Question

The following explanation and table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment. Depressed people are given two different types of treatments: Exercise, and Psychological Therapy.
Factor A is exercise, and there are 3 levels: intense exercise, moderate exercise, or no exercise.
Factor B is therapy, and there are 2 levels: Cognitive Behavior Therapy and Treatment as Usual.
There are n = 8 participants in each treatment condition

1. State the three different hypotheses for this test.
   
2. What are the critical values for… (2 points total)
   1. The main effect of factor A?

2. The main effect of factor B?

3. The interaction effect?

3. If alpha is .05, is there a significant effect of factor A, factor B, and/or the interaction of A and B?

4. If the p value associated with the finding for Factor A was .02, what would this mean about the relationship with the null distribution? The correct answer here is not a simple reject or not reject the null answer.

1 point for each blank. 15 points in this table.

Source	SS	Df	MS	F
Between groups	60		---	---
Factor A: exercise	16
Factor B: therapy	20
A x B: exercise X therapy
Within (error)				---
Total	150		---	---

Answer 1

Source	SS	Df	MS	F	F critical
Between groups	60	5	---	---
Factor A: exercise	16	2	8	3.73	3.22
Factor B: therapy	20	1	20	9.33	4.07
A x B: exercise X therapy	24	2	12	5.6	3.22
Within (error)	90	42	2.14	---
Total	150	47	---	---

(a) The hypothesis being tested is:

H₀: There is no main effect of Factor A

H_a: There is a main effect of Factor A

The hypothesis being tested is:

H₀: There is no main effect of Factor B

H_a: There is a main effect of Factor B

The hypothesis being tested is:

H₀: There is no interaction effect

H_a: There is an interaction effect

(b) The critical value for the main effect of factor A is 3.22.

The critical value for the main effect of factor B is 4.07.

The critical value for the interaction effect is 3.22.

(c) There is a significant effect of factor A. (F (2, 42) = 3.73, p < 0.05)

There is a significant effect of factor B. (F (1, 42) = 9.33, p < 0.05)

There is a significant interaction effect. (F (2, 42) = 5.6, p < 0.05)

(d) The p-value is 0.02.

Since the p-value (0.02) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant effect of factor A.