How to catch a cricket ball

A cricket or baseball fielder can run so as to arrive at just the right place at just the right time to catch a ball. It is shown that if the fielder runs so that d2(tan alpha)/dt2 = 0, where alpha is the angle of elevation of gaze from fielder to ball, then the ball will generally be intercepted before it hits the ground. This is true whatever the aerodynamic drag experienced by the ball. The only exception is if the ball is not approaching the fielder before he starts to run

How to use and report Bayesian hypothesis tests

This article provides guidance on interpreting and reporting Bayesian hypothesis tests, to aid their understanding. To use and report a Bayesian hypothesis test, predicted effect sizes must be specified. The article will provide guidance in specifying effect sizes of interest (which also will be of relevance to those using frequentist statistics). First, if a minimally interesting effect size can be specified, a null interval is defined as the effects smaller in magnitude than the minimally interesting effect. Then the proportion of the posterior distribution that falls in the null interval indicates the plausibility of the null interval hypothesis. Second, if a rough scale of effect can be determined, a Bayes factor can indicate evidence for a model representing that scale of effect versus a model of the null hypothesis. Both methods allow data to count against a theory that predicts a difference. By contrast, nonsignificance does not count against such a theory. Various examples are provided including the suitability of Bayesian analyses for demonstrating the absence of conscious perception under putative subliminal conditions, and its presence in supraliminal conditions

Measures of metacognition on signal-detection theoretic models

Analysing metacognition, specifically knowledge of accuracy of internal perceptual, memorial or other knowledge states, is vital for many strands of psychology, including determining the accuracy of feelings of knowing, and discriminating conscious from unconscious cognition. Quantifying metacognitive sensitivity is however more challenging than quantifying basic stimulus sensitivity. Under popular signal detection theory (SDT) models for stimulus classification tasks, approaches based on type II receiver-operator characteristic (ROC) curves or type II d-prime risk confounding metacognition with response biases in either the type I (classification) or type II (metacognitive) tasks. A new approach introduces meta-d′: the type I d-prime that would have led to the observed type II data had the subject used all the type I information. Here we (i) further establish the inconsistency of the type II d-prime and ROC approaches with new explicit analyses of the standard SDT model, and (ii) analyse, for the first time, the behaviour of meta-d′ under non-trivial scenarios, such as when metacognitive judgments utilize enhanced or degraded versions of the type I evidence. Analytically, meta-d′ values typically reflect the underlying model well, and are stable under changes in decision criteria; however, in relatively extreme cases meta-d′ can become unstable. We explore bias and variance of in-sample measurements of meta-d′ and supply MATLAB code for estimation in general cases. Our results support meta-d′ as a useful measure of metacognition, and provide rigorous methodology for its application. Our recommendations are useful for any researchers interested in assessing metacognitive accuracy

Temporal constraints of the word blindness posthypnotic suggestion on Stroop task performance

The present work investigated possible temporal constraints on the posthypnotic word blindness suggestion effect. In a completely within-subjects and counterbalanced design 19 highly suggestible individuals performed the Stroop task both with and without a posthypnotic suggestion that they would be unable to read the word dimension of the Stroop stimulus, both when response–stimulus interval (RSI) was short (500 ms) or equivalent to previous studies (3500 ms). The suggestion reduced Stroop interference in the short RSI condition (54 vs. 6 ms) but not in the long RSI condition (52 vs. 56 ms), and did not affect Stroop facilitation. Our results suggest that response to the suggestion involves reactive top-down control processes that persist only if levels of activation can be maintained

Application of the ex-Gaussian function to the effect of the word blindness suggestion on Stroop task performance suggests no word blindness

The aim of the present paper was to apply the ex-Gaussian function to data reported by Parris et al. (2012) given its utility in studies involving the Stroop task. Parris et al. showed an effect of the word blindness suggestion when Response-Stimulus Interval (RSI) was 500 ms but not when it was 3500 ms. Analysis revealed that: (1) The effect of the suggestion on interference is observed in μ, supporting converging evidence indicating the suggestion operates over response competition mechanisms; and, (2) Contrary to Parris et al. an effect of the suggestion was observed in μ when RSI was 3500 ms. The reanalysis of the data from Parris et al. (2012) supports the utility of ex-Gaussian analysis in revealing effects that might otherwise be thought of as absent. We suggest that word reading itself is not suppressed by the suggestion but instead that response conflict is dealt with more effectively. © 2013 Parris, Dienes and Hodgson

Facial beauty affects implicit and explicit learning of men and women differently

The present work explores the unconscious and/or conscious nature of learning attractive faces of same and opposite sex, that is, of stimuli that experimental and neuroimaging research has shown to be rewarding and thus highly motivating. To this end, we examined performance of men and women while classifying strings of average and attractive faces for grammaticality in the experimental task of artificial grammar learning (AGL), which reflects both conscious and unconscious processes. Subjective measures were used to assess participants’ conscious and unconscious knowledge. It was found that female attractiveness impaired performance in male participants. In particular, male participants demonstrated the lowest accuracy while classifying beautiful faces of women. Conversely, female attractiveness facilitated performance in female participants. The pattern was similar for conscious and unconscious knowledge. Presumably, objects with high incentive salience, as are beautiful faces, captured resources, which were used in task relevant versus task irrelevant ways by women versus men. The present findings shed light on the relation of conscious and unconscious processing with affective and reward-related stimuli, as well as on gender differences underlying this relation

Implicit learning of recursive context-free grammars

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning

Bayes to the rescue: does the type of hypnotic induction matter?

Studies comparing different forms of hypnotic induction (e.g., indirect vs. direct induction) on responsiveness to suggestion have typically found no significant difference between induction types. However, no firm conclusion can be drawn from a nonsignificant result. In contrast, Bayes factors (Jeffreys, 1939/1961) indicate whether evidence favors H0 and against the alternative hypothesis or whether data are simply insensitive. Here, we apply Bayes factors to those nonsignificant results to decide: Does the form of hypnotic induction really not matter, does it matter, or should we suspend judgment? As the claim that different inductions are differentially effective comes mostly from clinicians, we based the Bayes factors on hypnotherapists’ judgments of expected differences between inductions. In addition, we also used empirical differences between induction versus no-induction as an estimate of the order of size of effect that could be expected between different inductions, independent of clinical judgment. As a whole, the Bayesian reanalysis of the present evidence supports the claim that additional research should be done on the influence of the induction procedure on hypnotic responsiveness (at least with regard to the inductions considered in the present study), with several exceptions

The value of Bayesian statistics for assessing credible evidence of animal sentience

Determining what constitutes practically relevant, statistically significant evidence for animal sentience, under the precautionary principle, could be enhanced through Bayesian statistics. A Bayesian approach allows the incorporation of multiple evidence sources through prior probabilities, the tracking of changing evidence across time, and a principled means of adjusting evidentiary bars via Bayes factors