BFpack: Flexible Bayes Factor Testing of Scientific Theories in R

Abstract

There has been a tremendous methodological development of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constraints on the parameters of interest, and the interpretability of the outcome as the weight of evidence provided by the data in support of competing scientific theories. The available software tools for Bayesian hypothesis testing are still limited however. In this paper we present a new R-package called BFpack that contains functions for Bayes factor hypothesis testing for the many common testing problems. The software includes novel tools (i) for Bayesian exploratory testing (null vs positive vs negative effects), (ii) for Bayesian confirmatory testing (competing hypotheses with equality and/or order constraints), (iii) for common statistical analyses, such as linear regression, generalized linear models, (multivariate) analysis of (co)variance, correlation analysis, and random intercept models, (iv) using default priors, and (v) while allowing data to contain missing observations that are missing at random.

Is the approximate number system capacity limited? Extended display duration does not increase the limits of linear number estimation.

“…The smaller confidence intervals for the low number range in the long exposure duration reflect that in, the range below 20, exponent variability was reliably less when the 3 s display time was used, SD = 0.063, than when the briefer display time was used, SD = 0.135, F (19, 19) = 4.53, p = .002. There was no corresponding difference in variability for the exponents of estimates above 20, F (19, 19) = 1.38, p = .49 (the data were 3.5 more likely under the null; using the Bayesian version of the Bartlett test of variances in the BFpack R library, Mulder et al, 2019). Thus, increased display duration improved the quality of estimates for numbers below 20, but had no discernable influence on estimates above 20.…”

How Prospective Direct and Indirect Reciprocity Influence 4- to 6-Year-Old’s Sharing

“…The descriptive information is shown in Figure 1. We conducted Bayesian analyses using the R package (R Core Team, 2013) "Bayesian informative hypothesis testing" (Bain: Mulder et al, 2019;Gu et al, 2019;Hoijtink et al, 2019), and using the Bayes factor (BF) < 3 as weak support, 3 ≤ BF＜10 as moderate evidence, and BF ≥ 10 as moderate evidence in supporting the chosen hypothesis (van Doorn et al, 2021). The Bayesian analysis is suitable for examining small-sample data (McNeish, 2016).…”

Does empathy promote helping by activating altruistic motivation or concern about social evaluation? A direct replication of Fultz et al. (1986).

“…In Supplemental Materials, we report results based on the analyses described in the original preregistration, but the results of the original and amended analyses were not qualitatively different. We also report the results of non-preregistered Bayesian analyses, calculated using the BFpack package in R (Mulder et al, 2019), to evaluate the strength of the evidence for our hypotheses. We created interaction plots using the interact_plot() function from the Interactions package in R. All materials and procedures were approved by the institutional review boards at the University of Miami and the University of California, San Diego.…”