Tutorial on Bonferroni Correction as a Post Hoc analysis of a Significant Chi-Squared test: A Methodological Guide in Food Science

Abstract

Background: In medical research, analyzing the relationship between two categorical variables is common. While chi-square tests (e.g., Pearson's, McNemar's, and Cochran-Mantel-Haenszel) can determine if a significant association exists, they do not identify which specific categories differ. This tutorial aimed to examine post hoc tests that enable detailed pairwise comparisons of variable categories following a significant chi-square result.

Methods: This tutorial instructs on conducting pairwise Z-tests for comparing proportions, followed by the Bonferroni correction to adjust p-values for multiple comparisons. It also reviews and contrasts four alternative post-hoc approaches for contingency tables: standardized residuals, partitioning, cell comparison, and ransacking. A practical guide for implementing the Bonferroni-adjusted Z-test in common statistical software (R, SPSS, Stata) is provided.

Results: The Bonferroni-adjusted pairwise Z-test provides a straightforward and accessible method for pinpointing significant differences within a contingency table. This approach, readily available in major statistical software, simplifies interpretation by directly adjusting p-values and highlighting specific cells with significant deviations.

Conclusion: To mitigate the increased Type I error risk from multiple comparisons, the Bonferroni adjustment is a crucial tool for post hoc analysis after a significant chi-square test. Compared to other, more complex techniques, it offers a simpler and more intuitive framework for accurately identifying where significant differences lie.