title: Modeling the Overalternating Bias with an Asymmetric Entropy Measure.
abstract: Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception.
authors.affiliation: Department of Neuroscience, Psychology, Drug Research and Child's Health - Section of Psychology, University of Florence Florence, Italy.
authors.forename: Giorgio
authors.initials: G
authors.lastname: Gronchi
authors.affiliation: Formerly affiliated with the BioRobotics Institute, Scuola Superiore Sant'Anna Pisa, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Raglianti
authors.affiliation: Center for Assessment, University of Verona Verona, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Noventa
authors.affiliation: Department of Information Engineering, University of Pisa Pisa, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Lazzeri
authors.affiliation: Department of Sciences of Education and Psychology, University of Florence Florence, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Guazzini
keywords: Differential Evolution algorithm; Marcellin's entropy; Renyi's entropy; Shannon's entropy; asymmetric entropy; overalternating bias; randomness perception