Question

Problem Set 1: The One-way ANOVA

Research Scenario: Depressed patients are randomly assigned to 1 of 3 therapists. At the end of 3 months, each patient completes a standardized test of depression (higher scores indicate higher level of depression). The patients’ scores are shown below. Analyze the data to determine how effective these 3 therapists are at treating depression (assume that before the treatment, all 3 groups of patients had the same average depression score).

Using this table, enter the data into a new SPSS data file and run a one-way ANOVA to test whether there is a difference in patients’ depression scores among the three therapists. Create a boxplot to show the difference among these scores.

Data: Therapist 1: 35,37,35,37,36,33,39

Therapist 2: 36,37,37,31,39,35,32

Therapist 3: 29,32,25,28,33,30,32

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your boxplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts; Graph = 5 pts) Please include this section, as it it important!!!! Thank you!

Answer 1

Solution:

Here, we have to use one way analysis of variance or ANOVA F test for checking the given claim or hypothesis. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any significant difference in the average depression scores due to three different therapists.

Alternative hypothesis: H_a: There is a significant difference in the average depression scores due to three different therapists.

We assume level of significance = α = 0.05 = 5%

The required ANOVA table and box plot for this test by using SPSS are given as below:

The box plot is given as below:

From above box plots, it is observed that there is a significant difference between average depression scores due to three different therapists.

The ANOVA table is given as below:

Descriptive Statistics
Depression score
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
Therapist 1	7	36.0000	1.91485	.72375	34.2291	37.7709	33.00	39.00
Therapist 2	7	35.2857	2.87021	1.08484	32.6312	37.9402	31.00	39.00
Therapist 3	7	29.8571	2.79455	1.05624	27.2726	32.4417	25.00	33.00
Total	21	33.7143	3.71676	.81106	32.0224	35.4061	25.00	39.00

ANOVA
Depression score
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	158.000	2	79.000	12.022	.000
Within Groups	118.286	18	6.571
Total	276.286	20

From above ANOVA table, we have

P-value = 0.000

So, P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a significant difference in the average depression scores due to three different therapists.