[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-291045-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-291045-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","robust-bayes-factors-for-bayesian-anova-robust-bayesian-anova-thesis-overview","Robust Bayes factors for Bayesian ANOVA - Robust Bayesian ANOVA thesis - Overview","","Software Bain enables researchers to test informative hypotheses about group means by computing approximate adjusted fractional Bayes factors (AAFBF) from group mean estimates, their variances, and group sample sizes. Because sample mean and variance estimates are highly sensitive to non-normality and outliers, this thesis uses simulation to quantify how these adverse conditions affect AAFBF performance. It further evaluates a robust alternative (AAFBFROB) that replaces standard estimates with robust ones, and provides an example and computation instructions. Results show AAFBF declines with non-normality or outliers, while AAFBFROB is less affected, and recommendations are given on when to prefer the robust factor.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/robust-bayes-factors-for-bayesian-anova-robust-bayesian-anova-thesis-overview/291045/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/robust-bayes-factors-for-bayesian-anova-robust-bayesian-anova-thesis-overview/291045.png","ImageObject",300,407,{"name":42,"@type":43},"Ivy","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-09-17",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How does Bain compute the approximate adjusted fractional Bayes factor (AAFBF)?","Question",{"text":63,"@type":64},"Bain computes the AAFBF using group mean estimates, their variances, and group sample sizes as inputs for informative hypotheses about group means.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why can standard AAFBF be adversely affected by non-normality and outliers?",{"text":68,"@type":64},"The common sample mean and variance are highly susceptible to non-normality and outliers, which can degrade AAFBF performance and lead to biased or inaccurate inference.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the robust Bayes factor AAFBFROB and what does the simulation show?",{"text":72,"@type":64},"AAFBFROB mitigates adverse effects by replacing the sample mean and corresponding variance with robust estimates. Simulations show AAFBF performance decreases when non-normality or outliers are present, while AAFBFROB is less affected in most cases.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},291045,1789643300,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145,"preview_page_count":4},549758252649,"https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819","Research Master’s programme Methodology and Statistics for the Behavioural, Biomedical and Social Sciences  \nUtrecht University, the Netherlands  \nMSc Thesis Marlyne Bosman (3957675)  \nTITLE: Robust Bayes factors for Bayesian ANOVA: overcoming adverse effects of non-normality and outliers  \nMay 2018  \nSupervisor:  \nProf. Dr. Herbert Hoijtink  \nSecond grader:  \nDr. Rens van de Schoot  \nPreferred journal of publication: Psychological Methods  \nWord count: 7086  \nRunning head: ROBUST BAYES FACTORS FOR BAYESIAN ANOVA 1  \nRobust Bayes factors for Bayesian ANOVA: overcoming adverse effects of non-normality  \nand outliers  \nMarlyne Bosman  \nUtrecht University  \nROBUST BAYES FACTORS FOR BAYESIAN ANOVA 2  \nAbstract  \nThe software package Bain (Gu, Mulder, & Hoijtink, 2017) provides an easy way for researchers to evaluate informative hypotheses with regards to group means. Support in the data for pairs of informative hypotheses is quantified by Bain by computing the approximate adjusted fractional Bayes factor (AAFBF) . To compute the AAFBF, Bain only needs group mean estimates, their variances and group sample sizes as input. Unfortunately, the common sample mean and its variance are known to be highly susceptible to non-normality and outliers. Therefore, first of all, this paper investigates with a simulation study to what extent the AAFBF resulting from the sample mean and its variance is affected by non-normality and outliers. Furthermore, Bain provides an unique opportunity to combine Bayes factors with robust statistics. Hence, secondly, this paper investigates with a simulation study to what extent the effect of non-normality and outliers can be ameliorated by replacing the sample mean and the corresponding variance estimates by robust estimates, creating the robust Bayes factor AAFBFROB . Results of the simulation studies showed that the performance of the AAFBF decreases when  \nnon-normality or outliers are present and that the AAFBFROB is less affected in most instances. An example study is presented to show how the AAFBFROB can be used and instructions how to compute it are provided. Finally, recommendations for researchers as to when use of the AAFBFROB is preferred over use of the AAFBF are given.  \nKeywords: ANOVA, Bain, Bayes factor, informative hypotheses, robust statistics  \nROBUST BAYES FACTORS FOR BAYESIAN ANOVA 3  \nRobust Bayes factors for Bayesian ANOVA: overcoming adverse effects of non-normality  \nand outliers  \nIntroduction  \nAnalysis of variance (ANOVA) is a statistical approach for comparing means that is used by many researchers. ANOVA can only be validly applied when the data meets certain assumptions (Miller, 1998) . That is, ANOVA assumes that the data is normally distributed within each group, that within group variances are equal and that observations are independent. Unfortunately, violations of these assumptions can seriously bias results from an ANOVA (Miller, 1998 ; Wilcox, 2017 , pp. 9-11) . In this paper, the impact and approach for handling violations of the normality assumption will be investigated in the context of a Bayesian ANOVA. To deal with possible violations of the equal within group variances assumption, an unequal variances ANOVA can be used, as will be done in this paper. Violations of the independent observations assumption can be handled by modelling dependence between the observations, for example with a multi-level model (Hox, n.d.) . However, this paper will only investigate the situation where the observations are independent.  \nNotably, even a small departure from normality can seriously affect an ANOVA. For example, when a distribution is skewed (i.e. asymmetric) the sample mean no longer represents the central tendency, where the bulk of the data is located (Wilcox, 2017 , p. 5) . Furthermore, when a distribution is heavy-tailed (i.e. has more observations in the tails) the error variance of the mean increases, thereby leading to a reduced power of statistical tests involving the mean ","cbCaitmjW6cwl1dI","https://ap.wps.com/l/cbCaitmjW6cwl1dI","pdf",411003,45,"English","# Abstract\n# Introduction\n## Assumptions of ANOVA and their violations\n## Non-normality and its impact in Bayesian ANOVA\n## Outliers and their generating mechanisms","[{\"question\":\"How does Bain compute the approximate adjusted fractional Bayes factor (AAFBF)?\",\"answer\":\"Bain computes the AAFBF using group mean estimates, their variances, and group sample sizes as inputs for informative hypotheses about group means.\"},{\"question\":\"Why can standard AAFBF be adversely affected by non-normality and outliers?\",\"answer\":\"The common sample mean and variance are highly susceptible to non-normality and outliers, which can degrade AAFBF performance and lead to biased or inaccurate inference.\"},{\"question\":\"What is the robust Bayes factor AAFBFROB and what does the simulation show?\",\"answer\":\"AAFBFROB mitigates adverse effects by replacing the sample mean and corresponding variance with robust estimates. Simulations show AAFBF performance decreases when non-normality or outliers are present, while AAFBFROB is less affected in most cases.\"}]","Robust Bayes factors for Bayesian ANOVA - Robust Bayesian ANOVA thesis - Overview | PDF",113]