

(Psychology majors)

X₁

1

0

2

(Physical education majors)

X₂

8

10

12

(Business majors)

X₃

0

0

3

1. In terms of H₀, H₁, m₁, m₂, and m₃, write out the research hypothesis and null hypothesis for this example.

Calculate the following:

2. SSw ________

3. SSb ________

4. F __________

5. How many within-group degrees of freedom are there?

df = _____

6. How many between-group degrees of freedom are there?

df = _____

7. F_critical = _________

8. What is your decision concerning the null hypothesis? EXPLAIN.

9. Calculate R².

10. What does your obtained R² tell you in terms of how much of the total variability in your data is explained by differences between the means of the groups?

You want to know whether physical education majors attend more sporting events per year than business majors. Assume an alpha level of p < .01.

11. Calculate t.

12. What is t_critical in this example?

13. What is your decision concerning the null hypothesis? EXPLAIN in terms of whether the means for the two groups your are comparing are significantly different from one another.

14. What is the effect size in terms of Cohen's d for this example?

Cohen's d = ________

15. In terms of Cohen's conventions for effect size, this effect size is ______.

Answers:

1. Ho: m1 = m2 = m3 H₁: NOT Ho

2. SSw = 2+8+6 = 16

3. SSb = 27+108+27 = 162

4. F = MSb/MSw = (162/2)/(16/6) = 81/2.67 = 30.34

5. df = 6

6. df = 2

7. F_critical =10.93

8. Reject Ho ... F > F_critical.

9. R² = 162/(162+16) = .91

10. 91% of all variability is explained by variability between the means of the different groups.

11. t = (10-1)/1.53 = 5.88

12. t_critical = 3.75

13. Reject Ho ... the mean number of sporting events attended by phys. ed. majors is significantly greater than the mean number attended by business majors.

14. Cohen's d =(10-1)/1.87 = 4.81

15. In terms of Cohen's conventions for effect size, this effect size is gigantic.