Question

data

Therapy	Medication	Score
Cog	Zoloft	54
Cog	Zoloft	42
Cog	Zoloft	50
Cog	Zoloft	47
Cog	Zoloft	48
Cog	Zoloft	44
Cog	Prozac	70
Cog	Prozac	68
Cog	Prozac	66
Cog	Prozac	61
Cog	Prozac	61
Cog	Prozac	40
Cog	Lexapro	54
Cog	Lexapro	52
Cog	Lexapro	55
Cog	Lexapro	54
Cog	Lexapro	58
Cog	Lexapro	54
Assert	Zoloft	30
Assert	Zoloft	35
Assert	Zoloft	34
Assert	Zoloft	35
Assert	Zoloft	36
Assert	Zoloft	38
Assert	Prozac	50
Assert	Prozac	54
Assert	Prozac	55
Assert	Prozac	54
Assert	Prozac	55
Assert	Prozac	58
Assert	Lexapro	68
Assert	Lexapro	70
Assert	Lexapro	62
Assert	Lexapro	62
Assert	Lexapro	54
Assert	Lexapro	56

USE R to do it will soon, and if you use r, could you give me a code

Suppose that a clinical psychologist is interested in comparing the relative effectiveness of two forms of psychotherapy (cognitive-behavioral and assertiveness training) in combination with three different medications (Zoloft, Prozac, and Lexapro) for alleviating depression. Thirty-six individuals are randomly sampled and randomly assigned a combination of treatment. The Depression Scale of MMPI serves as the response (score). The goal is to lower the score.

(a) Write out the initial hypotheses to be tested in words.


(b) Write out the appropriate statistical model and explain all terms. (Let i be associated with therapy)


(c) Construct an interaction plot where medication is the “trace factor”. Based on the plot, does there appear to be evidence of an interaction? Hint: Since there are 3 different medications, you’ll have to modify the following arguments for the code in R for the interaction plot to ensure that all 3 types of medication the are plotted. Note that you can use any number in the pch argument and any colors in the col argument. You will need to save this as a PDF, Word doc, or png.

The code here is for two levels: pch=c(1,2), col = c("red", "blue")

What can you do for three levels?

(d) Calculate the degrees of freedom for each term including the residual. Make sure to show work on how you calculated the degrees of freedom. Source Degrees of Freedom

Note: The sample size is 36

(e) Obtain the ANOVA table in R and confirm the degrees of freedom you reported in part (d). Should the main effects or simple effects be analyzed?



(f) Based on your answer above, report the appropriate results. If the main effects are appropriate, specify the estimated difference in average score for the therapies and/or medications along with the corresponding 95% confidence intervals for those which are statistically different. If the simple effects are appropriate, provide the estimated difference in average scores at a given type therapy along with the corresponding 95% confidence intervals for those which are statistically different.


(g) If a psychiatrist is currently using assertiveness training with a patient and currently has access to Prozac, should they switch their patient to using Prozac instead of Lexapro? Justify your answer

Answer 1