Study Guide for Final Exam – this exam will include problems related to ANOVA – and will include a multiple-choice section related to content from across the semester. Sample problems are included here (with answers) – along with a list of concepts to study for the multiple-choice component of the exam.

- · 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)

X_{1}

1

0

2

(Physical education majors)

X_{2}

8

10

12

(Business majors)

X_{3}

0

0

3

1. In terms of H_{0}, H_{1}, m_{1}, m_{2}, and m_{3}, 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 R^{2}.

10. What does your obtained R^{2 }tell you in terms of how much of the total variability in your data is explained by differences between the means of the groups?

- CURRENT STUDENTS: The below content in RED will NOT be on the exam!

~~· 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 you 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 ______.~~

FORMULAS/ANSWERS:

1. Ho: m1 = m2 = m3 H_{1}: 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. R^{2} = 162/(162+16) = .91

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

~~Current Students: between-groups t-test will NOT be on the final exam!~~

~~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.~~

For the multiple-choice part of the exam, you’ll need to understand the following concepts:

You will need to understand the following concepts:

1. Measures of central tendency

2. Standard deviation and variance

3. Z scores

4. Correlation: Different patterns of correlation

5. Correlation: Correlation and causation

6. Bivariate regression: Its purpose

7. Bivariate regression: The difference between the raw score and Z-score prediction models.

8. Relate the concept of alpha level to a probability distribution

9. Characteristics of a normal distribution (related to raw and Z scores)

10. Hypothesis testing: Conclusions that can and cannot be drawn

11. One-tailed versus two-tailed tests

12. When to use a population distribution versus a distribution of means

13. Characteristics of a distribution of means

14. Type I and Type II error

15. Statistical Power (what it is and what influences it)

16. Alpha and Beta

17. Cohen’s d

18. t-tests:

A. Fundamental characteristics of t-tests

B. How the t distribution differs from a normal distribution

19. Different kinds of t-tests:

A. Repeated measures t-test (what it is used for and conclusions that can be drawn from it)

B. Independent means t-test (what it is used for and conclusions that can be drawn from it)

20. Analysis of Variance (ANOVA):

A. Characteristics of the F distribution

B. Intepreting the equation for F (What MS_{B} and MS_{W }represent)

C. What influences an obtained F score

D. What conclusions can and cannot be made based on an ANOVA