Is chi-square test parametric or non-parametric?

Answer 1

non-parametric

I believe the above is a reductionistic assumption bassed upon ill-informed logic. Chi-square is a statistic that is related to the central limit theorem in the sense that proportions are in fact means, and that proportions are normally distributed (with a mean of pi [not 3.141592653...] and a variance of pi*(1-pi)). Therefore, we can perform a normal curve test for examining the difference between proportions such that Z squared = chi square on one degree of freedom. Since Z is indubitably a parametric test, and chi square can be related to Z, we can infer that it is, in fact, parametric.

From another approach, a parametric test is a test that makes an assumption about the value of a parameter (the measure of the population rather than your sample) in a statistical density function. Since our expected frequencies are based upon either theory, or a mathematical assumption based upon the average of our presented frequencies, i.e. the mean, we are making an assumption about what the parameter of our distribution would be. Therefore, given this assumption, and the relationship of chi square to the normal curve, one can argue for chi square being a parametric test.