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 an α of 0.05?

                Psychotherapy

Medication	no	yes
no	10 11 9 13	12 10 13 8
yes	11 13 8 9	4 13 4 6

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  

Answer 1

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 an α of 0.05?

                Psychotherapy

Medication	no	yes
no	10 11 9 13	12 10 13 8
yes	11 13 8 9	4 13 4 6

Compute the corresponding effect size(s) and indicate magnitude(s).
Medication: η² = 0.15  ;  small effect
Psychotherapy: η² = 0.09  ;   trivial effect
Interaction: η² =  0.09 ;   trivial effect

Two factor ANOVA
		Psychotherapy
	Means:
		no	yes
	no	10.8	10.8	10.8
Medication	yes	10.3	6.8	8.5
		10.5	8.8	9.6
	4	replications per cell
ANOVA table
Source	SS	df	MS	F	p-value	Effect size
Medication	20.250	1	20.250	2.61	.1320	0.15
Psychotherapy	12.250	1	12.250	1.58	.2326	0.09
Interaction	12.250	1	12.250	1.58	.2326	0.09
Error	93.000	12	7.750
Total	137.750	15

Main effect Medication is not significant, F=2.61, P=0.132

Main effect Psychotherapy is not significant, F=1.58, P=0.2326

Interaction effect is not significant, F=1.58, P=0.2326