Normality of Data: An Essential Tool for Effective Research Study
Authors
Lagos State University (Nigeria)
Lagos State University (Nigeria)
Lagos State University (Nigeria)
Article Information
DOI: 110.47772/IJRISS.2025.91200212
Subject Category: Social science
Volume/Issue: 9/12 | Page No: 2808-2817
Publication Timeline
Submitted: 2025-12-19
Accepted: 2025-12-24
Published: 2026-01-06
Abstract
Statistical analysis is guided by a set of assumptions that ensure the validity and reliability of research findings. One of the most critical assumptions is the normality of data, particularly in the application of parametric statistical techniques. Despite its importance, many empirical studies either overlook normality testing or fail to report the results. This paper presents a conceptual review of data normality, its relevance in statistical analysis, and the implications of non-normal data for research conclusions. The review discusses graphical and statistical methods for assessing normality and examines strategies for handling non-normal data, including data transformation, non-parametric testing, robust methods, and bootstrapping. The paper concludes that assessing and reporting data normality are essential for methodological rigour, transparency, and valid inference in social science research.
Keywords
data, non-normal, non-parametric
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References
1. Albassam, M., Khan, N., & Aslam, M (2021). Neutrosophic D’Agostino test of normality: An application to water data. Journal of Mathematics. https://doi.org/10.1155/2021/5582102 [Google Scholar] [Crossref]
2. Babalola, M.A., Obubu, M., Oluwaseun, A.O., & Obiora-Ilono, H. (2018). Selection and validation of comparative study of normality test. American Journal of Mathematics and Statistics, 8(6): 190-201. DOI: 10.5923/j.ajms.20180806.05 [Google Scholar] [Crossref]
3. Biu, E.O., Nwakuya, M.T., & Wonu, N. (2019). Detection of non-normality in data sets and comparison between different normality tests. Asian Journal of Probability and Statistics. 5(4): 1-20. [Google Scholar] [Crossref]
4. Bridges, W.C., Calkin, N.J., Kenyon, C.M., & Saltzman, M.J. (2020). Log transformations: what not to expect when you’re expecting, Theory. Methods Commun. Stat. Theor. M. 1–8. [Google Scholar] [Crossref]
5. Curran-Everett, D., & Benos, D.J. (2004). Guidelines for reporting statistics in journals published by the American Physiological Society. Am JPhysiol Endocrinol Metab, 287(2), 189-91. [Google Scholar] [Crossref]
6. Elliott, A.C., & Woodward, W.A. (2007). Statistical analysis quick reference guidebook with SPSS examples (1st ed.). London: Sage Publications. [Google Scholar] [Crossref]
7. Field, A. (2009). Discovering statistics using SPSS (3rd ed.). London: SAGE publications Ltd. [Google Scholar] [Crossref]
8. Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. Int J Endocrinol Metab, 10(2):486-9. DOI: 10.5812/ijem.3505 [Google Scholar] [Crossref]
9. Guzik, P., & Więckowska, B. (2023). Data distribution analysis: A preliminary approach to quantitative data in biomedical research. Journal of Medical Science, 92(2); doi:10.20883/medical.e869 [Google Scholar] [Crossref]
10. Hernandez, H. (2021). Testing for normality: What is the best method? ForsChem Research Reports, 6(5), 2 – 38. [Google Scholar] [Crossref]
11. Jarque, C. M., & Bera, A. K. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters, 6(3): 255–259. doi:10.1016/0165-1765(80)90024-5. [Google Scholar] [Crossref]
12. Kim, H.Y. (2013). Statistical notes for clinical researchers: Assessing normal distribution using skewness and kurtosis. Restor Dent Endod. 38:52‑4. [Google Scholar] [Crossref]
13. Kim, T.K., & Park, J.H. (2019). More about the basic assumptions of t-test: normality and sample size. Korean Journal of Anesthesiology, 72(4). [Google Scholar] [Crossref]
14. Liu, J., Cosman, P. C., & Rao, B. D. (2018). Robust linear regression via L0 regularization. IEEE Transactions on Signal Processing, 66 (3):698–713. doi:10.1109/TSP.2017.2771720 [Google Scholar] [Crossref]
15. Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The importance of the normality assumption in large public health data sets. Annu. Rev. Public Health. 23:151–69. DOI: 10.1146/annurev.publheath.23.100901.140546 [Google Scholar] [Crossref]
16. Marmolejo-Ramos, F., & Gonza´lez-Burgos, J. (2012). A power comparison of various tests of univariate normality on ex-Gaussian distributions. European Journal of Research Methods for the Behavioural and Social Sciences. DOI: 10.1027/1614-2241/a000059. www.hogrefe.com/journals/methodology [Google Scholar] [Crossref]
17. Mayette S., & Emily A. B. (2013). Empirical power comparison of goodness of fit tests for normality in the presence of outliers. Journal of Physics. Conference Series 435 (2013) 012041.doi:10.1088/1742-6596/435/1/012041 [Google Scholar] [Crossref]
18. Mishra, P., Pandey, C.M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Ann Card Anaesth; 22:67-72. [Google Scholar] [Crossref]
19. Mohammad, M.H., Haneen, A., Sa'd, H., & Abdulaziz, A. (2022). Ultra-fine transformation of data for normality. Heliyon 8, e09370 [Google Scholar] [Crossref]
20. Nor A. A., Teh S. Y., Abdul-Rahman O., & Che-Rohani Y. (2011). Sensitivity of normality tests to non-normal data. Sains Malaysiana. 40(6): 637–641. [Google Scholar] [Crossref]
21. Okeniyi, J.O., Okeniyi, E.T., & Atayero, A.A. (2015). Programming development of Kolmogorov-Smirnov goodness-of-fit testing of data normality as a Microsoft ExcelR library function. Journal of Software & Systems Development, DOI: 10.5171/2015.238409 [Google Scholar] [Crossref]
22. Orcan, F. (2020). Parametric or non-parametric: Skewness to test normality for Mean comparison. International Journal of Assessment Tools in Education, 7(2), 255–265 https://doi.org/10.21449/ijate.656077 [Google Scholar] [Crossref]
23. Oztuna, D., Elhan, A.H., & Tuccar, E. (2006). Investigation of four different normality tests in terms of type 1 error rate and power under different distributions. Turkish Journal of Medical Sciences, 36(3):171-6. [Google Scholar] [Crossref]
24. Peat, J., & Barton, B. (2005). Medical statistics: A guide to data analysis and critical appraisal. Blackwell Publishing. [Google Scholar] [Crossref]
25. Priya, C. (2024). Robust Statistics, WallStreetsMojo [Google Scholar] [Crossref]
26. Sainani, K.L. (2012). Dealing with non-normal data. The American Academy of Physical Medicine and Rehabilitation. 4, 1001-1005. http://dx.doi.org/10.1016/j.pmrj.2012.10.013 [Google Scholar] [Crossref]
27. Singh, A.S., & Masuku, M.B. (2014). Assumption and testing of normality for statistical analysis. American Journal of Mathematics and Mathematical Sciences, 3(1), 169-175 [Google Scholar] [Crossref]
28. Steinskog, D.J. (2007). A cautionary note on the use of the Kolmogorov-Smirnov test for normality. American Meteor Soc. 135:1151-7. [Google Scholar] [Crossref]
29. Stephanie, G. (n.d). Jarque-Bera test from StatisticsHowTo.com: Elementary statistics for the rest of us! https://www.statisticshowto.com/jarque-bera-test/ [Google Scholar] [Crossref]
30. Ukponmwan, H.N., & Ajibade, F.B. (2017). Evaluation of techniques for univariate normality test using Monte Carlo simulation. American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics, 6(5-1): 51-61. doi: 10.11648/j.ajtas.s.2017060501.18 [Google Scholar] [Crossref]
31. Yap B. W. & Sim C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81(12), 2141-2155, DOI:10.1080/00949655.2010.520163 [Google Scholar] [Crossref]
32. Wilcox, R. R., & Rousselet, G. A. (2023). An updated guide to robust statistical methods in neuroscience. Current Protocols. 3. doi: 10.1002/cpz1.719 [Google Scholar] [Crossref]
33. Zhang, W., Yan, S., Tian, B., & Fei, D. (2022) Statistical assumptions and reproducibility in psychology: Data mining based on open science. Front. Psychol. 13:905977. doi: 10.3389/fpsyg.2022.905977 [Google Scholar] [Crossref]
34. Zimmerman, D.W. (2014). Robust statistical tests. In: Michalos, A.C. (eds) Encyclopedia of Quality of Life and Well-Being Research. Springer, Dordrecht. https://doi.org/10.1007/978-94-007- 0753- 5_2529 [Google Scholar] [Crossref]
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