Question

1. A clinical psychologist compares 3 different therapies for treatment of manic-depressive disorder. Clients are assigned at random to the different therapies, they undergo treatment for the same 6-month period, then all are assessed. The assessment consists of counting the number of manic-depressive episodes in the 2-month period following completion of therapy treatment. The results are tabled below. Use SPSS and the steps of hypothesis-testing to find out whether type of therapy matters.

Therapy A	Therapy B	Therapy C
5	3	5
2	2	4
3	3	3
1	1	6
4	4	5
4	5	6
3	3	7
0	2	4
2	2	7
4	1	5

1. State your hypotheses.

2. Determine the characteristics of the comparison distribution.

3. Determine the cut-off value for a 5% significance level.

4. Using SPSS, determine the observed F ratio.

5. Decide whether or not to reject the null and give a verbal explanation.

6. Calculate and interpret h².

7. Compute the power of the test. How many subjects are needed to detect an effect with a power of .80 and the given effect size?

8. Assuming a real difference exists, you have a number of a priori hypotheses about the nature of the differences. Using SPSS, compute the following planned contrast, state the rejection level that you used, and state your conclusions (i.e., if you have differences, interpret the difference . . . don’t just state that the means are different):

Contrast Hypothesis 1: μ_TherapyA ≠ μ_TherapyC

Assume now that the clinical psychologist had no a priori hypotheses about the nature of any differences. Instead, the researcher wants to compute all possible pairwise comparisons post-hoc. Use SPSS to compute all possible pairwise comparisons. What are your results? What do you conclude?

Answer 1

From the given data, the following Table is calculated:

	Therapy A	Therapy B	Therapy C	Total
N	10	10	10	30
	28	26	52	106
Mean	2.8	2.6	5.2	3.533
	100	82	286	468
Std. Dev.	1.5492	1.2649	1.3166	1.7953

From the above Table, ANOVA Table is Calculated as follows:

Source of variation	Sum of Squares	Degrees of freedom	Mean Square	F
Between Treatments	41.8667	2	20.9333	10.9535
Within treatments	51.6	27	1.9111
Total	93.4667	29

The F - Ratio = 10.9535. The p - value =0.0003. The result is significant at p <0.05

Question (a)

State your hypotheses:
H0 : Null Hypothesis:

HA: Alternative Hypothesis: (At least one mean is different from other 2 means)

Question (b):

Determine the characteristic of the comparison distribution:

F Distribution with Degrees of Freedom for numerator = 2 and Degrees of Freedom for denominator = 27

Question C:

Determine the cut off value for a 5% significance level:

From Table, critical value of F is given by:

3.354

As per the guideline i have solve first 5 Qs, kindly share other Qs individually. Thanks