Question

Question 5 Two new drugs are under development (drug A, drug B) with different mechanisms of action for treating high cholesterol. These two groups were used in a clinical trial along with a placebo control group.There were 21 patients with high cholesterol available, and 7 were randomized to each treatment group.The reductions in cholesterol level from baseline (as a percentage of baseline) are shown in the table below. We want to know if either of the two drug groups is a significant improvement on the placebo control Group Percent Reduction in cholesterol Level Drug A 24.0 15.9 21.2 20.4 17.1 6.5 13.3 Drug B 21.0 12.7 18.0 16.3 12.1 10.2 14.7 Placebo Control 6.2 11.9 7.0 1.1 4.5 9.0 4.8 We want to test the null hypothesis that the three drug groups have the same mean reduction in cholesterol levels vs. the alternative hypothesis that not all of the means are equal. a) Before carrying out any analysis, check the validity of any assumptions necessary for the ANOVA tests. Write a brief statement of your findings. b) Test the null hypothesis that the three treatment groups produce the same reduction in cholesterol levels, i.e., Test Ho: u1=u2=u3 vs. the alternative hypothesis Ha: not all of the means are equal. c) If the ANOVA test in (b) is significant, do any of the drugs (A,B) result in a significant mean reduction in cholesterol compared to placebo control? d) Briefly state your conclusions. (Use IBM SPSS for all calculations)

Answer 1

a) Test for equality of variances

i) The data provided is measured at ratio level.

ii) Here we have three categorical independent groups.

iii) The observations are independent, the observations are made on 21 different subjects which are randomly selected under each category.

iv) Equality of variances assumption

Test for Equal Variances: Drug A, Drug B, Placebo

Method

Null hypothesis	All variances are equal
Alternative hypothesis	At least one variance is different
Significance level	α = 0.05

Tests

Method	Test Statistic	P-Value
Levene	0.84	0.447

Test for Equal Variances: Drug A, Drug B, Placebo

Since p-value is more than level of significance we fail to reject null hypothesis and we conclude that the variances are equal.

b)

One-way ANOVA: Drug A, Drug B, Placebo

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Factor Information

Factor	Levels	Values
Factor	3	Drug A, Drug B, Placebo

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	442.9	221.45	11.12	0.001
Error	18	358.5	19.92
Total	20	801.4

Since p-value is less than level of significance we reject null hypothesis and we conclude that there is a significant differences between the groups of drugs.

c)

Tukey Pairwise Comparisons

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Drug B - Drug A	-1.91	2.39	(-8.00, 4.17)	-0.80	0.706
Placebo - Drug A	-10.56	2.39	(-16.65, -4.47)	-4.43	0.001
Placebo - Drug B	-8.64	2.39	(-14.73, -2.55)	-3.62	0.005

since the Tukey's interval for drug A - Drug B comparison includes zero hence these two are not significantly different.

d) From ANOVA we concluded that there exist a significant difference between the drugs, but from Tukey's simultaneous intervals we concluded that the drugs A and B are not significantly different, placebo vs drug A and Placebo vs drug B are significantly different which means the two drugs are different from placebo. If we see the comparison of placebo vs A and B there is more significant reduction happened in drug A, hence we can say drug A is slightly better than drug B.