Question

A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient. Assume an alpha of .05.

Cognitive/Behavioral Therapy	Relaxation Therapy	Attention-Placebo Group
5 6 6 4 7	6 8 6 9 7	5 8 9 7 6

Calculate SSBetween =

Calculate SS_{Within =}

Calculate MSBetween =

Calculate MSWithin =

Calculate F_{Crit =}

Calculate F_{Obt =}

Based on your results, what do you conclude? =

Answer 1

	Cognitive	Relaxation	Placebo	Total
Sum	28	36	35	99
Count	5	5	5	15
Mean, Sum/n	5.6	7.2	7
Sum of square, Ʃ(xᵢ-x̅)²	5.2	6.8	10

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 15

df(between) = k-1 = 2

df(within) = N-k = 12

df(total) = N-1 = 14

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 7.6

SS(within) = SS1 + SS2 + SS3 = 22

SS(total) = SS(between) + SS(within) = 29.6

MS(between) = SS(between)/df(between) = 3.8

MS(within) = SS(within)/df(within) = 1.8333

Critical value Fcrit = F.INV.RT(0.05, 2, 12) = 3.885

FObt = MS(between)/MS(within) = 2.0727

Decision:

Do not reject the null hypothesis.

There is not enough evidence to conclude that there is a difference between the means at 0.05 significance level.