Crowdsourcing prior information to improve study design and data analysis.

Though Bayesian methods are being used more frequently, many still struggle with the best method for setting priors with novel measures or task environments. We propose a method for setting priors by eliciting continuous probability distributions from naive participants. This allows us to include any relevant information participants have for a given effect. Even when prior means are near-zero, this method provides a principle way to estimate dispersion and produce shrinkage, reducing the occurrence of overestimated effect sizes. We demonstrate this method with a number of published studies and compare the effect of different prior estimation and aggregation methods.

Order-constrained linear optimization.

Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data.

Reevaluating the effectiveness of n-back training on transfer through the Bayesian lens: Support for the null.

A recent meta-analysis by Au et al. Psychonomic Bulletin & Review, 22, 366-377, (2015) reviewed the n-back training paradigm for working memory (WM) and evaluated whether (when aggregating across existing studies) there was evidence that gains obtained for training tasks transferred to gains in fluid intelligence (Gf). Their results revealed an overall effect size of g = 0.24 for the effect of n-back training on Gf. We reexamine the data through a Bayesian lens, to evaluate the relative strength of the evidence for the alternative versus null hypotheses, contingent on the type of control condition used. We find that studies using a noncontact (passive) control group strongly favor the alternative hypothesis that training leads to transfer but that studies using active-control groups show modest evidence in favor of the null. We discuss these findings in the context of placebo effects.

What counts as evidence for working memory training? Problems with correlated gains and dichotomization.

The question of whether computerized cognitive training leads to generalized improvements of intellectual abilities has been a popular, yet contentious, topic within both the psychological and neurocognitive literatures. Evidence for the effective transfer of cognitive training to nontrained measures of cognitive abilities is mixed, with some studies showing apparent successful transfer, while others have failed to obtain this effect. At the same time, several authors have made claims about both successful and unsuccessful transfer effects on the basis of a form of responder analysis, an analysis technique that shows that those who gain the most on training show the greatest gains on transfer tasks. Through a series of Monte Carlo experiments and mathematical analyses, we demonstrate that the apparent transfer effects observed through responder analysis are illusory and are independent of the effectiveness of cognitive training. We argue that responder analysis can be used neither to support nor to refute hypotheses related to whether cognitive training is a useful intervention to obtain generalized cognitive benefits. We end by discussing several proposed alternative analysis techniques that incorporate training gain scores and argue that none of these methods are appropriate for testing hypotheses regarding the effectiveness of cognitive training.