ANOVA Models: A Comprehensive Review of Analysis of Variance in Statistical Analysis and Experimental Design

ANOVA Models: A Comprehensive Review of Analysis of Variance in Statistical Analysis and Experimental Design | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 7 July 2025 V1 Latest version Share on ANOVA Models: A Comprehensive Review of Analysis of Variance in Statistical Analysis and Experimental Design Author : Surya Rao Rayarao 0009-0001-8467-7865 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175192372.29532537/v1 863 views 352 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Analysis of Variance (ANOVA) models represent a fundamental statistical framework for comparing means across multiple groups and understanding the sources of variation in experimental data. This comprehensive review examines the theoretical foundations, mathematical formulations, and practical applications of ANOVA models across various domains. We explore the evolution from simple one-way ANOVA to complex mixed-effects models, discussing the underlying assumptions, computational methods, and interpretation of results. Through detailed examples from agriculture, psychology, engineering, and biomedical research, this paper demonstrates the versatility and power of ANOVA techniques in hypothesis testing and experimental design. We also address common pitfalls, diagnostic procedures, and extensions to modern statistical computing environments. This review serves as both an educational resource and a reference guide for researchers and practitioners utilizing ANOVA models in their work. Supplementary Material File (anova_comprehensive_review_2025.pdf) Download 236.37 KB Information & Authors Information Version history V1 Version 1 07 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords analysis of variance anova experimental design f-test hypothesis testing mixed effects models statistical models 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 863 views 352 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Surya Rao Rayarao. ANOVA Models: A Comprehensive Review of Analysis of Variance in Statistical Analysis and Experimental Design. Authorea . 07 July 2025. DOI: https://doi.org/10.22541/au.175192372.29532537/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 . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); Cited by Luisa Knopf, Gregor Domes, Siri-Maria Kamp, An intricate relationship: stress markers and associative memory in a laboratory experiment in older adults, Frontiers in Aging Neuroscience, 17 , (2025). https://doi.org/10.3389/fnagi.2025.1666566 Crossref Loading... View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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