Concepts on the cm-square test of independence for analysing categorical data

الملخص EN

In this study we review the chi-square test of independence, the most widely used test in survey analysis in general and in categorical data in particular.

We trace the sampling distribution of cell counts in multidimensional tables forming the categorical data.

The distribution of the cell counts is assumed to be conditional on the total count this yields to the conditional multinomial distribution with corresponding probabilities for these cell counts to be estimated.

Using the maximum likelihood function the expected cell counts are estimated.

The resulting test, using the Uniform Most Powerful Test, is the likelihood ratio test, which is approximately equals the chi-square test presented by Karl Pearson(1900).

There may not be major differences between the two tests but chi-square test is shown to be an approximation to the likelihood ratio test Key Words: Categorical data, Cross-classified tables, Chi-squared test of independence.