The classical and exact chi-square test of independence for analysing categorical data : a comparative application

الملخص EN

In this study we presented the classical and exact chi-square test of independence for analysing categorical data.

Our objective is to compare the application of the chi-square test in its classical form and exact form for calculating the significance probability level, to see if the two forms give similar results and, consequently, if they lead to identical conclusions and interpretations.

The objective is extended to review measures of association that based on the chi-square test value to index the strength of associations between the variables forming the cross-tabulations.

The data of the study are collected from a random sample of students at the University College of Makkah (University of Umm Alqura), and the concern is to investigate any association between the academic performance level of students and their specialization, whether they live with their families, and the educational level of their guardians.

The study showed that the significance probability levels for the classical chi-square test, based on the asymptotic distributions of the test, were not quite different from the levels of the exact test, based on the exact distributions of the test.

This could be because of the absence of the sparse cells (with zero values) in the tables of cross-classifications.

As far as the measures of association, which are based on the chi-square test, are concerned these were appeared to have relatively low values and they seem to be so generally.

Even though, and since the chi-square test is used to test the significance of these measures, these measures were in fact significant enough to be large and important.

As far as the statistical packages are concerned, the study used SPSS (Statistical Package for the Social Sciences).