The following table was presented in an article summarizing a study to compare a
ID: 3177437 • Letter: T
Question
The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.
Characteristic*
New Drug
Standard Drug
Placebo
p
Age, years
45.2 (4.8)
44.9 (5.1)
42.8 (4.3)
0.5746
% Female
51%
55%
57%
0.1635
Annual Income, $000s
59.5 (14.3)
63.8 (16.9)
58.2 (13.6)
0.4635
% with Insurance
87%
65%
82%
0.0352
Disease Stage
0.0261
Stage I
35%
18%
33%
Stage II
42%
37%
47%
Stage III
23%
51%
20%
*Table entries and Mean (SD) or %
Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer.
Consider the test for differences in age among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).
Consider the test for differences in insurance coverage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).
Consider the test for differences in disease stage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).
Characteristic*
New Drug
Standard Drug
Placebo
p
Age, years
45.2 (4.8)
44.9 (5.1)
42.8 (4.3)
0.5746
% Female
51%
55%
57%
0.1635
Annual Income, $000s
59.5 (14.3)
63.8 (16.9)
58.2 (13.6)
0.4635
% with Insurance
87%
65%
82%
0.0352
Disease Stage
0.0261
Stage I
35%
18%
33%
Stage II
42%
37%
47%
Stage III
23%
51%
20%
Explanation / Answer
The p value corresponding to Percentage of insurance and Diseases stage are 0.0352 and 0.0261. Rejection rule based on P value states that reject H0 and conclude that result is statistically significant if Observed P is less than given significance level, alpha. In case, alpha is not given, assume it to be 0.05. Here, both the p values are less than 0.05, therefore, conclude that significant difference exists in Percentage of insurance and Diseases stage.
H0:muND age=muSD age=muP age=0 (there is no difference in population mean age among the three treatments)
H1:atleast one population mean age for a treatment is different from population mean age of another treatment.
H0:muND%I=muSD%I=muP%I=0 (there is no difference in population mean insurance coverage (%) among the three treatments)
H1:atleast onepopulation mean insurance coverage (%) is different.
H0:muS1=muSII=muSIII=0 (there is no difference in population mean disease stage among the three treatments)
H1:atleast one population mean disease stage is different.
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