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Bayesian Calibration of p‐Values from Fisher's Exact Test

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Summary

p‐Values are commonly transformed to lower bounds on Bayes factors, so‐called minimum Bayes factors. For the linear model, a sample‐size adjusted minimum Bayes factor over the class of g‐priors on the regression coefficients has recently been proposed (Held & Ott, The American Statistician 70(4), 335–341, 2016). Here, we extend this methodology to a logistic regression to obtain a sample‐size adjusted minimum Bayes factor for 2 × 2 contingency tables. We then study the relationship between this minimum Bayes factor and two‐sided p‐values from Fisher's exact test, as well as less conservative alternatives, with a novel parametric regression approach. It turns out that for all p‐values considered, the maximal evidence against the point null hypothesis is inversely related to the sample size. The same qualitative relationship is observed for minimum Bayes factors over the more general class of symmetric prior distributions. For the p‐values from Fisher's exact test, the minimum Bayes factors do on average not tend to the large‐sample bound as the sample size becomes large, but for the less conservative alternatives, the large‐sample behaviour is as expected.

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jthaman
366 days ago
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Maryland
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Those who live by ChatGPT are destined to get advice of unpredictable quality

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jthaman
403 days ago
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Maryland
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Improving a graph

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A lot of buses are being cancelled in Auckland at the moment. This is partly due to Covid, but also due to difficulty in recruiting bus drivers because of poor pay and conditions. And probably other reasons, too. I’ve put about six weeks of daily cancellation data in a Github gist Here’s a default graph: d<-read.table("https://gist.githubusercontent.com/tslumley/9ac8df14309ecc5936183de84b57c987/raw/9ebf665b2ff9a93c1dbc73caf5ff346909899827/busdata.txt",header=TRUE) d$date<-as.Date(paste(2022, d$mo, d$d,sep="-")) plot(cancels~date, data=d) There are a lot of cancellations, but otherwise it’s not all that clear.
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jthaman
479 days ago
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Maryland
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Let's practice what we preach: Planning and interpreting simulation studies with design and analysis of experiments

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Abstract Statisticians recommend design and analysis of experiments (DAE) for evidence‐based research but often use tables to present their own simulation studies. Could DAE do better? We outline how DAE methods can be used to plan and analyze simulation studies. Tools for planning include cause‐and‐effect diagrams and factorial and fractional factorial designs. Analysis is carried out via analysis of variance, main effect and interaction plots, and other DAE tools. We also demonstrate how Taguchi robust parameter design can be used to study the robustness of methods to a variety of uncontrollable population parameters. Résumé Les statisticiens prônent le recours aux plans et analyse d'expériences (DAE) en recherche factuelle, mais le plus souvent, ils se contentent de tableaux pour présenter leurs propres études de simulation. Les auteurs de ce travail examinent l'apport et l'amélioration que pourrait apporter l'adoption de l'approche (DAE). Pour y répondre, ils présentent une description de la façon dont les méthodes DAE peuvent être employées pour planifier et analyser les études de simulation. Les outils de planification proposés comprennent les diagrammes de cause à effet et les plans factoriels et fractionnaires. L'analyse préconisée repose sur l'ANOVA, les graphiques d'effets principaux et d'interactions et d'autres outils DAE. Les auteurs montrent également comment les plans robustes de Taguchi peuvent être utilisés pour étudier la robustesse des méthodes à divers paramètres de population non contrôlables.
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jthaman
545 days ago
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Maryland
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N is never large statmodeling.stat.columbia.edu/2005/07/31/n_i…

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jthaman
552 days ago
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Maryland
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“Statistics: A Life Cycle View”

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This article from Ron Kenett is a few years old but is still relevant:

Statistics has gained a reputation as being focused only on data collection and data analysis. This paper is about an expanded view of the role of statistics in research, business, industry and service organizations. . . . a “life cycle view” consisting of: 1) Problem elicitation, 2) Goal formulation, 3) Data collection, 4) Data analysis, 5) Formulation of findings, 6) Operationalization of findings, 7) Communication and 8) Impact assessment. These 8 phases are conducted with internal iterations that combine the inductive-deductive learning process . . . The envisaged overall approach is that applied statistics needs to involve a trilogy combining: 1) a life cycle view, 2) an analysis of impact and 3) an assessment of the quality of the generated information and knowledge. . . .

It can be hard to write, and to read, this sort of article, as advice about problem elicitation, goal formulation, etc., can sound so vague compared to harder-edged topics such as optimization, computing, and probability theory. But all these things are important, and I think it does help to think them through, in specific examples and more generally.

Statistics is a branch of engineering.

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jthaman
556 days ago
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Maryland
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