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.Cognitive/BehavioralTherapyRelaxationTherapyAttention-PlaceboGroup568476810978109109SS within = _________.

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Asked Nov 24, 2019
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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.

Cognitive/Behavioral
Therapy
Relaxation
Therapy
Attention-Placebo
Group
5
6
8
4
7
6
8
10
9
7
8
10
9
10
9

SS within = _________.

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Expert Answer

Step 1

The value of SS within is obtained below:

Introduction to one-way ANOVA:

One-way ANOVA is a statistical method for testing hypotheses regarding the mean difference among two or more independent populations or treatments.

Assumption:

  • Each of the populations is normally distributed.
  • Population variances are equal.
  • The observations in the sample from any particular populations or treatments are independent of one another.
  • Samples are selected independently.
Step 2

Step- by-step procedure to obtain SS within using Minitab software as follows:

  • Choose Stat > ANOVA > One-Way (Unstacked).
  • In Responses (in separate columns), enter the columns containing the separate response variables Cognitive/Beh...
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One-way ANOVA: Cognitive/Behavi, Relaxation Thera, Attention-Placeb Source DF SS MS F 2 26.13 13.07 6.88 0.010 Factor 22.80 12 1.90 Error Total 14 48.93 S 1.378 R-Sq (adj) = 45.64 R-Sq 53.41%

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