Volume 12, Issue 4 (December 2025)
J. Food Qual. Hazards Control 2025, 12(4): 317-324 |
Back to browse issues page
Ethics code: Not applicable
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Madadizadeh F, Abdoli M. Tutorial on Bonferroni Correction as a Post Hoc Analysis of a Significant Chi-Squared Test: A Methodological Guide in Food Science. J. Food Qual. Hazards Control 2025; 12 (4) :317-324
URL: http://jfqhc.ssu.ac.ir/article-1-1182-en.html
URL: http://jfqhc.ssu.ac.ir/article-1-1182-en.html
Student Research Committee, Hamadan University of Medical Sciences, Hamadan, Iran, Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran , abdoli_75@yahoo.com
Abstract: (75 Views)
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.
DOI: 10.18502/jfqhc.12.4.20410
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.
DOI: 10.18502/jfqhc.12.4.20410
Keywords: Chi-Square Distribution, Data Interpretation, Statistical, Biostatistics, Chi-Square Test, Paired Comparisons
Type of Study: Short communication |
Subject:
Special
Received: 24/02/11 | Accepted: 25/04/16 | Published: 25/12/21
Received: 24/02/11 | Accepted: 25/04/16 | Published: 25/12/21
References
1. Abdoli M., Amini M., Safari S., Aminorroaya A., Feizi A. (2021). Patterns of changes in abdominal obesity indices in prediabetic individuals: Results of a 16-year prospective cohort study among first-degree relatives of type 2 diabetic patients. Iranian Journal of Endocrinology and Metabolism. 22: 441-441.
2. Agresti A. (2007). An introduction to categorical data analysis. John Willey and Sons, Hoboken, New Jersey. [DOI: 10.1002/ 0470114754] [DOI:10.1002/0470114754]
3. Agresti A. (2013). Categorical data analysis. 3rd edition. John Willey and Sons, Hoboken, New Jersey. URL: https://www. wiley.com/en-us/Categorical+Data+Analysis% 2C+3rd+Edition-p-9780470463635.
4. Bahariniya S., Madadizadeh F. (2021). Review of the statistical methods used in original articles published in Iranian Journal of Public Health from 2015-2019. Iranian Journal of Public Health. 50: 1577. [DOI: 10.18502/ijph.v50i8.6803] [DOI:10.18502/ijph.v50i8.6803] [PMID] [PMCID]
5. Cabin R.J., Mitchell R.J. (2000). To Bonferroni or not to Bonferroni: when and how are the questions. Bulletin of the Ecological Society of America. 81: 246-248.
6. Casella G., Berger R.L. (2021). Statistical inference. 2nd Edition. Chapman and Hall/CRC, Boca Raton, Florida. URL: https://pages.stat.wisc.edu/~shao/stat610/Casella_Berger_Statistical_Inference.pdf.
7. Connelly L. (2019). Chi-square test. Medsurg Nursing. 28: 127-127.
8. Cox M.K., Key C.H. (1993). Post hoc pair-wise comparisons for the chi-square test of homogeneity of proportions. Educational and Psychological Measurement. 53: 951-962. [DOI:10.1177/ 0013164493053004008] [DOI:10.1177/0013164493053004008]
9. Fedrizzi M., Ferrari F. (2018). A chi-square-based inconsistency index for pairwise comparison matrices. Journal of the Operational Research Society. 69: 1125-1134. [DOI:10.1080/01605682.2017.1390523]
10. Goodman L.A. (1969). How to ransack social mobility tables and other kinds of cross-classification tables. American Journal of Sociology. 75: 1-40. [DOI:10.1086/224743]
11. Goodman L.A. (1971). Partitioning of chi-square, analysis of marginal contingency tables, and estimation of expected frequencies in multidimensional contingency tables. Journal of the American Statistical Association. 66: 339-344. [DOI: 10.2307/2283933] [DOI:10.2307/2283933]
12. Lachenbruch P.A. (2014). McNemar test. Wiley StatsRef: Statistics Reference Online. [DOI: 10.1002/9781118445112.stat04876] [DOI:10.1002/9781118445112.stat04876] [PMCID]
13. Laurencelle L. (2021). The exact binomial test between two independent proportions: a companion. The Quantitative Methods for Psychology. 17: 76-79. [DOI: 10.20982/tqmp.17.2. p076] [DOI:10.20982/tqmp.17.2.p076]
14. Liu H., Cui S.W., Chen M., Li Y., Liang R., Xu F., Zhong F. (2019). Protective approaches and mechanisms of microencapsulation to the survival of probiotic bacteria during processing, storage and gastrointestinal digestion: a review. Critical Reviews In Food Science and Nutrition. 59: 2863-2878. [https://www.tandfonline. com/doi/ full/ 10.1080/10408398.2018.1462763] [DOI:10.1080/10408398.2017.1377684] [PMID]
15. MacDonald P.L., Gardner R.C. (2000). Type I error rate comparisons of post hoc procedures for I j Chi-Square tables. Educational and Psychological Measurement. 60: 735-754. [DOI: 10.1177/ 00131640021970871] [DOI:10.1177/00131640021970871]
16. Madadizadeh F., Bahariniya S. (2022a). Frequency of the statistical methods and relation with acceptance period in archives of Iranian medicine articles: a review from 2015-2019. Archives of Iranian Medicine. 25: 267-273. [DOI: 10.34172/aim.2022.43] [DOI:10.34172/aim.2022.43] [PMID] [PMCID]
17. Madadizadeh F., Bahariniya S. (2022b). Statistical methods used in Iranian red crescent medical Journal articles and their relationship with acceptance period: a review from 2014-2021. Iranian Red Crescent Medical Journal. 24.
18. McHugh M.L. (2013). The chi-square test of independence. Biochemia medica. 23: 143-149. [DOI: 10.11613/BM.2013.018] [DOI:10.11613/BM.2013.018] [PMID] [PMCID]
19. Narum S.R. (2006). Beyond Bonferroni: less conservative analyses for conservation genetics. Conservation Genetics. 7: 783-787. [DOI: 10.1007/s10592-005-9056-y] [DOI:10.1007/s10592-005-9056-y]
20. Preacher K.J. (2001). Calculation for the chi-square test: an interactive calculation tool for chi-square tests of goodness of fit and independence. URL: http://quantpsy.org.
21. Read C.B. (1977). Partitioning chi-squape in contingency tables: a teaching approach. Communications in Statistics-Theory and Methods. 6: 553-562. [DOI: 10.1080/03610927708827513] [DOI:10.1080/03610927708827513]
22. Safari S., Abdoli M., Amini M., Aminorroaya A., Feizi A. (2021). A 16-year prospective cohort study to evaluate effects of long-term fluctuations in obesity indices of prediabetics on the incidence of future diabetes. Scientific Reports. 11: 11635. [DOI:10.1038/s41598-021-91229-9] [PMID] [PMCID]
23. Sharpe D. (2015). Chi-square test is statistically significant: now what? Practical Assessment, Research, and Evaluation. 20: 8. [DOI: 10.7275/tbfa-x148]
24. Turner R.J. (2020). Safe tests for 2 x 2 contingency tables and the Cochran-Mantel-Haenszel test. BNAIC /BeneLearn. 2020: 438. URL: https://enablingpersonalizedinterventions.nl/2020-11-09/ BNAICBENELEARN_2020_Final_paper_13.pdf.
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
