I'm a beginner in statistics and would like to understand one of the requirements for the chi-square test to work. It is that the random variable being measured has to follow a normal distribution.
My question then is, what other models should I use if the random variables I'm measuring do not follow a normal distribution? This is similar to how the Student-t test should be used instead of the Standard Normal for a small sample, is there an equivalent for chi-square test for a small sample?
Best Answer
Normality is a requirement for the chi square test that a variance equals a specified value but there are many tests that are called chi-square because their asymptotic null distribution is chi-square such as the chi-square test for independence in contingency tables and the chi square goodness of fit test. Neither of these tests require normality. This agrees with Peter Ellis' comment.
Regarding your question when specific parametric assumptions are not made (normality being just one such assumption) there are nonparametric procedures (rank tests, permutation tests and the bootstrap) that can be applied sith more generality. In regression, robust regression is an alternative to ordinary least squares.