Academic journal article Psychonomic Bulletin & Review

The Effect of Iconicity of Visual Displays on Statistical Reasoning: Evidence in Favor of the Null Hypothesis

Academic journal article Psychonomic Bulletin & Review

The Effect of Iconicity of Visual Displays on Statistical Reasoning: Evidence in Favor of the Null Hypothesis

Article excerpt

Published online: 4 December 2013

© Psychonomic Society, Inc. 2013

Abstract 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.

Keywords Iconicity · Bayesian reasoning · Visual displays · Nested sets · Bayes factor

Research has firmly established that people struggle with statistical reasoning, but has also identified some methods of improvement (e.g., Cosmides & Tooby, 1996; Gigerenzer & Hoffrage, 1995; Girotto & Gonzalez, 2001). In Bayesian reasoning, for example, presenting statistical information in a nested-sets structure leads to more Bayesian inferences than in a normalized structure (e.g., "4outof6chances" vs. "67 % chance";Sloman,Over, Slovak, & Stibel, 2003). Visual displays accompanying a Bayesian task represent another source of improvement (Brase, 2009; Cosmides & Tooby, 1996; Sedlmeier, 1999; Sloman et al., 2003; Yamagishi, 2003). Indeed, visual dis- plays accompanying problems with normalized structures benefit participants unambiguously (Sedlmeier, 1999; Sloman et al., 2003). However, the evidence is more mixed for problems entailing nested-sets structures-whereas vi- sual displays did not improve Bayesian performance in tasks involving natural frequencies (Cosmides & Tooby, 1996) or nested-sets probabilities (Sloman et al., 2003), they did benefit performance in tasks featuring a chances format (Brase, 2009).

Since the authors used different visual displays, such con- tradictory evidence raise a question as to what specifically in visuals promoted the improved statistical performance. A better understanding of the underlying mechanisms would enable the design of more effective visual displays; it would also inform a theoretical debate between the two accounts of Bayesian reasoning: the ecological-rationality account and the nested-sets account . According to some proponents of the ecological-rationality account, visuals facilitate performance to the extent they mimic the natural occurrence of statistical information- the individuated objects with a natural- sampling structure-because these tap into an evolutionary designed frequency-coding mechanism (Brase, 2009; Cosmides & Tooby, 1996). In contrast, according to some proponents of the nested-sets account, visuals facilitate per- formance to the extent they make the relationships between the sets, the nested-sets structure, more "visible" to partici- pants (Barbey & Sloman, 2007;Slomanetal.,2003;Tversky & Kahneman, 1983). When the statistical format already highlights the nested-sets structure, the presence of a visual is redundant and does not promote Bayesian reasoning.

Thus, two separate properties of visuals were proposed to enable the facilitation: (1) the iconicity of the visual elements1 (i. …

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