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Unit 12: Hypothesis Testing

12.6.3 K Sample Test Notes

We can use the Mann Whitney test; when two populations are involved, the Kruskal-Wallis test
is used, when more than two populations are involved. This test will enable us to know whether
independent samples have been drawn from the same population or from different populations
having the same distribution. This test is an extension of “Mann Whitney test”.

This is a type of Rank Sum test. This test is used to find out whether two or more independent
samples are drawn from an identical population. This test is also called the H Test. Mann
Whitney test is used when only two populations are involved and Kruskal- Wallis test is used
when more than two populations are involved.

Example: In an assembling unit, three different workers do assembly work in shifts. The
data is tabulated as follows:

Shift No. Worker-1 Worker-2 Worker-3
1 25 28 29
2 31 28 30
3 35 29 27
4 33 28 36
5 35 32 31
6 31 32 34

Check whether there is any difference in the production quantum of the three workers:

Example: (Kruskal-Wallis Test, H-Test)
Let us assume that there are three categories of workers involved in a building construction. The
wages depends on the skills possessed by them and their availability. The wages of three
categories, namely painter carpenter and plumber are as follows:

Item Sample 1 Sample 2 Sample 3
Daily wages Daily wages Daily wages
(Painter ) (Carpenter ) (Plumber )
1 64 72 51
2 66 74 52
3 72 75 54
4 74 78 56
5 80

Use H-test and state whether the three populations are same or different.

Solution:
H - The wages of the three occupations are the same.
0
H - The wages of the three occupations is not the same.
1

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