The output below reflects the results of a study examining t

The output below reflects the results of a study examining three therapeutic intervention styles on depression ratings following 10 weeks of treatment. State the null and research hypotheses, assess the assumptions of ANOVA, and interpret the results (F-ratio, post hoc results when applicable), and describe the outcome of the study with respect to null hypothesis.

Between-Subjects Factors

Value Label

N

treatment

BMOD

behavior mod therapy

15

CCT

client centered therapy

15

RET

rational-emotive therapy

15

Descriptive Statistics

Dependent Variable:rating

treatment

Mean

Std. Deviation

N

behavior mod therapy

8.40

.99

15

client centered therapy

3.13

1.06

15

rational-emotive therapy

4.20

.94

15

Total

5.24

2.50

45

Levene\'s Test of Equality of Error Variances^a

Dependent Variable:rating

F

df1

df2

Sig.

.073

2

42

.930

Tests the null hypothesis that the error variance of the dependent variable is equal across groups.

a. Design: Intercept + treatment

Tests of Between-Subjects Effects

Dependent Variable:rating

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Corrected Model

232.58^a

2

116.29

117.03

.000

.848

Intercept

1237.69

1

1237.69

1245.60

.000

.967

treatment

232.58

2

116.29

117.03

.000

.848

Error

41.73

42

.99

Total

1512.00

45

Corrected Total

274.31

44

a. R Squared = .848 (Adjusted R Squared = .841)

b. Computed using alpha = .05

Multiple Comparison

LSD

(I) treatment

(J) treatment

Mean Difference (I-J)

Std. Error

Sig.

behavior mod therapy

client centered therapy

5.27^*

.36

.000

rational-emotive therapy

4.20^*

.36

.000

client centered therapy

behavior mod therapy

-5.27^*

.36

.000

rational-emotive therapy

-1.07^*

.36

.005

rational-emotive therapy

behavior mod therapy

-4.20^*

.36

.000

client centered therapy

1.07^*

.36

.005

Based on observed means.

The error term is Mean Square(Error) = .994.

*. The mean difference is significant at the .05 level.

Between-Subjects Factors
	Value Label	N
treatment	BMOD	behavior mod therapy	15
CCT	client centered therapy	15
RET	rational-emotive therapy	15

Solution

From the output, the significant value for the corrected model F =117.03 and the corresponding P-value 0.00

Since P-value is 0.000, we reject the null hypothesis. which is the means of three therapeutic intervention styles are not equal.

From the multiple comaprision tests, it was observed the mean difference between behavior mod therapy,client centered therapy is significant.

Also the mean difference betwee behavior mod therapy,rational-emotive therapy is significant.

Also the mean difference between rational-emotive therapy, client centered therapy is significant.

R squared value =0.848 , which means it explains 84.8% of the variaion in scores of depression.