Question

A group of 32 rats were randomly assigned to each of 4 diets labelled (A, B,C, and D). Researchers measured the liver weight as a percentage of body weight (note: two rats escaped and another died), resulting in the following data

A	B	C	D
3.42	3.17	3.34	3.65
3.96	3.63	3.72	3.93
3.87	3.38	3.81	3.77
4.19	3.47	3.66	4.18
3.58	3.39	3.55	4.21
3.76	3.41	3.51	3.88
3.84	3.55		3.96
	3.44		3.91

Using the the Krusal-Wallis test, is there evidence, at a significance level of 0.05, that the diet impacted the liver weight as a percentage of the body weight of the rats? Show the appropriate output from Minitab to support your claim. Note – you may need to modify the format of the data in order to have it work in Minitab.

Answer 1

Ho: There is no significant difference between diets which impact on liver weight.

vs

H1: There is significant difference between diets which impact on liver weight.

Minitab: data and coding

data   coding
3.42   1
3.96   1
3.87   1
4.19   1
3.58   1
3.76   1
3.84   1
3.17   2
3.63   2
3.38   2
3.47   2
3.39   2
3.41   2
3.55   2
3.44   2
3.34   3
3.72   3
3.81   3
3.66   3
3.55   3
3.51   3
3.65   4
3.93   4
3.77   4
4.18   4
4.21   4
3.88   4
3.96   4
3.91   4

Minitab Command Line

MTB > Stack 'A'-'D' c5.
MTB > Kruskal-Wallis 'data' 'coding'.

Output

Kruskal-Wallis Test: data versus coding

Descriptive Statistics

coding	N	Median	Mean Rank	Z-Value
1	7	3.840	18.5	1.25
2	8	3.425	6.4	-3.34
3	6	3.605	11.9	-1.00
4	8	3.920	22.8	3.05
Overall	29		15.0

Test

Null hypothesis	H₀: All medians are equal
Alternative hypothesis	H₁: At least one median is different

Method	DF	H-Value	P-Value
Not adjusted for ties	3	16.79	0.001
Adjusted for ties	3	16.80	0.001

P-value< alpha=0.05

Therefore Reject Ho

Conclusion: There is significant difference between diets which impact on liver weight.