Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses

Bayesian evidence synthesis as a flexible alternative to meta-analysis: A simulation study and empirical demonstration

Synthesizing results across multiple studies is a popular way to increase the robustness of scientific findings. The most well-known method for doing this is meta-analysis. However, because meta-analysis requires conceptually comparable effect sizes with the same statistical form, meta-analysis may not be possible when studies are highly diverse in terms of their research design, participant characteristics, or operationalization of key variables. In these situations, Bayesian evidence synthesis may constitute a flexible and feasible alternative, as this method combines studies at the hypothesis level rather than at the level of the effect size. This method therefore poses less constraints on the studies to be combined. In this study, we introduce Bayesian evidence synthesis and show through simulations when this method diverges from what would be expected in a meta-analysis to help researchers correctly interpret the synthesis results. As an empirical demonstration, we also apply Bayesian evidence synthesis to a published meta-analysis on statistical learning in people with and without developmental language disorder. We highlight the strengths and weaknesses of the proposed method and offer suggestions for future research.

Bayesian evaluation of diverging theories of episodic and affective memory distortions in dysphoria

People suffering from dysphoria retrieve autobiographical memories distorted in content and affect, which may contribute to the aetiology and maintenance of depression. However, key memory difficulties in dysphoria remain elusive because theories disagree how memories of different valence are altered. Here, we assessed the psychophysiological expression of affect and retrieved episodic detail while participants with dysphoria (but without a diagnosed mental illness) and participants without dysphoria relived positive, negative, and neutral memories. We show that participants with dysphoria retrieve positive memories with diminished episodic detail and negative memories with enhanced detail, compared to participants without dysphoria. This is in line with negativity bias but not overgeneral memory bias theories. According to confirmatory analyses, participants with dysphoria also express diminished positive affect and enhanced negative affect when retrieving happy memories, but exploratory analyses suggest that this increase in negative affect may not be robust. Further confirmatory analyses showed that affective responses to memories are not related to episodic detail and already present during the experience of new emotional events. Our results indicate that affective memory distortions may not emerge from mnemonic processes but from general distortions in positive affect, which challenges assumptions of memory theories and therapeutics. Protocol registration: The Stage 1 protocol for this Registered Report was accepted in principle on the 18rd of March 2021. The protocol, as accepted by the journal, can be found at https://doi.org/10.6084/m9.figshare.14605374.v1 .

Reduced Thickness of the Retina in de novo Parkinson's Disease Shows A Distinct Pattern, Different from Glaucoma

Background

Parkinson's disease (PD) patients experience visual symptoms and retinal degeneration. Studies using optical coherence tomography (OCT) have shown reduced thickness of the retina in PD, also a key characteristic of glaucoma.

Objective

To identify the presence and pattern of retinal changes in de novo, treatment-naive PD patients compared to healthy controls (HC) and early primary open angle glaucoma (POAG) patients.

Methods

Macular OCT data (10×10 mm) were collected from HC, PD, and early POAG patients, at the University Medical Center Groningen. Bayesian informative hypotheses statistical analyses were carried out comparing HC, PD-, and POAG patients, within each retinal cell layer.

Results

In total 100 HC, 121 PD, and 78 POAG patients were included. We showed significant reduced thickness of the inner plexiform layer and retinal pigment epithelium in PD compared to HC. POAG patients presented with a significantly thinner retinal nerve fiber layer, ganglion cell layer, inner plexiform layer, outer plexiform layer, and outer photoreceptor and subretinal virtual space compared to PD. Only the outer segment layer and retinal pigment epithelium were significantly thinner in PD compared to POAG.

Conclusions

De novo PD patients show reduced thickness of the retina compared to HC, especially of the inner plexiform layer, which differs significantly from POAG, showing a more extensive and widespread pattern of reduced thickness across layers. OCT is a useful tool to detect retinal changes in de novo PD, but its specificity versus other neurodegenerative disorders has to be established.

Bayesian sequential designs in studies with multilevel data

In many studies in the social and behavioral sciences, the data have a multilevel structure, with subjects nested within clusters. In the design phase of such a study, the number of clusters to achieve a desired power level has to be calculated. This requires a priori estimates of the effect size and intraclass correlation coefficient. If these estimates are incorrect, the study may be under- or overpowered. This may be overcome by using a group-sequential design, where interim tests are done at various points in time of the study. Based on interim test results, a decision is made to either include additional clusters or to reject the null hypothesis and conclude the study. This contribution introduces Bayesian sequential designs as an alternative to group-sequential designs. This approach compares various hypotheses based on the support in the data for each of them. If neither hypothesis receives a sufficient degree of support, additional clusters are included in the study and the Bayes factor is recalculated. This procedure continues until one of the hypotheses receives sufficient support. This paper explains how the Bayes factor is used as a measure of support for a hypothesis and how a Bayesian sequential design is conducted. A simulation study in the setting of a two-group comparison was conducted to study the effects of the minimum and maximum number of clusters per group and the desired degree of support. It is concluded that Bayesian sequential designs are a flexible alternative to the group sequential design.

Multibridge: an R package to evaluate informed hypotheses in binomial and multinomial models

The multibridge R package allows a Bayesian evaluation of informed hypotheses [Formula: see text] applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 𝜃: (a) hypotheses that postulate equality constraints (e.g., 𝜃1 = 𝜃2 = 𝜃3); (b) hypotheses that postulate inequality constraints (e.g., 𝜃1 < 𝜃2 < 𝜃3 or 𝜃1 > 𝜃2 > 𝜃3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 𝜃1 < 𝜃2 = 𝜃3); and (d) hypotheses that postulate combinations of (a)-(c) (e.g., 𝜃1 < (𝜃2 = 𝜃3),𝜃4). Any informed hypothesis [Formula: see text] may be compared against the encompassing hypothesis [Formula: see text] that all category proportions vary freely, or against the null hypothesis [Formula: see text] that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

Comparing the prevalence of statistical reporting inconsistencies in COVID-19 preprints and matched controls: a registered report

The COVID-19 outbreak has led to an exponential increase of publications and preprints about the virus, its causes, consequences, and possible cures. COVID-19 research has been conducted under high time pressure and has been subject to financial and societal interests. Doing research under such pressure may influence the scrutiny with which researchers perform and write up their studies. Either researchers become more diligent, because of the high-stakes nature of the research, or the time pressure may lead to cutting corners and lower quality output. In this study, we conducted a natural experiment to compare the prevalence of incorrectly reported statistics in a stratified random sample of COVID-19 preprints and a matched sample of non-COVID-19 preprints. Our results show that the overall prevalence of incorrectly reported statistics is 9-10%, but frequentist as well as Bayesian hypothesis tests show no difference in the number of statistical inconsistencies between COVID-19 and non-COVID-19 preprints. In conclusion, the literature suggests that COVID-19 research may on average have more methodological problems than non-COVID-19 research, but our results show that there is no difference in the statistical reporting quality.

Sample size determination for Bayesian ANOVAs with informative hypotheses

Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Bayesian ANOVA, Bayesian Welch's ANOVA, and Bayesian robust ANOVA are available. Using the R package SSDbain and/or the tables provided in this paper, researchers in the social and behavioral sciences can easily plan the sample size if they intend to use a Bayesian ANOVA.

Bayesian Testing of Scientific Expectations under Multivariate Normal Linear Models

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated measures analysis. Statistical criteria for a model selection problem where models may have equality as well as order constraints on the model parameters based on scientific expectations are limited however. This paper presents a default Bayes factor for this inference problem using fractional Bayes methodology. Group specific fractions are used to properly control prior information. Furthermore the fractional prior is centered on the boundary of the constrained space to properly evaluate order-constrained models. The criterion enjoys various important properties under a broad set of testing problems. The methodology is readily usable via the R package 'BFpack'. Applications from the social and medical sciences are provided to illustrate the methodology.

Do Open-Science Badges Increase Trust in Scientists Among Undergraduates, Scientists, and the Public?

In three experimental studies, we investigated whether badges for open-science practices have the potential to affect trust in scientists and topic-specific epistemic beliefs by student teachers (n = 270), social scientists (n = 250), or the public (n = 257), all of whom were at least 16 years old. Furthermore, we analyzed the moderating role of epistemic beliefs for badges and trust. Each participant was randomly assigned to two of three conditions: badges awarded, badges not awarded, and no badges (control). In all samples, our Bayesian analyses indicated that badges influence trust as expected, with one exception in the public sample: An additional positive effect of awarded badges (compared with no badges) was not supported. For students and scientists, we found evidence for the relation of badges and epistemic beliefs as well as epistemic beliefs and trust. Further, we found evidence for the absence of moderation by epistemic beliefs.

Dynamic relational event modeling: Testing, exploring, and applying

The relational event model (REM) facilitates the study of network evolution in relational event history data, i.e., time-ordered sequences of social interactions. In real-life social networks it is likely that network effects, i.e., the parameters that quantify the relative importance of drivers of these social interaction sequences, change over time. In these networks, the basic REM is not appropriate to understand what drives network evolution. This research extends the REM framework with approaches for testing and exploring time-varying network effects. First, we develop a Bayesian approach to test whether network effects change during the study period. We conduct a simulation study that illustrates that the Bayesian test accurately quantifies the evidence between a basic (‘static’) REM or a dynamic REM. Secondly, in the case of the latter, time-varying network effects can be studied by means of a moving window that slides over the relational event history. A simulation study was conducted that illustrates that the accuracy and precision of the estimates depend on the window width: narrower windows result in greater accuracy at the cost of lower precision. Third, we develop a Bayesian approach for determining window widths using the empirical network data and conduct a simulation study that illustrates that estimation with empirically determined window widths achieves both good accuracy for time intervals with important changes and good precision for time intervals with hardly any changes in the effects. Finally, in an empirical application, we illustrate how the approaches in this research can be used to test for and explore time-varying network effects of face-to-face contacts at the workplace.

Interaction effect: Are you doing the right thing?

How to correctly interpret interaction effects has been largely discussed in scientific literature. Nevertheless, misinterpretations are still frequently observed, and neuroscience is not exempt from this trend. We reviewed 645 papers published from 2019 to 2020 and found that, in the 93.2% of studies reporting a statistically significant interaction effect (N = 221), post-hoc pairwise comparisons were the designated method adopted to interpret its results. Given the widespread use of this approach, we aim to: (1) highlight its limitations and how it can lead to misinterpretations of the interaction effect; (2) discuss more effective and powerful ways to correctly interpret interaction effects, including both explorative and model selection procedures. The paper provides practical examples and freely accessible online materials to reproduce all analyses.

Benchmarked effectiveness of family and school involvement in group exposure therapy for adolescent anxiety disorder

Although cognitive-behavioral therapy (CBT) is an effective treatment for adolescents with anxiety disorders, the majority remain impaired following treatment. We developed a group CBT program (RISK) with high degrees of exposure practice and family and school involvement delivered in a community-based setting and investigated its effectiveness. The treatment involved adolescents (N = 90), with a primary diagnosis of anxiety disorder (82%) or obsessive-compulsive disorder (18%), and their families who received 38 hours of group treatment over 10 weeks. Diagnostic status and symptom severity were assessed at pre- and post-treatment, and a 12-month follow-up and benchmarked against previous effectiveness studies. Our results showed that, at post-treatment, the RISK-treatment was comparably effective as benchmarks on measures of diagnostic status, parent-rated measures, adolescent-rated measures, and clinician-rated measures. At 12-month follow-up all outcomes were superior to benchmarks, including the proportion of participants in remission (79.5%, 95% Highest Posterior Density Interval [74.7, 84.2]), indicating that the RISK-treatment enhanced effectiveness over time. The combination of group format, a high degree of exposure practice, and school and family involvement is a promising format for real-world settings that may help sustain and increase treatment effectiveness. Trial registered at helseforskning.etikkom.no (reg. nr. 2017/1367).

A network analysis of rest-activity rhythms in young people with emerging bipolar disorders

AIMS

Actigraphy studies of individuals with bipolar disorders (BD) suggest that illness progression may be associated with a range of progressive disruptions in 24-hour rest-activity rhythms (RAR). However, those longitudinal studies were undertaken in older adults with extended histories or illness and treatment rather than young people with emerging BD. To our knowledge, this is the first study to use network modelling to examine the statistical associations between clinical phenotypes of BD and different subsets of RAR markers.

METHODS

This study of adolescents and young adults (mean age 22 years; 69% female) uses network modelling to examine which self-rated or actigraphic markers of RAR are more strongly associated with full threshold BD (referred to as Stage 2; N = 15) compared with BD-at risk syndromes (subthreshold presentations referred to as Stage 1; N = 25).

RESULTS

Network analysis demonstrated that some RAR are associated with both stage of BD and a family history of BD (such as longer sleep duration and higher levels of daytime impairment). Markers of circadian rhythmicity indicated that regulation of this system is weaker in Stage 2 compared with Stage 1 of BD.

LIMITATIONS

The small subgroup samples may have undermined the ability to detect some associations between phenotypes and RAR.

CONCLUSIONS

Network modelling may offer a useful strategy for visualizing and analysing patterns of association between RAR and clinical phenotypes defined by stage of illness, familial loading or symptom profile. This could prove useful in understanding the underlying pathophysiology of sleep-wake cycle and circadian rhythm disturbances in BD.

Bayesian One-Sided Variable Selection

This paper presents a novel Bayesian variable selection approach that accounts for the sign of the regression coefficients based on multivariate one-sided tests. We propose a truncated g prior to specify a prior distribution of coefficients with anticipated signs in a given model. Informative priors for the direction of the effects can be incorporated into prior model probabilities. The best subset of variables is selected by comparing the posterior probabilities of the possible models. The new Bayesian one-sided variable selection procedure has higher chance to include relevant variables and therefore select the best model, if the anticipated direction is accurate. For a large number of candidate variables, we present an adaptation of a Bayesian model search method for the one-sided variable selection problem to ensure fast computation. In addition, a fully Bayesian approach is used to adjust the prior inclusion probability of each one-sided model to correct for multiplicity. The performance of the proposed method is investigated using several simulation studies and two real data examples.

EXPRESS: Feature specific retrieval of the knowledge of having lied before: Persons and questions independently retrieve truth-related information

Previous research on event coding has shown that, by default, bindings are binary and elemental, that is, individual objects or single features of these objects can retrieve responses separately and independently. In our study, we applied these findings to the automatic retrieval of former deceptions. Specifically, we investigated whether the person or the question to which one has answered deceptively can retrieve this knowledge independently, or whether there is also evidence for configural retrieval processes that use a combination of person and question information to retrieve the truth status of former episodes. We found evidence for retrieval based on single cues (i.e., person or question), supporting that the elementary retrieval of episodes by independent cues also holds in the context of retrieving knowledge about former lies.

Bridging the Gap Between Science and Practice: Research Collaboration and the Perception of Research Findings

Research collaboration promises a useful approach to bridging the gap between research and practice and thus promoting evidence-informed education. This study examines whether information on research collaboration can influence the reception of research knowledge. We assume that the composition of experts from the field and scientists in a research team sends out signals that influence trust in as well as the relevance and applicability of the finding. In a survey experiment with practitioners from the field of adult education the influence of different research team compositions around an identical finding is tested. The results show overall high trust, relevance and applicability ratings with regard to the finding, regardless of the composition of the research team. We discuss the potential importance of additional information about research collaborations for effective knowledge translation and point out the need for more empirical research.

Bayes factor testing of equality and order constraints on measures of association in social research

Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is proposed for testing multiple hypotheses with constraints on the measures of association between ordinal and/or continuous variables, possibly after correcting for certain covariates. This test can be used to obtain a direct answer to the research question how much evidence there is in the data for a social science theory relative to competing theories. The stand-alone software package 'BCT' allows users to apply the methodology in an easy manner. The methodology will also be available in the R package 'BFpack'. An empirical application from leisure studies about the associations between life, leisure and relationship satisfaction and an application about the differences about egalitarian justice beliefs across countries are used to illustrate the methodology.

Empirical Investigation of the Verbal Cues Involved in Delivering Experiential Metaphors

Delivering metaphors experientially has been emphasized in several psychotherapies, such as acceptance and commitment therapy. However, few research has analyzed the variables involved in the efficacy of metaphors. This experimental analog study aims to advance in this topic by analyzing the effect of two components involved in the experiential delivery of metaphors in psychotherapy. The first component is presenting the metaphor by asking the individual to imagine herself as the protagonist of the story versus presenting the metaphor in the third person (Self vs. Other). The second component is the inclusion of verbal cues prompting the relational elaboration of the rules derived from the metaphor content versus not including these prompts (Elaboration vs. No Elaboration). The effect of these components was tested in a double-blind, randomized, 2 × 2 factorial experiment that used the cold pressor task (CPT). Eighty-four participants were exposed to the CPT at the pretest. Afterward, participants were randomly assigned to four experimental protocols. The protocols were audiotaped and consisted of the same metaphor presented in four slightly different ways. Specifically, the protocol of Condition A involved a metaphor with Self and Elaboration, Condition B involved Self and No Elaboration, Condition C involved Other and Elaboration, and Condition D involved Other and No Elaboration. Then, participants were re-exposed to the CPT in the posttest. We hypothesized that Condition A (Self and Elaboration) would show a higher mean increase in pain tolerance than the remaining conditions, which would show similar results. The results were consistent with this hypothesis because Condition A showed a higher percentual increase in pain tolerance (Condition A: M = 268.21, SD = 167.47; Condition B: M = 180.86, SD = 73.01; Condition C: M = 204.81, SD = 100.19; Condition D: M = 175.41, SD = 76.00). A Bayesian informative hypothesis evaluation showed that this hypothesis obtained the highest posterior model probability. Thus, the results indicate that introducing metaphors by asking the individual to imagine herself as the protagonist of the story and providing prompts for relational elaboration might increase the therapeutic effect of the metaphor.

Bayesian updating: increasing sample size during the course of a study

Background

A priori sample size calculation requires an a priori estimate of the size of the effect. An incorrect estimate may result in a sample size that is too low to detect effects or that is unnecessarily high. An alternative to a priori sample size calculation is Bayesian updating, a procedure that allows increasing sample size during the course of a study until sufficient support for a hypothesis is achieved. This procedure does not require and a priori estimate of the effect size. This paper introduces Bayesian updating to researchers in the biomedical field and presents a simulation study that gives insight in sample sizes that may be expected for two-group comparisons.

Methods

Bayesian updating uses the Bayes factor, which quantifies the degree of support for a hypothesis versus another one given the data. It can be re-calculated each time new subjects are added, without the need to correct for multiple interim analyses. A simulation study was conducted to study what sample size may be expected and how large the error rate is, that is, how often the Bayes factor shows most support for the hypothesis that was not used to generate the data.

Results

The results of the simulation study are presented in a Shiny app and summarized in this paper. Lower sample size is expected when the effect size is larger and the required degree of support is lower. However, larger error rates may be observed when a low degree of support is required and/or when the sample size at the start of the study is small. Furthermore, it may occur sufficient support for neither hypothesis is achieved when the sample size is bounded by a maximum.

Conclusions

Bayesian updating is a useful alternative to a priori sample size calculation, especially so in studies where additional subjects can be recruited easily and data become available in a limited amount of time. The results of the simulation study show how large a sample size can be expected and how large the error rate is.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01334-6.

Sample-size determination for the Bayesian t test and Welch's test using the approximate adjusted fractional Bayes factor

When two independent means μ₁ and μ₂ are compared, H₀ : μ₁ = μ₂, H₁ : μ₁≠μ₂, and H₂ : μ₁ > μ₂ are the hypotheses of interest. This paper introduces the R package SSDbain, which can be used to determine the sample size needed to evaluate these hypotheses using the approximate adjusted fractional Bayes factor (AAFBF) implemented in the R package bain. Both the Bayesian t test and the Bayesian Welch’s test are available in this R package. The sample size required will be calculated such that the probability that the Bayes factor is larger than a threshold value is at least η if either the null or alternative hypothesis is true. Using the R package SSDbain and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments.

Beyond Discrete Choices - Investigating the Effectiveness of a Proximity Nudge With Multiple Alternative Options

Nudges are defined as small adjustments in the choice architecture that stimulate desirable behavior. Nudging techniques can be used as a promising policy tool, but research has hardly systematically taken into account the complexity of the situation in which nudges have been implemented. In the current studies, we investigated the effectiveness of a proximity nudge on food choice in a realistic situation with multiple options in the immediate surroundings of the target option. In two studies, we presented participants from a community sample with an assortment of either three or nine different types of chocolate. For half of the participants, the target chocolate was placed most proximally on a table. Across two studies, we demonstrated that the proximity nudge was effective in stimulating the choice for a specific piece of chocolate in a simple and more complex situation. Results were further qualified by Bayesian analyses, which revealed most support for the hypothesis that the proximity effect existed in both the conditions with three and nine options, regardless of the number of options in the choice set. Results imply that the proximity effect can remain robust in realistic situations that include multiple options in the immediate environment to choose from.

Encoding or consolidation? The effects of pre- and post-learning propranolol on the impact of an emotional scene

BACKGROUND AND OBJECTIVES

Researchers have conceived of post-traumatic stress disorder (PTSD) as a disorder of memory, and proposed that blocking the impact of stress-related noradrenaline release in the aftermath of trauma may be a way of preventing the 'over-consolidation' of trauma-related memories. Experimental research in humans has been limited by typically focusing on declarative memory for emotional stories, and has mainly given propranolol before learning. In contrast, the clinical studies that we comprehensively review are hampered by practical challenges, such as reliably administering propranolol in a time window sufficiently close to the traumatic event. In this study, we aimed to assess the impact of both pre- and post-learning propranolol on emotional and declarative memory for an emotional scene, using the 'trauma film paradigm'.

METHODS

To control for drug and timing effects, participants received a pill (40 mg propranolol or placebo) both 60 min before and within 5 min after viewing a 12 min, emotionally arousing trauma film, and were assigned to one of the three conditions: propranolol-placebo (n = 25), placebo-propranolol (n = 25), or placebo-placebo (n = 25). We assessed participants' immediate emotional responses to the scene, as well as delayed impact (intrusions, Impact of Events Scale) and declarative memory.

RESULTS

Using Bayesian informative hypothesis testing, we found that pre-learning propranolol reduced the initial emotional impact of the 'trauma film'. However, we did not find strong evidence for an impact of pre- or post-learning propranolol on later consequences of having watched the emotional film (intrusions, Impact of Events, or tests of declarative memory). Exploratorily restricting analyses to women, we did find evidence suggesting that pre-encoding propranolol could reduce the rate of intrusions and self-reported negative impact of the emotional scene one week later.

LIMITATIONS

Floor effects in the delayed impact of the emotional scene could preclude observing differences as a function of propranolol, and propranolol dosage may need to be increased.

CONCLUSIONS

An impact of propranolol on encoding could raise difficulties in interpretation when only pre-encoding propranolol is used to make inferences about consolidation. We discuss the challenges of elucidating the mechanistic underpinnings of propranolol's reported effects on memory.

Parental Age and Offspring Childhood Mental Health: A Multi-Cohort, Population-Based Investigation

To examine the contributions of maternal and paternal age on offspring externalizing and internalizing problems, this study analyzed problem behaviors at age 10-12 years from four Dutch population-based cohorts (N = 32,892) by a multiple informant design. Bayesian evidence synthesis was used to combine results across cohorts with 50% of the data analyzed for discovery and 50% for confirmation. There was evidence of a robust negative linear relation between parental age and externalizing problems as reported by parents. In teacher-reports, this relation was largely explained by parental socio-economic status. Parental age had limited to no association with internalizing problems. Thus, in this large population-based study, either a beneficial or no effect of advanced parenthood on child problem behavior was observed.

Bayesian evaluation of informative hypotheses for multiple populations

The software package Bain can be used for the evaluation of informative hypotheses with respect to the parameters of a wide range of statistical models. For pairs of hypotheses the support in the data is quantified using the approximate adjusted fractional Bayes factor (BF). Currently, the data have to come from one population or have to consist of samples of equal size obtained from multiple populations. If samples of unequal size are obtained from multiple populations, the BF can be shown to be inconsistent. This paper examines how the approach implemented in Bain can be generalized such that multiple-population data can properly be processed. The resulting multiple-population approximate adjusted fractional Bayes factor is implemented in the R package Bain.

Bayes factors for superiority, non-inferiority, and equivalence designs

Background

In clinical trials, study designs may focus on assessment of superiority, equivalence, or non-inferiority, of a new medicine or treatment as compared to a control. Typically, evidence in each of these paradigms is quantified with a variant of the null hypothesis significance test. A null hypothesis is assumed (null effect, inferior by a specific amount, inferior by a specific amount and superior by a specific amount, for superiority, non-inferiority, and equivalence respectively), after which the probabilities of obtaining data more extreme than those observed under these null hypotheses are quantified by p-values. Although ubiquitous in clinical testing, the null hypothesis significance test can lead to a number of difficulties in interpretation of the results of the statistical evidence.

Methods

We advocate quantifying evidence instead by means of Bayes factors and highlight how these can be calculated for different types of research design.

Results

We illustrate Bayes factors in practice with reanalyses of data from existing published studies.

Conclusions

Bayes factors for superiority, non-inferiority, and equivalence designs allow for explicit quantification of evidence in favor of the null hypothesis. They also allow for interim testing without the need to employ explicit corrections for multiple testing.

Perception of action-outcomes is shaped by life-long and contextual expectations

The way humans perceive the outcomes of their actions is strongly colored by their expectations. These expectations can develop over different timescales and are not always complementary. The present work examines how long-term (structural) expectations - developed over a lifetime - and short-term (contextual) expectations jointly affect perception. In two studies, including a pre-registered replication, participants initiated the movement of an ambiguously rotating sphere by operating a rotary switch. In the absence of any learning, participants predominantly perceived the sphere to rotate in the same direction as their rotary action. This bias toward structural expectations was abolished (but not reversed) when participants were exposed to incompatible action-effect contingencies (e.g., clockwise actions causing counterclockwise percepts) during a preceding learning phase. Exposure to compatible action-effect contingencies, however, did not add to the existing structural bias. Together, these findings reveal that perception of action-outcomes results from the combined influence of both long-term and immediate expectations.

Simple Bayesian testing of scientific expectations in linear regression models

Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the second predictor, and the second predictor is expected to be larger than the third predictor. The goal is then to test such expectations against competing scientific expectations or theories. In this paper, a simple default Bayes factor test is proposed for testing multiple hypotheses with equality and order constraints on the effects of interest. The proposed testing criterion can be computed without requiring external prior information about the expected effects before observing the data. The method is implemented in R-package called 'lmhyp' which is freely downloadable and ready to use. The usability of the method and software is illustrated using empirical applications from the social and behavioral sciences.