Question

The researcher conducted a second part of the study where one paired group of subjects were chosen. This experiment compared how cognitive behavior therapy (CBT) works to impact the number of times schizophrenics hear voices. Subjects (n = 5) first came in to the lab to take a baseline rating and then went through 2 months of CBT before they were tested again. You want to know if CBT impacts the number of times the participants heard voices. The mean number of voices heard before CBT was 6.8 (SD = 1.92) and the mean heard after CBT was 5.8 (SD = 1.64). The variance was calculated to be 0.50. a. Calculate the appropriate statistic to determine if there were group differences. Conduct a two-tailed test with an alpha level of 0.05. b. Calculate Cohen's d as a measure of effect size. Is the effect considered small, medium, or large? c. Based on the results and effect sizes from the two studies would you recommend a schizophrenic take Clozapine or engage in cognitive behavior therapy (CBT)? Why?

Answer 1

a)

Ho :   µd=   0                  
Ha :   µd ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
sample size ,    n =    5                  
                          
mean of sample 1,    x̅1=   6.800                  
                          
mean of sample 2,    x̅2=   5.800                  
                          
mean of difference ,    D̅ =    1.0000                  
                          
std dev of difference , Sd =        0.7071                  
                          
std error , SE = Sd / √n =    0.7071   / √   5   =   0.3162      
                          
t-statistic = (D̅ - µd)/SE = (   1   -   0   ) /    0.3162   =   3.162
                          
Degree of freedom, DF=   n - 1 =    4                        
                          
p-value =        0.0341   [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis              

b)

cohen's d = |Dbar/ std dev| =    1.414

Large effect

c)

Yes we would recommend because CBT has significant effect on the patient

Please let me know in case of any doubt.

Thanks in advance!

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