Zoltán Dienes

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.

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.

The implicit-explicit distinction is applied to knowledge representations. Knowledge is taken to be an attitude towards a proposition which is true. The proposition itself predicates a property to some entity. A number of ways in which knowledge can be implicit or explicit emerge. If a higher aspect is known explicitly then each lower one must also be known explicitly. This partial hierarchy reduces the number of ways in which knowledge can be explicit. In the most important type of implicit knowledge, representations merely reflect the property of objects or events without predicating them of any particular entity. The clearest cases of explicit knowledge of a fact are representations of one's own attitude of knowing that fact. These distinctions are discussed in their relationship to similar distinctions such as procedural-declarative, conscious-unconscious, verbalizable-nonverbalizable, direct-indirect tests, and automatic-voluntary control. This is followed by an outline of how these distinctions can be used to integrate and relate the often divergent uses of the implicit-explicit distinction in different research areas. We illustrate this for visual perception, memory, cognitive development, and artificial grammar learning.

Towards a Characterisation of Implicit Learning. The Control of Complex Systems. Implicit Concept Formation. Sequence Learning. Computational Models of Implicit Learning. Neuropsychological Evidence. Practical Implications. Theoretical Implications. References.