a= .05 A therapist would like to evaluate the effectiveness of a procedure for t
ID: 3330778 • Letter: A
Question
a= .05
A therapist would like to evaluate the effectiveness of a procedure for treating depression. A sample of n = 16 depressed clients is obtained and each person’s level of depression is measured using a standardized questionnaire before they begin the therapy program. Two weeks after therapy, each client’s level of depression is measured again. The average level of depression dropped by 6.8 points following therapy. The difference scores had a variance of 64.
a. State the null hypothesis.
b. Which statistical test would you use to test this hypothesis?
c. Calculate the appropriate test statistic and state your conclusions. Show your work.
d. Compute an effect size.
Explanation / Answer
a. The null hypothesis is the hypothesis of no difference, which means that there is no change in mean depression level before and after the therapy.
H0:mud=0 , where, d=(befor-after)
b. Check for assumptions: Paired data: The data are paired, as same set of clients were tested before and after the therapy. Independence: Each client is independent of another. Randomization: clients were selected at random. Nearly normal condition: it is expected that differences in depression score is nearly normal. Thus, the asumptions and conditions are successfully met, use Student's t model with (n-1)=15 degrees of freedom and perform a paired t test.
c. t=(dbar-0)/(sdbar/sqrt n), where, dbar is average of differences, sdbar is standard deviation of differences and n is sample size.
=(6.8-0)/(8/sqrt 16)
=3.40
p value is:0.0019
Per rejection rule based on p avalue, reject null hypothesis if p value is less than alpha=0.05, here, 0.0019 is less than 0.05, therefore, reject null hypothesis and conclude that therapy has been effective.
d. The Cohen's d=dbar/sdbar=6.8/8=0.85, according to Cohen, effect size is small is d<0.2, medium if d is between 0.2 and 0.8 anf considered large if d is greater than 0.8. Thus, the effect size (d=0.85) is large.
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