Chi-squared approximation may be incorrect

The chi-squared approximation can be incorrect under certain circumstances. Specifically, it is based on the assumption that the sample data comes from a population that follows a normal distribution, and that the sample size is sufficiently large. If these assumptions are not met, then the chi-squared approximation may be inappropriate.

In cases where the sample size is small, or the data does not follow a normal distribution, then alternative methods may be necessary. For example, the Fisher exact test can be used to analyze small sample sizes, and nonparametric tests such as the Wilcoxon rank-sum test can be used for non-normal data.

It is important to carefully consider the assumptions and limitations of any statistical method before using it to analyze data.