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      New normative standards of conditional reasoning and the dual-source model

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          Abstract

          There has been a major shift in research on human reasoning toward Bayesian and probabilistic approaches, which has been called a new paradigm. The new paradigm sees most everyday and scientific reasoning as taking place in a context of uncertainty, and inference is from uncertain beliefs and not from arbitrary assumptions. In this manuscript we present an empirical test of normative standards in the new paradigm using a novel probabilized conditional reasoning task. Our results indicated that for everyday conditional with at least a weak causal connection between antecedent and consequent only the conditional probability of the consequent given antecedent contributes unique variance to predicting the probability of conditional, but not the probability of the conjunction, nor the probability of the material conditional. Regarding normative accounts of reasoning, we found significant evidence that participants' responses were confidence preserving (i.e., p-valid in the sense of Adams, 1998) for MP inferences, but not for MT inferences. Additionally, only for MP inferences and to a lesser degree for DA inferences did the rate of responses inside the coherence intervals defined by mental probability logic (Pfeifer and Kleiter, 2005, 2010) exceed chance levels. In contrast to the normative accounts, the dual-source model (Klauer et al., 2010) is a descriptive model. It posits that participants integrate their background knowledge (i.e., the type of information primary to the normative approaches) and their subjective probability that a conclusion is seen as warranted based on its logical form. Model fits showed that the dual-source model, which employed participants' responses to a deductive task with abstract contents to estimate the form-based component, provided as good an account of the data as a model that solely used data from the probabilized conditional reasoning task.

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          Advances in prospect theory: Cumulative representation of uncertainty

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            Mixed-effects modeling with crossed random effects for subjects and items

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              Random effects structure for confirmatory hypothesis testing: Keep it maximal.

              Linear mixed-effects models (LMEMs) have become increasingly prominent in psycholinguistics and related areas. However, many researchers do not seem to appreciate how random effects structures affect the generalizability of an analysis. Here, we argue that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades. Through theoretical arguments and Monte Carlo simulation, we show that LMEMs generalize best when they include the maximal random effects structure justified by the design. The generalization performance of LMEMs including data-driven random effects structures strongly depends upon modeling criteria and sample size, yielding reasonable results on moderately-sized samples when conservative criteria are used, but with little or no power advantage over maximal models. Finally, random-intercepts-only LMEMs used on within-subjects and/or within-items data from populations where subjects and/or items vary in their sensitivity to experimental manipulations always generalize worse than separate F 1 and F 2 tests, and in many cases, even worse than F 1 alone. Maximal LMEMs should be the 'gold standard' for confirmatory hypothesis testing in psycholinguistics and beyond.
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                Author and article information

                Affiliations
                1Institut für Psychologie, Albert-Ludwigs-Universität Freiburg Freiburg, Germany
                2Department of Psychology, Durham University Durham, UK
                Author notes

                Edited by: Shira Elqayam, De Montfort University, UK

                Reviewed by: Gordon Pennycook, University of Waterloo, Canada; Niki Pfeifer, Ludwig-Maximilians-Universität München, Germany

                *Correspondence: Henrik Singmann, Abteilung für Sozialpsychologie und Methodenlehre, Institut für Psychologie, Albert-Ludwigs-Universität Freiburg, Engelbergerstr. 41, D-79085 Freiburg, Germany e-mail: henrik.singmann@ 123456psychologie.uni-freiburg.de

                This article was submitted to Cognitive Science, a section of the journal Frontiers in Psychology.

                Contributors
                Journal
                Front Psychol
                Front Psychol
                Front. Psychol.
                Frontiers in Psychology
                Frontiers Media S.A.
                1664-1078
                11 February 2014
                17 April 2014
                2014
                : 5
                4029011 10.3389/fpsyg.2014.00316
                Copyright © 2014 Singmann, Klauer and Over.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                Counts
                Figures: 5, Tables: 3, Equations: 9, References: 72, Pages: 14, Words: 11934
                Categories
                Psychology
                Original Research Article

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