We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries. T he lack of reproducibility of scientific studies has caused growing concern over the credibility of claims of new discoveries based on 'statistically significant' findings. There has been much progress toward documenting and addressing several causes of this lack of reproducibility (for example, multiple testing, P-hacking, publication bias and under-powered studies). However, we believe that a leading cause of non-reproducibility has not yet been adequately addressed: statistical standards of evidence for claiming new discoveries in many fields of science are simply too low. Associating statistically significant findings with P < 0.05 results in a high rate of false positives even in the absence of other experimental, procedural and reporting problems.For fields where the threshold for defining statistical significance for new discoveries is P < 0.05, we propose a change to P < 0.005. This simple step would immediately improve the reproducibility of scientific research in many fields. Results that would currently be called significant but do not meet the new threshold should instead be called suggestive. While statisticians have known the relative weakness of using P ≈ 0.05 as a threshold for discovery and the proposal to lower it to 0.005 is not new 1,2 , a critical mass of researchers now endorse this change.We restrict our recommendation to claims of discovery of new effects. We do not address the appropriate threshold for confirmatory or contradictory replications of existing claims. We also do not advocate changes to discovery thresholds in fields that have already adopted more stringent standards (for example, genomics and high-energy physics research; see the 'Potential objections' section below).We also restrict our recommendation to studies that conduct null hypothesis significance tests. We have diverse views about how best to improve reproducibility, and many of us believe that other ways of summarizing the data, such as Bayes factors or other posterior summaries based on clearly articulated model assumptions, are preferable to P values. However, changing the P value threshold is simple, aligns with the training undertaken by many researchers, and might quickly achieve broad acceptance.

Sample correlations converge to the population value with increasing sample size, but the estimates are often inaccurate in small samples. In this report we use Monte-Carlo simulations to determine the critical sample size from which on the magnitude of a correlation can be expected to be stable. The necessary sample size to achieve stable estimates for correlations depends on the effect size, the width of the corridor of stability (i.e., a corridor around the true value where deviations are tolerated), and the requested confidence that the trajectory does not leave this corridor any more. Results indicate that in typical scenarios the sample size should approach 250 for stable estimates.

Publication bias and questionable research practices in primary research can lead to badly overestimated effects in meta-analysis. Methodologists have proposed a variety of statistical approaches to correct for such overestimation. However, much of this work has not been tailored specifically to psychology, so it is not clear which methods work best for data typically seen in our field. Here, we present a comprehensive simulation study to examine how some of the most promising meta-analytic methods perform on data that might realistically be produced by research in psychology. We created such scenarios by simulating several levels of questionable research practices, publication bias, heterogeneity, and using study sample sizes empirically derived from the literature. Our results clearly indicated that no single meta-analytic method consistently outperformed all others. Therefore, we recommend that meta-analysts in psychology focus on sensitivity analyses-that is, report on a variety of methods, consider the conditions under which these methods fail (as indicated by simulation studies such as ours), and then report how conclusions might change based on which conditions are most plausible. Moreover, given the dependence of meta-analytic methods on untestable assumptions, we strongly recommend that researchers in psychology continue their efforts on improving the primary literature and conducting large-scale, pre-registered replications. We provide detailed results and simulation code at https://osf.io/rf3ys and interactive figures at

We conducted preregistered replications of 28 classic and contemporary published findings, with protocols that were peer reviewed in advance, to examine variation in effect magnitudes across samples and settings. Each protocol was administered to approximately half of 125 samples that comprised 15,305 participants from 36 countries and territories. Using the conventional criterion of statistical significance ( p < .05), we found that 15 (54%) of the replications provided evidence of a statistically significant effect in the same direction as the original finding. With a strict significance criterion ( p < .0001), 14 (50%) of the replications still provided such evidence, a reflection of the extremely high-powered design. Seven (25%) of the replications yielded effect sizes larger than the original ones, and 21 (75%) yielded effect sizes smaller than the original ones. The median comparable Cohen’s ds were 0.60 for the original findings and 0.15 for the replications. The effect sizes were small (< 0.20) in 16 of the replications (57%), and 9 effects (32%) were in the direction opposite the direction of the original effect. Across settings, the Q statistic indicated significant heterogeneity in 11 (39%) of the replication effects, and most of those were among the findings with the largest overall effect sizes; only 1 effect that was near zero in the aggregate showed significant heterogeneity according to this measure. Only 1 effect had a tau value greater than .20, an indication of moderate heterogeneity. Eight others had tau values near or slightly above .10, an indication of slight heterogeneity. Moderation tests indicated that very little heterogeneity was attributable to the order in which the tasks were performed or whether the tasks were administered in lab versus online. Exploratory comparisons revealed little heterogeneity between Western, educated, industrialized, rich, and democratic (WEIRD) cultures and less WEIRD cultures (i.e., cultures with relatively high and low WEIRDness scores, respectively). Cumulatively, variability in the observed effect sizes was attributable more to the effect being studied than to the sample or setting in which it was studied.

This article was originally submitted for publication to the Editor of Advances in Methods and Practices in Psychological Science (AMPPS) in 2015. When the submitted manuscript was subsequently posted online (Silberzahn et al., 2015), it received some media attention, and two of the authors were invited to write a brief commentary in Nature advocating for greater crowdsourcing of data analysis by scientists. This commentary, arguing that crowdsourced research "can balance discussions, validate findings and better inform policy" (Silberzahn & Uhlmann, 2015, p. 189), included a new figure that displayed the analytic teams' effectsize estimates and cited the submitted manuscript as the source of the findings, with a link to the preprint. However, the authors forgot to add a citation of the Nature commentary to the final published version of the AMPPS article or to note that the main findings had been previously publicized via the commentary, the online preprint, research presentations at conferences and universities, and media reports by other people. The authors regret the oversight.

Unplanned optional stopping rules have been criticized for inflating Type I error rates under the null hypothesis significance testing (NHST) paradigm. Despite these criticisms this research practice is not uncommon, probably as it appeals to researcher's intuition to collect more data in order to push an indecisive result into a decisive region. In this contribution we investigate the properties of a procedure for Bayesian hypothesis testing that allows optional stopping with unlimited multiple testing, even after each participant. In this procedure, which we call Sequential Bayes Factors (SBF), Bayes factors are computed until an a priori defined level of evidence is reached. This allows flexible sampling plans and is not dependent upon correct e↵ect size guesses in an a priori power analysis. We investigated the long-term rate of misleading evidence, the average expected sample sizes, and the biasedness of e↵ect size estimates when an SBF design is applied to a test of mean di↵erences between two groups. Compared to optimal NHST, the SBF design typically needs 50% to 70% smaller samples to reach a conclusion about the presence of an e↵ect, while having the same or lower long-term rate of wrong inference.

A sizeable literature exists on the use of frequentist power analysis in the null-hypothesis significance testing (NHST) paradigm to facilitate the design of informative experiments. In contrast, there is almost no literature that discusses the design of experiments when Bayes factors (BFs) are used as a measure of evidence. Here we explore Bayes Factor Design Analysis (BFDA) as a useful tool to design studies for maximum efficiency and informativeness. We elaborate on three possible BF designs, (a) a fixed-n design, (b) an open-ended Sequential Bayes Factor (SBF) design, where researchers can test after each participant and can stop data collection whenever there is strong evidence for either H 1 or H 0 , and (c) a modified SBF design that defines a maximal sample size where data collection is stopped regardless of the current state of evidence. We demonstrate how the properties of each design (i.e., expected strength of evidence, expected sample size, expected probability of misleading evidence, expected probability of weak evidence) can be evaluated using Monte Carlo simulations and equip researchers with the necessary information to compute their own Bayesian design analyses.

The interplay of personality and social relationships is as fascinating as it is complex and it pertains to a wide array of largely separate research domains. Here, we present an integrative and unified framework for analysing the complex dynamics of personality and social relationships (PERSOC). Basic principles and general processes on the individual and dyadic level are outlined to show how personality and social relationships influence each other and develop over time. PERSOC stresses the importance of social behaviours and interpersonal perceptions as mediating processes organized in social interaction units. The framework can be applied to diverse social relationships such as first encounters, short-term acquaintances, friendships, relationships between working group members, educational or therapeutic settings, romantic relationships and family relationships. It has important consequences for how we conceptualize, understand, and investigate personality and social relationships.