Chi 2 tests: how useful are they in the analysis of medical research data?

This paper has outlined analyses of data for which the chi 2 test is commonly applied and has shown that on its own, a chi 2 test provides very little information about the interpretation of the data. In goodness to fit tests, at best, the chi 2 test is a mere first step in the interpretation of the data and much more information can be gleaned from the deviations between the observed and theoretical distributions, and graphical methods are more sensitive for assessing Normality. Similarly, the chi 2 test as the analysis of a 2 x 2 contingency table misses the most important features of the data. A chi 2 value and associated p value should not be presented without an estimation of the effect and its confidence interval. The use of NS, (not significant), after a chi 2 value (or any other test statistic) is particularly meaningless as it does not even specify a level of significance. The analysis of 2 x 2 contingency tables should specify a measure of the effect such as the difference between two proportions, their ratio or the odds ratio. Confidence intervals should be calculated and least importantly, statistical significance assessed by the Standard Normal Deviate. Chi 2 has no useful role to play in the analysis of 2 x 2 contingency tables. In fact, even with larger two dimensional tables, although chi 2 can be used to test the significance of associations between the rows and columns, such results are seldom of much interest as they give no indication of where in the table associations may exist. They are insensitive particularly if the categories of the row or column variables are quantitative since chi 2 takes no account of the ordering of the rows and columns. Although simple analyses of such tables are inefficient the advent of desk-top computers means that more sophisticated techniques such as logistic regression for proportions and Poisson regression for larger or multidimensional contingency tables can be applied. Although these methods may involve chi 2 tests for testing the significance of including or excluding variables, they are always associated with estimates of effects as measured by regression coefficients. The use of chi 2 for the simple analysis of contingency tables has no place in the interpretation of medical research data.