No scientific conclusion follows automatically from a statistically non-significant result, yet people routinely use non-significant results to guide conclusions about the status of theories (or the effectiveness of practices). To know whether a non-significant result counts against a theory, or if it just indicates data insensitivity, researchers must use one of: power, intervals (such as confidence or credibility intervals), or else an indicator of the relative evidence for one theory over another, such as a Bayes factor. I argue Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches. Specifically, Bayes factors use the data themselves to determine their sensitivity in distinguishing theories (unlike power), and they make use of those aspects of a theory’s predictions that are often easiest to specify (unlike power and intervals, which require specifying the minimal interesting value in order to address theory). Bayes factors provide a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive. They allow accepting and rejecting the null hypothesis to be put on an equal footing. Concrete examples are provided to indicate the range of application of a simple online Bayes calculator, which reveal both the strengths and weaknesses of Bayes factors.

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.

Researchers are often confused about what can be inferred from significance tests. One problem occurs when people apply Bayesian intuitions to significance testing-two approaches that must be firmly separated. This article presents some common situations in which the approaches come to different conclusions; you can see where your intuitions initially lie. The situations include multiple testing, deciding when to stop running participants, and when a theory was thought of relative to finding out results. The interpretation of nonsignificant results has also been persistently problematic in a way that Bayesian inference can clarify. The Bayesian and orthodox approaches are placed in the context of different notions of rationality, and I accuse myself and others as having been irrational in the way we have been using statistics on a key notion of rationality. The reader is shown how to apply Bayesian inference in practice, using free online software, to allow more coherent inferences from data.

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This paper investigates the dissociation between conscious and unconscious knowledge in an implicit learning paradigm. Two experiments employing the artificial grammar learning task explored the acquisition of unconscious and conscious knowledge of structure (structural knowledge). Structural knowledge was contrasted to knowledge of whether an item has that structure (judgment knowledge). For both structural and judgment knowledge, conscious awareness was assessed using subjective measures. It was found that unconscious structural knowledge could lead to both conscious and unconscious judgment knowledge. When structural knowledge was unconscious, there was no tendency for judgment knowledge to become more conscious over time. Furthermore, conscious rather than unconscious structural knowledge produced more consistent errors in judgments, was facilitated by instructions to search for rules, and after such instructions was harmed by a secondary task. The dissociations validate the use of these subjective measures of conscious awareness.