Question

You can assume that the data followed all three assumptions for ANOVA analysis, namely, independence, equal variance, and normality.

Placebo	Dose2	Dose5
4.3	3.7	1.3
9.1	3.5	1
6.1	5.2	0.7
4.7	9.3	1.2
4.1	6.7	1.3
7.8	5.2	1.6
5.7	4.1	2.4
5.8	5.3	1.9

This is my answer to the first part of the question.

Based on the results of the one-way ANOVA test, an F value of 21.093being greater than a p-value <0.05, there is a significant difference in the mean between the response index between placebo, dose 2, and dose 5. We should reject the null hypothesis and accept the alternative (There is a significant difference in the mean response index between placebo, dose 2, and dose 5).

Post hoc analysis should be carried out to test which pair of treatment differ significantly with respect to mean response index.  

I need help with Q2.

Q2: For Drug X, which dose level appeared to be better in regard to anti-tumor efficacy? [You must provide the key statistical evidence to support your decision; otherwise, you will lose some points.] [6 points] [Pay attention to my assumption about this data set: independence, equal variance, and normality]

Answer 1

The ANOVA output is:

	Mean	n	Std. Dev
	5.95	8	1.739	Placebo
	5.38	8	1.896	Dose2
	1.43	8	0.534	Dose5
	4.25	24	2.514	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	97.090	2	48.5450	21.09	9.48E-06
Error	48.330	21	2.3014
Total	145.420	23
Post hoc analysis
p-values for pairwise t-tests
		Dose5	Dose2	Placebo
		1.43	5.38	5.95
Dose5	1.43
Dose2	5.38	3.68E-05
Placebo	5.95	6.39E-06	.4568

Dose 5 is statistically significant with Dose 2 and Placebo. Therefore, Dose 5 level appeared to be better in regard to anti-tumor efficacy.