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It introduces Bayesian testing, contrasts it with conventional p-value logic, and demonstrates the approach through a real-world example using posterior odds ratios.",{"@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/bayesian-posterior-odds-ratios-statistical-tools-for-collaborative-evaluations/591589/",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/bayesian-posterior-odds-ratios-statistical-tools-for-collaborative-evaluations/591589.png","ImageObject",300,407,{"name":42,"@type":43},"supergirl","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",8,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the role of priors in Bayesian modeling?","Question",{"text":63,"@type":64},"A prior represents the probability of a modeling hypothesis apart from the data. 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A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices more defensible. This article describes howevaluators and stakeholders could combine their expertise to select rigorous priors for analysis. The article first introduces Bayesian testing, then situates it within a collaborative framework, and finally illustrates the method with a real example.  \nKeywords  \nBayesian statistics, collaborative evaluation, Bayes’s factor, posterior odds ratios  \nBayesian methods are promising statistical tools for evaluators (Pollard, 1986) . Yet a lesser known fact is that they could facilitate collaboration. Evaluators have multiple reasons for collaborating with stakeholders (Azzam, 2010; Brandon, 1989; Cousins & Earl, 1992; Fetterman, 2001; House & Howe, 1998; Orr, 2010; Patton, 1978; Smith, 1999) . For example, collaboration could improve relevance, shared ownership, and accuracy of evaluations (Rodrı´guez-Campos, 2012) . This article clarifies how authentic collaboration could increase the rigor of data analysis with Bayesian methods.  \nBayesian methods, in particular Bayesian testing, have a different logic than conventional statistical tests, such as t tests, F tests, and w2 tests. Because Bayesian logic may be unfamiliar, we begin with an overview to foreground the methods described in this article in their theoretical context. After we present an overview, we provide an example illustrating the focal procedure in an actual collaborative evaluation.  \nThe Bayesian Approach to Statistical Testing  \nThis section introduces the logic of Bayesian methods to newcomers, and those already familiar with it can skip this section. Suppose a fortune-teller claimed to be a reliable predictor of the future.  \n1 University of Kansas, Lawrence, KS, USA  \n2 University of South Florida, Tampa, FL, USA  \nCorresponding Author:  \nTyler Hicks, Department of Special Education, University of Kansas, 1450 Jayhawk Blvd, Lawrence, KS 66045, USA. Email: [tahicks@ku.edu](tahicks@ku.edu)  \nSkeptical, you test her claim. You discover that in 10 of 12 attempts, she predicted the outcome of a fair coin toss. Perhaps she got lucky. You decide to formally test this model (i.e., she was guessing) .  \nTraditional tests only “reject” or “fail to reject” models depicting null hypotheses. This binary is not optimal. It makes accepting the null model impossible—a “failure to reject” is not the same as an “accept.” Although you prefer the null model, you proceed with the conventional test. Much to your frustration, thep value comes out very low (p \u003C .05) . Thus, the test rejects the null model atthe 5% level.  \nDespite the unwelcome outcome, you persist in clinging to the null model. You still find it to be defensible in comparison to the alternative (i.e., the fortune-teller predicted the future) . You argue to yourself that, despite thep value, the best science supports the null model. Albeit less certain, you are not yet ready to give up the null model.  \nYour reaction in the above scenario strikes Bayesians as prudent (Berger, 1985) . One problem with traditional tests, according to Bayesians, is that they may exclude knowledge that should stay in play ","cbCaiiQ1Xu7LULJc","https://ap.wps.com/l/cbCaiiQ1Xu7LULJc","pdf",418964,12,"English","# Abstract\n# The Bayesian Approach to Statistical Testing\n# Bayesian Testing","[{\"question\":\"What is the role of priors in Bayesian modeling?\",\"answer\":\"A prior represents the probability of a modeling hypothesis apart from the data. The article emphasizes that Bayesians must be able to defend their prior choice to others.\"},{\"question\":\"How does Bayesian testing differ from traditional p-value testing?\",\"answer\":\"Traditional tests focus on rejecting or failing to reject a null hypothesis, which does not directly give the probability of the null given the data. Bayesian testing compares model probabilities using posterior quantities.\"},{\"question\":\"What do posterior odds ratios provide in Bayesian testing?\",\"answer\":\"Posterior odds ratios compare the posterior probabilities of a null model versus an alternate model given the observed data. They help express how much more probable one model is than the other.\"}]","Bayesian Posterior Odds Ratios - Statistical Tools for Collaborative Evaluations | PDF",1792072786]