Question

B. Determine the characteristics of the comparison distribution.

Problem Set #8 Hypothesis Testing with the F Distribution (One-Way ANOVA) 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. 1. Therapy A Therapy B Therapy C 2 2 4 4 4 3 0 2 4 4 6 4 7 a. State your hypotheses. HA: Not all n ove equa b. Determine the characteristics of the comparison distribution. C. Determine the cut-off value for a 5% significance level.

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

Answer 1

From the given data, the following Table is calculated:

	Therapy A	Therapy B	Therapy C	Total
N	10	10	10	30
$\sum X$	28	26	52	106
Mean	2.8	2.6	5.2	3.533
$\sum X^{2}$	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: $\mu 1=\mu 2=\mu 3$

HA: Alternative Hypothesis: $\mu 1\neq \mu 2\neq \mu 3$ (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