arXiv subjects

František Bartoš

Publications and source records attributed to František Bartoš.

20 records · Page 2Linked to original sources

arXiv2022

When Evidence and Significance Collide

Null hypothesis statistical significance testing (NHST) is the dominant approach for evaluating results from randomized controlled trials. Whereas NHST comes with long-run error rate guarantees, its main inferential tool -- the $p$-value -- is only an indirect measure of evidence against the null hypothesis. The main reason is that the $p$-value is based on the assumption the null hypothesis is true, whereas the likelihood of the data under any alternative hypothesis is ignored. If the goal is to quantify how much evidence the data provide for or against the null hypothesis it is unavoidable that an alternative hypothesis be specified (Goodman & Royall, 1988). Paradoxes arise when researchers interpret $p$-values as evidence. For instance, results that are surprising under the null may be equally surprising under a plausible alternative hypothesis, such that a $p=.045$ result (`reject the null') does not make the null any less plausible than it was before. Hence, $p$-values have been argued to overestimate the evidence against the null hypothesis. Conversely, it can be the case that statistically non-significant results (i.e., $p>.05)$ nevertheless provide some evidence in favor of the alternative hypothesis. It is therefore crucial for researchers to know when statistical significance and evidence collide, and this requires that a direct measure of evidence is computed and presented alongside the traditional $p$-value.

stat.ME↗

arXiv2021

Bayesian Model-Averaged Meta-Analysis in Medicine

We outline a Bayesian model-averaged meta-analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness $δ$ and across-study heterogeneity $τ$. We construct four competing models by orthogonally combining two present-absent assumptions, one for the treatment effect and one for across-study heterogeneity. To inform the choice of prior distributions for the model parameters, we used 50% of the Cochrane Database of Systematic Reviews to specify rival prior distributions for $δ$ and $τ$. The relative predictive performance of the competing models and rival prior distributions was assessed using the remaining 50\% of the Cochrane Database. On average, $\mathcal{H}_1^r$ -- the model that assumes the presence of a treatment effect as well as across-study heterogeneity -- outpredicted the other models, but not by a large margin. Within $\mathcal{H}_1^r$, predictive adequacy was relatively constant across the rival prior distributions. We propose specific empirical prior distributions, both for the field in general and for each of 46 specific medical subdisciplines. An example from oral health demonstrates how the proposed prior distributions can be used to conduct a Bayesian model-averaged meta-analysis in the open-source software R and JASP. The preregistered analysis plan is available at https://osf.io/zs3df/.

stat.ME↗