One-way Analysis of Variance: A Comprehensive Review of Theory, Applications, and Statistical Inference

One-way Analysis of Variance: A Comprehensive Review of Theory, Applications, and Statistical Inference | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 8 July 2025 V1 Latest version Share on One-way Analysis of Variance: A Comprehensive Review of Theory, Applications, and Statistical Inference Author : Surya Rao Rayarao 0009-0001-8467-7865 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175199900.09144757/v1 510 views 262 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract One-way Analysis of Variance (ANOVA) is a fundamental statistical technique used to compare means across multiple groups simultaneously. This paper provides a comprehensive review of the theoretical foundations, assumptions, methodology, and applications of one-way ANOVA. We examine the mathematical framework underlying ANOVA, discuss the Ftest statistic and its distribution, and explore post-hoc analysis techniques. Through detailed examples and case studies, we demonstrate the practical implementation of one-way ANOVA in various fields including medicine, psychology, engineering, and social sciences. The paper also addresses assumption validation, effect size measures, and power analysis considerations. This review serves as both an educational resource and a reference guide for researchers and practitioners utilizing one-way ANOVA in their statistical analyses. Supplementary Material File (onewayanova_comprehensivereview_rayaraos.pdf) Download 171.05 KB Information & Authors Information Version history V1 Version 1 08 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords anova experimental design f-test hypothesis testing post-hoc analysis statistical inference Authors Affiliations Surya Rao Rayarao 0009-0001-8467-7865 [email protected] Department of Statistics and Data Sciences Department of Computer Science, The University of Texas at Austin Austin View all articles by this author Metrics & Citations Metrics Article Usage 510 views 262 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Surya Rao Rayarao. One-way Analysis of Variance: A Comprehensive Review of Theory, Applications, and Statistical Inference. Authorea . 08 July 2025. DOI: https://doi.org/10.22541/au.175199900.09144757/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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