On the Use and Misuse of Chi-Square
Kevin L. Delucchi
Developmental Studies Center, San Ramon, California
One of the most useful tools available to any data analyst--especially one who deals with social science data--is Pearson's statistic known as chi-square. Its usefulness stems primarily from the fact that much of the data collected by social scientists is categorical in nature--whether ordered or unordered. Not only are variables such as sex, school, ethnicity, and experimental group categorical, but one can argue that many other measures are best, that is, conservatively, analyzed by being treated as categorical variables. This would include, for example, the ubiquitous Likert-type item often found in questionnaires and other measures.
As well as being applicable in many common analysis situations, the chi- square statistic is also quite widely known, relatively easy to compute, and available on most computer packages of statistical software. Like the good- natured nextdoor neighbor who always lends a hand without complaining, however, the chi-square statistic is easy to take for granted and easy to misuse.
The title of this chapter comes from a 1949 landmark article by Lewis and Burke entitled "The Use and Misuse of the Chi-Square Test," which appeared in Psychological Bulletin. The purpose of their article was to counteract the improper use of this statistic by researchers in the behavioral sciences. It addressed nine major sources of error, cited examples from the literature to illustrate these points, and caused a stir among practicing researchers. The Lewis and Burke paper was followed by several responses ( Edwards, 1950; Pastore, 1950; Peters, 1950) and a rejoinder by Lewis and Burke ( 1950).
Since then, use of the chi-square statistic among social scientists has increased, a great deal of research has been conducted on its behavior under a variety of conditions, and several methods have been developed to handle some