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. Using the HSD test with a = 0.05, the appropriate critical value is _________.
A) ±2.179
B) 3.08
C) 3.77
D) 5.05

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.  Using the HSD test with a = 0.05, the appropriate critical value is _________.
A) ±2.179 
B) 3.08 
C) 3.77 
D) 5.05

Quizplus · Accepted Answer

To find the critical value for the HSD test with a = 0.05, we need to first calculate the mean square within groups (MSW) and the mean square between groups (MSB).

MSW = (SSW) / (dfW) = 60 / 12 = 5

MSB = (SSB) / (dfB) = 120 / 2 = 60

where SSW is the sum of squares within groups, dfW is the degrees of freedom within groups (n - k), SSB is the sum of squares between groups, and dfB is the degrees of freedom between groups (k - 1).

Next, we can calculate the HSD value using the formula:

HSD = q(alpha) * sqrt(MSW / n)

where q(alpha) is the critical value for the studentized range distribution at the given level of alpha (0.05), MSW is the mean square within groups, and n is the number of observations per group (in this case, n = 5).

Using a studentized range distribution table, we can find that the critical value for q(0.05) with dfW = 12 and dfB = 2 is approximately 3.77.

Substituting in the values:

HSD = 3.77 * sqrt(5) = 8.48

Therefore, the appropriate critical value is 3.77.

A Clinical Psychologist Is Interested in Comparing the Effectiveness of Short