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Edited by: Zheng Jin, Zhengzhou Normal University, China

Reviewed by: Victoria Simms, Ulster University, UK; Daniel Ansari, University of Western Ontario, Canada

*Correspondence: Thomas J. Faulkenberry

This article was submitted to Cognition, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In their recent article, Sevos et al. (

The purpose of this commentary is to raise a point for further discussion. The claim that patients with schizophrenia lack this sensorimotor facilitation is based upon two non-significant effects reported in Experiments 1 and 2 of Sevos et al. (

One common approach to help mitigate this problem is to report power. Mathematically, a test with sufficient power is less likely to produce a Type II error, and this allows one to feel somewhat assured that reported null effects are not simply false negatives. Though better than nothing, this approach still does not give any direct measure of evidence supporting an obtained null effect. However, recent methods based on Bayesian inference (Wagenmakers,

Though the specifics of Bayesian inference are beyond the scope of this short commentary (see Wagenmakers, _{0} over another hypothesis _{1}; such a Bayes factor would be denoted _{01}. This Bayes factor represents the odds in favor of the null hypothesis over the alternative hypothesis after the data have been observed. Further, _{01} can be converted into a posterior probability, which is the probability that the null hypothesis _{0} is true given data

To this end, we will describe how to compute _{01} and the posterior probabilities for the null effects reported in Experiments 1 and 2 of Sevos et al. (

The first step in the computation is estimating the Bayes factor _{01}. Following Wagenmakers (_{01} that is based on the Bayesian Information Criterion, or BIC. _{01} is estimated as

where

In Equation (2), _{1} − _{0} represents the difference in the number of free parameters between the two models being compared. Note that in the case of a comparison between a null and alternative hypothesis for a single two-level factor (i.e., prime, present vs. absent), _{1} − _{0} = 1. Finally, if we assume that the null and alternative hypothesis are equally likely before collecting data (that is, equal priors), the Bayes factor _{01} can be converted into a posterior probability estimate via the equation:

Now, let us compute Bayes factors for the reported null effects in Experiment 1 and 2 of Sevos et al. (_{(1, 17)} = 2.584,

Substituting this into Equation (1) then gives us the estimate

This means that, given the data, a null interaction is only 1.21 times more likely than a true interaction between response and orientation. According to Jeffreys (

Additionally, we can use Equation (3) to compute the posterior probability of the null hypothesis:

According to Masson (

A similar computation can be carried out for the effect of action prime in Experiment 2. Sevos et al. (_{(1, 17)} = 1.288, _{01} ~ 2.208, implying that the null interaction is only 2.21 times more likely than the true interaction. Equation 3 yields a posterior probability of _{0}|

It is worth noting that this method is not the only approach to computing Bayes factors to assess null effects. The software package JASP (available as a free download from

In summary, a Bayesian analysis of these two results indicates that at present, there is not much support for the null effects reported in Experiments 1 and 2. As such, any interpretations of these null effects should be met with caution. It is important to note that the points raised in this commentary are not meant to be unfairly critical of the results obtained by Sevos et al. (

TF wrote the draft of the manuscript and performed calculations, and LT provided revisions and clarifications.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.