A psychotherapist is having doubts about her treatment methods and wants to see

Question

A psychotherapist is having doubts about her treatment methods and wants to see whether different methods may alter the effectiveness in treating patients with depression. The psychotherapist has been using psychoanalysis as the method for treating her patients but also wishes to see if there are any differences in the treatment of depression using cognitive therapy as well as applied behavioral analysis therapy. To evaluate the efficacy of the three different therapy techniques in influencing depression, the psychotherapist randomly selects 33 participants from a pool of eligible depressed patients. The psychotherapist then randomly assigns n = 11 participants to receive psychoanalysis, n =11 participants to receive cognitive therapy, and n= 11 participants to receive applied behavioral analysis therapy. After therapy, the psychotherapist asks each participant to complete The Depression Inventory as a measure of their depression levels. The Depression Inventory has a range of scores from 0-50 (where higher scores indicate higher levels of depression). Below are the results of the experiment in table format: a) State the Independent Variable in this research study, including its levels. b) State the Dependent Variable in this research study. c) What is the appropriate hypothesis test to conduct based on this research design? d) State the null and alternate hypotheses. e) Calculate the appropriate test statistic. f) Determine the critical region for this test at alpha = 0.01. g) What is the correct decision with respect to your hypotheses? Provide ONE reason why. h) Calculate a measure of effect size (eta^2) i) Depending on the result of your overall hypothesis test, conduct a post-hoc test (Tukey's HSD), making sure to note the critical mean difference value (HSD) as well as state which of the pairs of means are significantly different from one another based on the value for HSD at alpha = 0.01. j) Interpret (in words) the result of this hypothesis test, including proper statistical notation. Additionally, interpret (in words) any significant pairwise (mean) comparisons that were found using your post hoc test results.

Explanation / Answer

Answers:

a. The Independent Variables in this research study are the different treatment the psychotherapist is using to treat the patients. Those are - Psychoanalysis (X1) , Cognitive Therapy (X2) and Applied Behavioural Analysis (X3). It's levels vary from 0 to 50, where higher value implies higher level of depression.

b. The Dependent Variable in this research study is Depression, as that is the problem the psychotherapist is trying to measure.

c. The appropriate test would be a t-test for the equality of means.

d. The null hypothesis would be that - all the 3 treatments have same mean outcomes and the alternative hypothesis would be that - they are different.

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