Bayesian Reanalyses From Summary Statistics: A Guide for Academic Consumers

Abstract

Across the social sciences, researchers have overwhelmingly used the classical statistical paradigm to draw conclusions from data, often focusing heavily on a single number: p. Recent years, however, have witnessed a surge of interest in an alternative statistical paradigm: Bayesian inference, in which probabilities are attached to parameters and models. We feel it is informative to provide statistical conclusions that go beyond a single number, and -regardless of one's statistical preference-it can be prudent to report the results from both the classical and the Bayesian paradigm. In order to promote a more inclusive and insightful approach to statistical inference we show how the opensource software program JASP (https://jasp-stats.org) provides a set of comprehensive Bayesian reanalyses from just a few commonly-reported summary statistics such as t and N . These Bayesian reanalyses allow researchers -and also editors, reviewers, readers, and reporters-to quantify evidence on a continuous scale, assess the robustness of that evidence to changes in the prior distribution, and gauge which posterior parameter ranges are more credible than others by examining the posterior distribution of the effect size. The procedure is illustrated using the seminal Festinger and Carlsmith (1959) study on cognitive dissonance.

A Bayesian Analysis of Evidence in Support of the Null Hypothesis in Gerontological Psychology (or Lack Thereof)

“…However, these analytical techniques are becoming increasingly common (van de Schoot et al, 2017), and free new statistical software such as JASP (JASP Team, 2019;Quintana & Williams, 2018) and introductory primer papers (e.g., Dienes, 2014;Etz & Vandekerckhove, 2018;Kruschke & Liddell, 2018a) are lowering the entry barriers for researchers. Additionally, NON-SIGNIFICANT RESULTS IN GERONTOLOGICAL PSYCHOLOGY 19 JASP allows for easy and efficient calculation of BFs from NHST summary statistics (i.e., the sample size and test statistic) for researchers wanting to have a very light introduction to Bayesian analyses, and/or for those reading or reviewing papers where the raw data is not publicly available (Ly et al, 2018).…”

“…Specifically, just as replication of a significant finding increases confidence in that result, the same logic must be applied to null effects (which may be harder to practice given a bias toward publishing only results that are significant; Kühberger, Fritz, & Scherndl, 2014). Increased sample sizes, testing the strength of evidence in favor of the null hypothesis through BFs, and calculating BFs in published research using only summary statistics (Ly et al, 2018) are simple ways to audit and increase confidence in null findings.…”

“…Close approximations of BFs can easily be calculated on test statistics and do not necessarily require raw data for calculation (Ly et al, 2018). Rouder, Speckman, Sun, Morey, & Iverson (2009) provide the following formula for calculating a BF01 using only N and t values, based on the Bayesian Information Criterion (Wagenmakers, 2007): differences were in fact inconclusive.…”

La inferencia bayesiana como replicación y cuantificación en la investigación clínica

“…Para el fin de la presente carta se tuvo en cuenta el tamaño de la muestra (n = 51) y el valor de correlación 4 de AU-CV (r = 0,342) reportado por Soto y otros 2 lo cual permite estimar la credibilidad de las hipótesis estadísticas de acuerdo a la muestra de estudio. 4 El factor Bayes permite inferir dos interpretaciones: FB 10 (a favor de la hipótesis alternativa de significancia) y BF 01 (a favor de la hipótesis nula) y el intervalo de cre-dibilidad al 95%. Los resultados obtenidos del factor Bayes son: BF 10 = 3,281 y BF 01 = 0,305 e IC95% [0,069 a 0,553].…”

Estimating evidential value from ANOVA summaries: A comment on Ly et al. (2018)

“…In summary, the interactive Bayes factor calculator provides a useful supplement to the tools described by Ly et al (2018) for assessing evidential value from studies. Like Figure 1 .…”