A clinical psychologist is interested in comparing the effectiveness of two new
ID: 3182282 • Letter: A
Question
A clinical psychologist is interested in comparing the effectiveness of two new drugs that have been developed for treating schizophrenia in conjunction with individual counseling sessions. To make the comparison, five patients suffering from schizophrenia are randomly assigned to each of four treatment groups. Group I received drug A and individual counseling; group II received drug B and individual counseling; group III received a placebo drug and individual counseling; and group IV received no drug, just the individual counseling. Schizophrenia was measured before the treatments began and again after 3 months, after 6 months and after 1 year of treatment. The data are as follows:
Schizophrenia Scores
Group Subject initial 3 mos 6 mos 1 yr
1 1 95 85 82 79
1 2 89 81 81 79
1 3 98 95 91 85
1 4 91 83 78 79
1 5 93 81 83 78
2 1 90 84 81 80
2 2 85 79 80 75
2 3 96 82 80 81
2 4 88 84 81 79
2 5 92 85 83 80
3 1 94 89 87 86
3 2 92 90 88 87
3 3 83 81 82 78
3 4 89 85 83 83
3 5 95 91 92 89
4 1 96 94 95 94
4 2 88 89 87 85
4 3 92 89 91 90
4 4 85 85 82 79
4 5 91 89 87 86
1) Test the null hypothesis that no differences exist among the four treatment groups at the 5% significance level. Specify the hypotheses, the calculated value of the F-statistic, the degrees of freedom associated with the critical value, either an F-critical value or a p-value, and your decision regarding the null hypothesis.
2) Test the null hypothesis that there is no group by time interaction at the 1% significance level. Specify the hypotheses, the calculated value of the F-statistic, the degrees of freedom associated with the critical value, either an F-critical value or a p-value, and your decision regarding the null hypothesis.
Explanation / Answer
Solution:
1.
Null Hypothesis (Ho): There is no difference between the four treatment groups.
Alternative Hypothesis (Ha): There is difference between the four treatment groups.
Test Statistics: F = 12.58
Degrees of freedom, df = 3, 76
F-critical value = 2.7249
P-value = 0.000
Since p-value is less than 0.05 significance level, we reject the null hypothesis.
Hence, we can conclude that there is difference between the four treatment groups.
b.
Null Hypothesis (Ho): There is no group by time interaction.
Alternative Hypothesis (Ha): There is group by time interaction.
Test Statistics F = 1.2198
Degrees of freedom, df = 9, 64
F-critical value =2.0298
P-value = 0.2989
Since p-value is greater than 0.01 significance level, we fail to reject the null hypothesis.
Hence, we can conclude that there is no group by time interaction.
SUMMARY Groups Count Sum Average Variance Column 1 20 1822 91.1 16.30526 Column 2 20 1721 86.05 20.15526 Column 3 20 1694 84.7 22.43158 Column 4 20 1652 82.6 24.25263 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 784.2375 3 261.4125 12.57626 9.24E-07 2.724944 Within Groups 1579.75 76 20.78618 Total 2363.988 79Related Questions
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