CHI-SQUARE(X2) DISTRIBUTION

The c2 distribution is used in categorical data analysis.
Categorical data analysis deals with data that can be organized into categories. The data are organized into a contingency table.
To test whether two criteria of classification are independent . For example socioeconomic status and area of residence of people in a city are independent.
We divide our sample according to status (low, medium and high) and the same samples is categorized according to residence (urban and rural).
Put the first criterion in columns equal in number to classification of 1st criteria ( Socioeconomic status) and the 2nd in rows equal to the no. of categories of 2nd criteria (residence).
Oi j : The frequencies in row and column given in any contingency table are called observed frequencies that result form the cross classification according to the two classifications.
ei j :Expected frequencies on the assumption of independence of two criterion are calculated by multiplying the marginal totals of any cell and then dividing by total frequency.
?E = ?O for each row or column.