What factor influences whether chi-square is a reliable statistic in data analysis?

The reliability of the chi-square statistic in data analysis is heavily influenced by the expected frequencies in the contingency table. Specifically, for the chi-square test to yield valid results, it is essential that the expected frequency for each cell in the table is sufficiently large. Generally, a common rule of thumb is that the expected frequency should be at least 5 in each cell. When the expected frequencies are small, the approximation to the chi-square distribution might not hold, leading to erroneous conclusions from the statistical test. This is pivotal, as small expected frequencies can result in inflated Type I and Type II error rates, compromising the validity of the findings derived from the analysis.

This is particularly relevant in categorical data analysis where the chi-square test is widely utilized to assess associations between variables. If the expected frequencies are not adequate, alternative statistical methods or methods of combining categories may need to be considered to maintain the robustness of the analysis.