Post hoc analysis of X[2] data

ABSTRACT

It is advisable to go beyond the overall consequence estimate in under to pinpoint both within and without differences. Karl Pearson [1900] introduced the chi-square [X[2]] statistic. X[2] is a frequency-based statistic. It serves two purposes: [i] it tests whether or not a significant difference exists between observed number of cases and expected number of cases specified by the null hypothesis, and [ii] it tests whether or not there is an association between two or more variables. In both cases the same X[2] formula [N-ARY Summation] [fo-fe] [2]/fe is used, and researcher gets an overall estimate in both cases. ANOVA [F] yields an overall estimate of sample means. Provided F is significant, attempt is made to pinpoint which pair AB, AC, or BC, differs, and -which does not differ between themselves and within themselves. Such an attempt is called post hoc analysis. Scheffe [1953] and Tukey [1953] statistics are widely used post hoc statistics. Unlike F, authors of text books especially designed for behavioral sciences as well as researchers have not gone beyond the overall result of X[2] test. We, here, attempt to use X[2] for two more possible points of difference i.e., within difference and between difference. Illustrative examples are given below both for the measure of goodness of fit and for the measure of association between variables