Question

A group of biochemistry researchers developed a new medication for treating depression. To assess if the new medication is effective at treating depression, the researchers obtained a sample of depressive patients from a local clinic. The patients were then randomly assigned into taking the medication for a month or not. In addition, the patients were also randomly assigned into receiving psychotherapy for a month or not. At the end of the study, the patients were asked to fill out a depression inventory in which a higher score indicates more depression. The data are below. What can be concluded with α = 0.01?

                Psychotherapy

Medication	no	yes
no	10 11 9 13	12 10 13 8
yes	11 13 8 9	4 3 4 14

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Medication: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Psychotherapy: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Medication: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Psychotherapy: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a medication difference in depression.There is no medication difference in depression.    

There is a psychotherapy difference in depression.There is no psychotherapy difference in depression.    

There is a medication by psychotherapy interaction in depression.There is no medication by psychotherapy interaction in depression.    

Answer 1

	Psychotherapy			Anova: Two-Factor With Replication
Medication	no	yes
no	10	12		SUMMARY	no	yes	Total
	11	10		no
	9	13		Count	4	4	8
	13	8		Sum	43	43	86
yes	11	4		Average	10.75	10.75	10.75
	13	3		Variance	2.916666667	4.916667	3.357143
	8	4
	9	14		yes
				Count	4	4	8
				Sum	41	25	66
				Average	10.25	6.25	8.25
				Variance	4.916666667	26.91667	18.21429
				Total
				Count	8	8
				Sum	84	68
				Average	10.5	8.5
				Variance	3.428571429	19.42857
				ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Medication	25	1	25	2.521008403	0.138324038	4.747225
				Psychotherapy	16	1	16	1.613445378	0.228084693	4.747225
				Interaction	16	1	16	1.613445378	0.228084693	4.747225
				Within	119	12	9.916667
				Total	176	15

a) two-way ANOVA

b) Medication: F-ratio=2.5210, p-value =0.1383  ; Decision: Fail to reject H0
Psychotherapy: F-ratio=1.6134, p-value =0.2281 ; Decision: Fail to reject H0
Interaction:F-ratio=1.6134, p-value =0.2281 ; Decision: Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Medication: η² =25/176=0.1420 ; Large effect
Psychotherapy: η² =16/176=0.09 ; medium effect
Interaction: η² =16/176=0.09 ; medium effect

(d) There is no medication difference in depression.

There is no psychotherapy difference in depression.    

There is no medication by psychotherapy interaction in depression.