Question

You are a cognitive psychologist who has developed a new treatment for depression. Currently, the most effective treatments for depression are behavioral treatments and pharmacological treatments (treatments involving medication). In order to validate your new treatment, you need to show that it is at least as effective as behavioral treatment and medication. You conduct a clinical trial to determine the effectiveness of your treatment by randomly assigning 60 individuals with depression to four treatment groups: a Control group (n = 15), a Cognitive Therapy group (n = 15), a Behavioral Therapy group (n = 15), and a Pharmacological Therapy group (n = 15). After 6 weeks of treatment, you assess depression using the Beck Depression Inventory (BDI; range: 0 – 63 with 0 indicating no depression and 63 indicating severe depression). Use the 6 steps of hypothesis testing and SPSS to determine whether the groups differ in terms of scores on the BDI. Use the SPSS #2 to conduct the statistical test, record your answers on the answer sheet and attach SPSS output.

Control	Pharmacological Therapy	Behavioral Therapy	Cognitive Therapy
74	79	44	55
70	89	68	48
83	89	71	64
66	75	35	40
90	67	62	30
97	74	65	31
104	90	70	63
100	81	65	30
75	65	45	64
92	68	41	69
89	85	46	45
70	71	68	39
83	69	69	31
95	67	39	66
108	70	42	3

a) What is the appropriate statistical test to answer question? (0.5 pt)

b) Step 1: What is your prediction regarding the results of the statistical test? (0.5 pt)

c) Step 2: Set up hypotheses (2 pts)

H₀ (1 pt):
H₁ (1 pt):   

d) Step 3: Set criteria for decision (2 pts)

Critical value (1 pt):
Decision Rule (1 pt):   

e) Step 5: Report Results (2 pts) – Must include test statistic (0.5 pts), degrees of freedom (0.5 pts), p-value (0.5 pts), and appropriate measure of effect size (0.5 pts)

f) Post-hoc comparisons (1 pt) – Conduct Tukey’s HSD and report differences between groups by using “>”, “<”, or “=” to demonstrate which group’s mean is greater than the other (The first two have been filled out as a guide).

Post-hoc Comparisons
Control	=	Pharmacological
Control	<	Behavioral
Control		Cognitive
Behavioral		Pharmacological
Behavioral		Pharmacological
Cognitive		Pharmacological

g) Step 6: Interpret the results of the statistical test in terms of the research question (1 pt)

SPSS DATA
Control   74
Control   70
Control   83
Control   66
Control   90
Control   97
Control   104
Control   100
Control   75
Control   92
Control   89
Control   70
Control   83
Control   95
Control   108
Pharmacological Therapy   79
Pharmacological Therapy   89
Pharmacological Therapy   89
Pharmacological Therapy   75
Pharmacological Therapy   67
Pharmacological Therapy   74
Pharmacological Therapy   90
Pharmacological Therapy   81
Pharmacological Therapy   65
Pharmacological Therapy   68
Pharmacological Therapy   85
Pharmacological Therapy   71
Pharmacological Therapy   69
Pharmacological Therapy   67
Pharmacological Therapy   70
Behavioral Therapy   44
Behavioral Therapy   68
Behavioral Therapy   71
Behavioral Therapy   35
Behavioral Therapy   62
Behavioral Therapy   65
Behavioral Therapy   70
Behavioral Therapy   65
Behavioral Therapy   45
Behavioral Therapy   41
Behavioral Therapy   46
Behavioral Therapy   68
Behavioral Therapy   69
Behavioral Therapy   39
Behavioral Therapy   42
Cognitive Therapy   55
Cognitive Therapy   48
Cognitive Therapy   64
Cognitive Therapy   40
Cognitive Therapy   30
Cognitive Therapy   31
Cognitive Therapy   63
Cognitive Therapy   30
Cognitive Therapy   64
Cognitive Therapy   69
Cognitive Therapy   45
Cognitive Therapy   39
Cognitive Therapy   31
Cognitive Therapy   66
Cognitive Therapy   36

Answer 1

Part a

Appropriate statistical test to answer the question is the one way analysis of variance or one way ANOVA F test.

Part b

Our prediction regarding the statistical test is there is a difference in the average effectiveness due to different types of therapy.

Part c

Null hypothesis: H₀: There is no any significant difference in the average effectiveness due to different types of therapy.

Alternative hypothesis: H_a: There is a significant difference in the average effectiveness due to different types of therapy.

Part d

Critical value = 2.769431 (by using F-table or calculator)

Reject H₀ if F > 2.769431

Part e

Required SPSS outputs are given as below:

ANOVA
Effectiveness
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	14614.267	3	4871.422	29.570	.000
Within Groups	9225.467	56	164.740
Total	23839.733	59

The p-value is given as 0.00 < α = 0.05, so we reject the null hypothesis

There is sufficient evidence to conclude that there is a significant difference in the average effectiveness due to different types of therapy.