The following table was presented in an article summarizing

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 %.

a) Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer.

b) 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).

c) 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).

d) 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%

Solution

There are three treatments as new treatment, standard drug and placebo.

Here this output is form ANOVA.

a) Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer.

Here P-value for % with Insurance is 0.0352 and P-value for Disease Stage is 0.0261.

Assume alpha = 0.05.

Both P-values < 0.05

Reject H0 at 5% level of significance.

Statistically significant differences in the characteristics shown among the treatments are  % with Insurance and  Disease Stage.

b) Consider the test for differences in age among treatments. Write the hypotheses and the formula of the test statistic used.

That is here null hypothesis is,

H0 : mu1 = mu2 = mu3   

H1 : at least one of the mean is not 0.

where mu1 = Population mean of the new drug.

mu2 = Population mean of the standard drug.

mu3 = Population mean of placebo

Here we use F-test.

The test statistic is,

F = MST / MSE

MST = SST / d.f.

MSE = SSE / d.f

If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that not all of population means are equal.

The differences between some of the means are statistically significant.

c) Consider the test for differences in insurance coverage among treatments. Write the hypotheses and the formula of the test statistic used

That is here null hypothesis is,

H0 : mu1 = mu2 = mu3   

H1 : at least one of the mean is not 0.

where mu1 = Population mean of the new drug.

mu2 = Population mean of the standard drug.

mu3 = Population mean of placebo

Here we use F-test.

The test statistic is,

F = MST / MSE

MST = SST / d.f.

MSE = SSE / d.f

If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that not all of population means are equal.

The differences between some of the means are statistically significant.

d) Consider the test for differences in disease stage among treatments. Write the hypotheses and the formula of the test statistic used

That is here null hypothesis is,

H0 : mu1 = mu2 = mu3   

H1 : at least one of the mean is not 0.

where mu1 = Population mean of the new drug.

mu2 = Population mean of the standard drug.

mu3 = Population mean of placebo

Here we use F-test.

The test statistic is,

F = MST / MSE

MST = SST / d.f.

MSE = SSE / d.f

If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that not all of population means are equal.

The differences between some of the means are statistically significant.