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. Use the lecture notes as your guide for this problem.
A: State the three different hypotheses for this test

B: What are the critical values for the main effect of factor A? Factor B? Interaction effect?

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

D: If the p value associated with the finding for Factor A was .02, what would this mean about the relationship with the null distribution?

E: Fill in this table

Source	SS	Df	MS	F
Between Groups	60		--	--
Factor A: Exercise	16
Factor B: Therapy	20
AxB: 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.

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