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# (Solved): A researcher is interested in what therapeutic strategies will best engage refugees in a treatment ...

A researcher is interested in what therapeutic strategies will best engage refugees in a treatment for post-traumatic stress disorder. The researcher recruited 18 refugees and randomly assigned them to one of 3 equally sized groups. In each group, a different semi-structured interview was administered, and then the client was asked to rate on a scale from 1 to 100 how engaged they felt where higher scores indicate feelings of greater engagement. The data that was collected is presented below. Group 1 = Post-traumatic growth (mean = 53; standard deviation = 8) Group 2 = Post-traumatic growth + culturally adapted (mean = 64; standard deviation = 12) Group 3 = Standard (mean = 45; standard deviation = 4) YOU MAY ASSUME HOMOGENEITY OF VARIANCE FOR THIS PROBLEM. (6 pts) (a) Conduct a one-way ANOVA with \alpha =.05 using the information provided above. Show all your work including the calculation of Between-groups and Within-groups SS, df, MS, as well as the critical F value. (3 pts) (b) State your conclusion regarding the null hypothesis. What can the researcher conclude about the different interview techniques? (3 pts) (c) In addition to performing the omnibus test, the planned two additional comparisons of interest: (1) group 1 vs. group 2; and (2) the average of groups 1 and 2 vs. group 3. What multiple comparison procedure should be used for determining the significance of these contrasts, and why? (6 pts) (d) Carry out by hand the test of the second contrast (taking into account the fact that a total of two contrasts are to be tested). Show all your work and state your conclusion. (6 pts) (e) Compute the limits of a 95% simultaneous confidence interval around the estimated value of the second contrast above. Show all your work (4 pts) (f) What proportion of the Between-groups SS would the combined SS associated with both contrasts account for? Justify your answer in words (Hint: you should be able to answer this without calculating the value of the first contrast).

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