1 The following table was presented in an article summarizin

1.     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

a) As p value corresponding to age, % of female and annual income is greater than 0.05, thus we can say that there is no significant difference among the different treatments age wise, gender wise and income wise.

b) Null hypothesis: there is no difference among the effect of all drugs age wise.

Alternative hypothesis: there is significant difference among the effect of drugs age wise.

Test statistic would be F statistic

F statistic = mean sum of square due to treatments with respect to age / mean sum of square due to residuals with respect to age.

c) Null hypothesis: there is no difference among the effect of all drugs insurance coverage wise.

Alternative hypothesis: there is significant difference among the effect of drugs insurance coverage wise.

ANOVA test would be appropriate here, because comparison is made between more than 2 groups. Thus test statistic would be F statistic

F statistic = mean sum of square due to treatments with respect to % with insurance coverage / mean sum of square due to residuals with respect to % with insurance coverage

d)

Null hypothesis; There is no difference among the % of patients observed in different stages while considering three types of treatments.

Alternative hypothesis: There is significant difference among the % of patients observed in different stages while considering three types of treatments.

Two way ANOVA would be appropriate here to test the above hypothesis.

And test statistic would be F

F = Mean sum of square for between groups / Mean sum of square for within groups