The Differential Effects of Good Luck Belief on Cognitive Performance in Boys and Girls.

There is evidence that inducing a luck-related superstition leads to better performance on a variety of motor dexterity and cognitive tasks. However, some replication efforts have failed to succeed. At the same time, our previous findings suggest that the effect of good luck belief on cognitive performance interacts with gender. The present research aimed at replicating the study with a sample of adolescents among whom the superstitious beliefs are particularly prevalent. The participants (N = 99) were allocated to either a control or experimental group, and were asked to solve eight problems focused on cognitive reflection, conjunction fallacy, denominator neglect, and probabilistic reasoning. The experimental manipulation negatively affected boys' performance. Yet, it facilitated performance in girls via increase in their self-efficacy, measured as subjective estimate of future success in the tasks. Thus, gender seems to moderate the effect of luck-related belief on solutions to cognitive problems, which are an important part of our day-to-day decisions. Given initial gender gap in the present tasks, the crucial question to be addressed in future research is possibility of gender being a proxy for prior competence. It would imply that good luck beliefs might help low scorers, for instance in becoming less anxious and more confident, but could be harmful for high scorers.

Now you Bayes, now you don't: effects of set-problem and frequency-format mental representations on statistical reasoning.

People appear to be Bayesian when statistical information is presented in terms of natural frequencies and non-Bayesian when presented in terms of single-event probabilities, unless the probabilities resemble natural frequencies, for example, as chances. The isomorphic format of chances, however, does not always facilitate performance to the extent that the format of natural frequencies does. Prior research has not addressed the underlying mechanism that accounts for this gap despite its theoretical significance. The mechanism explaining this external format gap could lie in the interpretation of the problem as a set-problem, which cues relevant problem model and arithmetic operations (the problem interpretation hypothesis) and/or in the interpretation of the format as frequencies, which may be easier to process (the format interpretation hypothesis). In two parallel experiments, we found support for the problem interpretation hypothesis only: set representations mediated solely the isomorphic format gap (Experiment 1: part A) and accounted for the transfer effect to natural frequencies (Experiment 1: part B); priming set representations improved performance with chances (Experiment 2). We discuss how the supported explanation corroborates the nested-sets rather than the ecological rationality account of statistical reasoning and how it helps explain individual differences in Bayesian reasoning.

How to train your Bayesian: a problem-representation transfer rather than a format-representation shift explains training effects.

People improve their Bayesian reasoning most when they are trained to represent single-event probabilities as natural frequencies; nevertheless, the underlying mechanism of this representational training remains unclear. Several authors suggested that people learn to shift the initial format to natural frequencies, and improve their reasoning because natural frequencies align with an evolutionary designed frequency-coding mechanism--the format-representation shift hypothesis. Alternatively, people may acquire a generic problem representation in terms of nested sets that is then transferred to similar problems--the problem-representation transfer hypothesis. To disentangle the effect of the format shift from problem representation transfer, we devised two types of training with problems featuring a nonfrequency format and a concealed nested-sets structure. Participants learnt the adequate problem representation in both training manipulations, but in only one did they learn, in addition, to shift the format to frequencies. Substantial evidence (BF01 = 5, where BF = Bayes factor) indicates that both types of training improved reasoning in an immediate and a one-week follow-up posttest to the same extent. Such findings support the problem-representation transfer hypothesis because learning an adequate nested-sets problem representation accounts for the performance improvement, whereas the frequency format per se confers no additional benefit. We discuss the implications of these findings for two dominant accounts of statistical reasoning.

The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis.

Knowing which properties of visual displays facilitate statistical reasoning bears practical and theoretical implications. Therefore, we studied the effect of one property of visual diplays - iconicity (i.e., the resemblance of a visual sign to its referent) - on Bayesian reasoning. Two main accounts of statistical reasoning predict different effect of iconicity on Bayesian reasoning. The ecological-rationality account predicts a positive iconicity effect, because more highly iconic signs resemble more individuated objects, which tap better into an evolutionary-designed frequency-coding mechanism that, in turn, facilitates Bayesian reasoning. The nested-sets account predicts a null iconicity effect, because iconicity does not affect the salience of a nested-sets structure-the factor facilitating Bayesian reasoning processed by a general reasoning mechanism. In two well-powered experiments (N = 577), we found no support for a positive iconicity effect across different iconicity levels that were manipulated in different visual displays (meta-analytical overall effect: log OR = -0.13, 95% CI [-0.53, 0.28]). A Bayes factor analysis provided strong evidence in favor of the null hypothesis-the null iconicity effect. Thus, these findings corroborate the nested-sets rather than the ecological-rationality account of statistical reasoning.