Question

A study was conducted to compare the effects of three different drugs on the alleviation of anxious depression in non-psychotic patients. Twelve non-psychotic patients, all suffering from moderate to severe depression and anxiety, were grouped according to initial level of severity. Patients in each severity level group were randomly assigned to the three treatments (drugs). At the end of the experimental period, a combined anxiety and depression score as determined by the MMPI and Taylor Manifest Anxiety Scale was recorded for each patient. The researcher hypothesizes that there is a difference in average anxiety/depression scores for the three drugs. The data are as follows: Initial Severity Level Drug A Drug B Drug C I 35 30 25 2 40 25 20 3 25 25 20 4 30 25 25 What statistical test is appropriate for testing the researcher’s hypothesis? Answer the following questions: What type of research question is being asked? What is the level of measurement of the response variable? What is the research design (1, 2, 2+ groups)? Were samples independently selected or were they matched? What is the appropriate statistical test for analysis?

Answer 1

The appropriate test for testing the researcher’s hypothesis is one way ANOVA.

Research Question: A study was conducted to compare the effects of three different drugs on the alleviation of anxious depression in non-psychotic patients. Is there a difference in average anxiety/depression scores for the three drugs?

The research design (1, 2, 2+ groups): completely randomised design (CRD)

Since twelve non-psychotic patients, all suffering from moderate to severe depression and anxiety, were grouped according to initial level of severity so the samples were matched with initial level of severity.

The appropriate statistical test for analysis is one way ANOVA.

One-way ANOVA: Average anxiety scores versus Drug

Source DF SS MS F P
Drug 2 204.2 102.1 5.44 0.028
Error 9 168.8 18.8
Total 11 372.9

From the above ANOVA table we see that p-value<0.05 so we conclude that there is a difference in average anxiety/depression scores for at least one drug from other two.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Drug

Individual confidence level = 97.91%

Drug = A subtracted from:

Drug Lower Center Upper
B -14.802 -6.250 2.302
C -18.552 -10.000 -1.448
  

Drug = B subtracted from:

Drug Lower Center Upper  
C -12.302 -3.750 4.802   
  

From above confidence intervals we observe that there is a difference in average anxiety/depression scores for Drug A and Drug C (since the C.I. of Drug A-Drug C does not contain zero).