1. Home
  2. Vol 5, No 1 (2026)
  3. Ayenigba

A Review of Chi-Square Test of Hypothesis and Its Applications in Real-Life Situations

Alfred Ayo Ayenigba(1), Olutunde Michael Ajao(2),


(1) Department of Mathematical Sciences, Faculty of Natural Sciences, Ajayi Crowther University Oyo, Oyo State, Nigeria
(2) Department of Mathematical Sciences, Faculty of Natural Sciences, Ajayi Crowther University Oyo, Oyo State, Nigeria
Corresponding Author

Abstract


The chi square test is an essential method in statistical research because it allows scholars to examine whether two categorical variables share a meaningful relationship by comparing observed and expected frequencies to evaluate evidence against the null hypothesis. This paper presents an overview of the chi square probability distribution and its core properties, including its mean, variance, moment generating function, and characteristic function. It also outlines the types of data that suit the chi square framework, the conditions required for valid use, and the limitations that researchers must consider along with alternative statistical options when assumptions are not satisfied. The discussion further explores the three major applications of the chi square procedure which are the goodness of fit test, the test of homogeneity, and the test of association or independence, each illustrated through examples drawn from research settings and educational contexts

Keywords


hi-square tests, categorical variables, probability, moment-generating function, goodness of fit test, test of association, test of homogeneity

References


Ahad, N., Okwonu, F., Apanapudor, J. S., Arunaye, F., & Ojobor, S. A. (2023). Chi-square and adjusted standardised residual analysis. American Statistical and Mathematical Sciences, 2023, Article 985. https://doi.org/10.32802/asmscj.2023.985

Aslam, M., & Smarandache, F. (2023). Chi-square test for imprecise data in consistency table. Frontiers in Applied Mathematics and Statistics, 9, Article 1279638. https://doi.org/10.3389/fams.2023.1279638

Bolboac?, S. D., Jäntschi, L., ?e?tra?, A. F., ?e?tra?, R. E., & Pamfil, D. (2011). Pearson–Fisher chi-square statistic revisited. Information, 2(3), 528–545. https://doi.org/10.3390/info2030528

Cao, Y., Chen, R. C., & Katz, A. J. (2024). Why is a small sample size not enough? The Oncologist. 29(9): 761–76. https://doi.org/10.1093/oncolo/oyae162

Gurvich, V., & Naumova, M. (2025). Critical issues with Pearson’s chi-square test. Modern Mathematics and Modeling, 3(2), 101-109. https://doi.org/10.64700/mmm.75

Kelter, R. (2021). Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality. Computational Statistics, 36, 1263–1288. https://doi.org/10.1007/s00180-020-01034-7

McHugh, M. L. (2013). The chi-square test of independence. Biochemia Medica, 23(2), 143–149. https://doi.org/10.11613/BM.2013.018

Petcu, F.-?., Iorga, M., Semenescu, A., & Marcu, D. (2025). Analysis of research hypotheses regarding the use of electronic means of communication with ANAF. In Proceedings of the International Conference on Business Excellence (PICBE). https://doi.org/10.2478/picbe-2025-0422

Pho, K.-H., & Truong, B.-C. (2023). Pearson chi-squared and unweighted residual sum of square tests of fit for a probit model. Communications in Statistics – Simulation and Computation, 52(4). https://doi.org/10.1080/03610918.2023.2202369

Syahara, R., Sari, I. N., & Silalahi, R. D. (2025). The relationship of the quality of nursing services with family satisfaction in the perinatology room of RSUD Muhammad Sani 2024. Jurnal Kesehatan, 15(2), Article 1686. https://doi.org/10.37776/zk.v15i2.1686

Valarmathi S., Hemapriya, A. S., & Sundar, J. S. (2024). Chi-square tests: A quick guide for health researchers. International Journal of Advanced Research, 12(10), 1214-1222. https://doi.org/10.21474/ijar01/19746

Zhang, S. (2025). Analysis and optimization of the applicability of hypothesis testing methods. Computational Science and Technology, 24(261). https://doi.org/10.54254/3029-0880/2025.24261


Full Text: PDF

Article Metrics

Abstract View : 241 times
PDF Download : 39 times

DOI: 10.56534/acjpas.v5i1.187

Refbacks

  • There are currently no refbacks.