Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning

Abstract

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, on the basis of 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 as probabilities, were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.

Intuitive Conceptions of Probability and the Development of Basic Math Skills

“…Disputes still exist about the theoretical implications of these effects for our human cognitive architecture, and specifically whether or not it implies that the human mind is inherently predisposed to process natural frequencies (Brase 2008). Distinguishing between these two theoretical interpretations is difficult because the statistical reasoning tasks traditionally used in this research involve exactly the sorts of computations that get simpler with the use of natural frequencies (Gigerenzer and Hoffrage 1995).…”

“…The counter-argument is that such statements are really about the multiple chances (be they real or hypothetical), and therefore these chances can be just as validly defined as frequencies. Recent research to clarify this issue (Brase 2008) found that research participants-when asked-did report differing interpretations of the "chances" numbers in Bayesian reasoning tasks (some interpreted them as frequencies; others as single-event probabilities). These participants, however, performed better when given equivalent frequencies as compared to isomorphic tasks that involved chances.…”

Sample representativeness affects whether judgments are influenced by base rate or sample size

“…Bayesian reasoning is improved, however, when data are presented as unstandardized natural frequencies that express probability in terms of subsets within a greater super set (Brase, 2008;Gigerenzer & Hoffrage, 1995;Obrecht, Anderson, Schulkin, & Chapman, 2012). For example, analogous to the problem above:…”

Retrospective Frequency Formats Promote Consistent Experience‐Based Bayesian Judgments

“…This advantage of natural frequencies over probabilities has been well established (e.g. Gigerenzer & Hoffrage, 1995, Brase, 2008, and explanations of the effect have been debated extensively (Brase, 2008, Evans, Handley, Perham, Over & Thompson, 2000Fiedler, Brinkmann, Betsch, & Wild, 2000;Gigerenzer & Hoffrage, 1995;Girotto & Gonzalez, 2001;Macchi, 2000;Neace, Michaud, Bolling, Deer, & Zecevic, 2008;Yamagishi, 2003), although one often-cited view is that natural frequencies are a more ecological format. The current experiment does not contribute to that debate directly but is focused on the manner in which participants acquire the data from which they make judgments.…”