Question

A researcher wants to investigate the bioactivity of a new drug.

Dosage                             Observations

20g	26	28	37	30
30g	427	49	36	405
40g	42	47	52	38

1. Conduct a one-way ANOVA by hand and provide the ANOVA table. Use alpha=0.05. Please show your work clearly.
2. Provide Tukey’s HSD test for multiple comparison by hand. Use alpha=0.05.

Answer 1

a) The Grand  mean is calculated with the following formula

where k are different levels and n is the no of observation in each levels.

Total Sum of square is calculated with the following formula

The mean for individual levels is calculated with the following formula

Sum of square individual levels is calculated with the following formulla

and Error sum of square is calculated with

Dosage	Observations
20g	26	28	37	30	30.25	68.75
30g	427	49	36	405	229.25	139828.75
40g	42	47	52	38	44.75	110.75
					SSE	140008.25

Also We know that

ANOVA table is given below

Source	DF	SS	MS	F	P
Factor	2	98469	49234	3.16	0.091
Error	9	140008	15556
Total	11	238477

B) Turkeys criteria T is defined as

q is obtained from Studentized Range q Table

Absolute Value of paired means are as follows

|X1-X2|	199	<246	Not significant
|X1-X3|	14.5	<246	Not significant
|X3-X2|	184.5	<246	Not significant