Brase, G.L. (2014). The power of representation and interpretation: Doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers. Journal of Cognitive Psychology, 26, 81-97. (original) (raw)
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Applied Cognitive Psychology, 2009
In an ongoing debate between two visions of statistical reasoning competency, ecological rationality proponents claim that pictorial representations help tap into the frequency coding mechanisms of the mind, whereas nested sets proponents argue that pictorial representations simply help one to appreciate general subset relationships. Advancing this knowledge into applied areas is hampered by this present disagreement. A series of experiments used Bayesian reasoning problems with different pictorial representations (Venn circles, iconic symbols and Venn circles with dots) to better understand influences on performance across these representation types. Results with various static and interactive presentations of pictures all indicate a consistent advantage for iconic representations. These results are more consistent with an ecological rationality view of how these pictorial representations achieve facilitation in statistical task performance and provide more specific guidance for applied uses.
Journal of Cognitive Psychology, 2014
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Psychonomic Bulletin & Review, 2008
The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as “chances” similarly facilitate performance, based on the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies rather than chances phrasing, but also that participants who interpreted chances as frequencies rather than probabilities were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.
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 setproblem, 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.
Advances in psychology research, 2006
This chapter reviews ongoing research on human statistical reasoning, looking at the relationships between how information is presented, how numerical information is subsequently represented in the mind, and how the resulting judgments are made. At each of these stages there are both emerging conclusions and ongoing debates. Information presented in the form of frequencies appears to be more easily accepted into the cognitive judgment mechanisms, as is information presented in clearly organized relationships. Clarifications are necessary, however, regarding what constitute frequency presentations and the isomorphism of organizational relationships that have been proposed to be facilitatory. The actual reasoning processes are constrained (or enabled, as it were) by the nature of these mental representations. Finally, the benchmarks by which human judgments are evaluated – the markers for claiming that humans are “good” or “poor” at statistical reasoning – are assessed.
Mental representations of statistical information
This chapter reviews ongoing research on human statistical reasoning, looking at the relationships between how information is presented, how numerical information is subsequently represented in the mind, and how the resulting judgments are made. At each of these stages there are both emerging conclusions and ongoing debates. Information presented in the form of frequencies appears to be more easily accepted into the cognitive judgment mechanisms, as is information presented in clearly organized relationships. Clarifications are necessary, however, regarding what constitute frequency presentations and the isomorphism of organizational relationships that have been proposed to be facilitatory. The actual reasoning processes are constrained (or enabled, as it were) by the nature of these mental representations. Finally, the benchmarks by which human judgments are evaluated-the markers for claiming that humans are "good" or "poor" at statistical reasoning-are assessed.
Journal of Physics Conference Series
Numerous studies have examined students' difficulties in understanding some notions related to statistical problems. Some authors observed that the presentation of distinct visual representations could increase statistical reasoning, supporting the principle of graphical facilitation. But other researchers disagree with this viewpoint, emphasising the impediments related to the use of illustrations that could overcharge the cognitive system with insignificant data. In this work we aim at comparing the probabilistic statistical reasoning regarding two different formats of problem presentations: graphical and verbal-numerical. We have conceived and presented five pairs of homologous simple problems in the verbal numerical and graphical format to 311 undergraduate Psychology students (n=156 in Italy and n=155 in Spain) without statistical expertise. The purpose of our work was to evaluate the effect of graphical facilitation in probabilistic statistical reasoning. Every undergradua...
Representation facilitates reasoning: what natural frequencies are and what they are not
Cognition, 2002
A good representation can be crucial for finding the solution to a problem. Gigerenzer and Hoffrage (Psychol. Rev. 102 (1995) 684; Psychol. Rev. 106 (1999) 425) have shown that representations in terms of natural frequencies, rather than conditional probabilities, facilitate the computation of a cause's probability (or frequency) given an effect -a problem that is usually referred to as Bayesian reasoning. They also have shown that normalized frequencies -which are not natural frequencies -do not lead to computational facilitation, and consequently, do not enhance people's performance. Here, we correct two misconceptions propagated in recent work (Cognition 77 (2000) 197; Cognition 78 (2001) 247; Psychol. Rev. 106 (1999) 62; Organ. Behav. Hum. Decision Process. 82 (2000) 217): normalized frequencies have been mistaken for natural frequencies and, as a consequence, "nested sets" and the "subset principle" have been proposed as new explanations. These new terms, however, are nothing more than vague labels for the basic properties of natural frequencies. q
心理学报, 2007
What happens when format manipulations improve Bayesian reasoning? One view is that naturally sampled frequencies help induce a privileged representational system that is relatively specific in its operation. A contrasting view is that naturally sampled frequencies are but one way to induce a more general process of appreciating nested set relationships. This later view implies that fairly brief and immediate interventions (e.g., simple directives) should produce improvement, whereas the former view implies that more extensive interventions and/or more insightful understanding are necessary for improvement. The present research indicates that neither brief and immediate interventions nor pre-existing representational biases or representational flexibility facilitate performance. Some evidence emerged, on the other hand, that frequentist problem interpretation can improve statistical reasoning performance and increase confidence in responses at times. These results support the privileged representational system view.
The measurement of statistical reasoning in verbal-numerical and graphical forms: a pilot study
Journal of Physics: Conference Series, 2013
Numerous subjects have trouble in understanding various conceptions connected to statistical problems. Research reports how students' ability to solve problems (including statistical problems) can be influenced by exhibiting proofs. In this work we aim to contrive an original and easy instrument able to assess statistical reasoning on uncertainty and on association, regarding two different forms of proof presentation: pictorial-graphical and verbal-numerical. We have conceived eleven pairs of simple problems in the verbal-numerical and pictorial-graphical form and we have presented the proofs to 47 undergraduate students. The purpose of our work was to evaluate the goodness and reliability of these problems in the assessment of statistical reasoning. Each subject solved each pair of proofs in the verbalnumerical and in the pictorial-graphical form, in different problem presentation orders. Data analyses have highlighted that six out of the eleven pairs of problems appear to be useful and adequate to estimate statistical reasoning on uncertainty and that there is no effect due to the order of presentation in the verbal-numerical and pictorial-graphical form.