Elementary Statistics and Computer Application

x2-test for independence of attributes

-test for independence of attributes

• At times we may consider two charactertistics on attributes simultaneously. Our interest will be to test the association between these two attributes

Example

• An entomologist may be interested to know the effectiveness of different concentrations of the chemical in killing the insects. The concentrations of chemical form one attribute. The state of insects ‘killed & not killed’ forms another attribute. The result of this experiment can be arranged in the form of a contingency table. In general one attribute may be divided into m classes as A 1,A 2, …….A m and the other attribute may be divided into n classes as B 1,B 2, ……B n . Then the contingency table will have m x n cells. It is termed as m x n contingency table


• where Oij’s are observed frequencies.
• The expected frequencies corresponding to Oij is calculated as . The is computed as


where

Oij – observed frequencies
Eij – Expected frequencies
n= number of rows
m= number of columns
It can be verified that

This is distributed as with (n-1) (m-1) d.f.