The power of representation and interpretation: Doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers

Abstract

In an ongoing debate about statistical reasoning competency, one view claims that pictorial representations help tap into the frequency coding mechanisms, whereas another view argues that pictorial representations simply help one to appreciate general subset relationships. The present experiments used Bayesian reasoning problems, expressed in an ambiguous numerical format (chances) and with different pictorial representations, to better understand influences on performance across these representation types. Although a roulette wheel diagram had some positive effect on performance, both abstract icons and pictographs improved performance markedly more. Furthermore, a frequency interpretation of the ambiguous numerical information was also associated with superior performance. These findings support the position that the human mind is more easily able to use frequency-based information, as opposed to grasping subset relations, as an explanation for improved statistical reasoning. These results also provide practical implications for how to present quantitative information to substantially improve public understanding.

Keywords:

• Frequencies
• Judgments under uncertainty
• Mental representation
• Pictorial representation
• Statistical probability

Notes

¹ There is sometimes a degree of confusion between frequencies (whole number counts) and the organization of quantitative information into a subset structure. Frequencies embedded within a natural sampling (i.e., subset) framework, which is often called “natural frequencies”, have both a frequency format and a subset structure. It is also possible to have frequencies that are not in a natural sampling (i.e., subset) structure, which creates a confound in terms of numerical format and computational complexity for Bayesian reasoning tasks. It is not possible, in contrast, to have natural sampling structures while simultaneously using numerical formats with standardised reference classes (e.g., percentages). These issues are discussed in several places, including Brase (2002, 2008), and Hoffrage et al. (2002).