Natural frequencies facilitate diagnostic inferences of managers

Abstract

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes’ rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in terms of probabilities or percentages. Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates. The present research replicates the beneficial effect of natural frequencies with four tasks from the domain of management, and with management students as well as experienced executives as participants. The percentage of Bayesian responses was almost twice as high when information was presented in natural frequencies compared to a presentation in terms of percentages. In contrast to most tasks previously studied, the majority of numerical responses were lower than the Bayesian solutions. Having heard of Bayes’ rule prior to the study did not affect Bayesian performance. An implication of our work is that textbooks explaining Bayes’ rule should teach how to represent information in terms of natural frequencies instead of how to plug probabilities or percentages into a formula.

Toward an ecological analysis of Bayesian inferences: how task characteristics influence responses

“…To explore how characteristics of Bayesian inference tasks influence responses and the usage of response strategies, we reanalyzed data that was obtained by prior research. In particular, we pooled the data from Hoffrage et al (2015) and the data from Study 1 of Gigerenzer and Hoffrage (1995) . Our pooled data set consists of 19 different tasks (4 tasks from Hoffrage et al, 2015 and 15 tasks from Gigerenzer and Hoffrage, 1995 ), presented to a total of 500 different participants who provided 1,773 responses.…”

“…In particular, we pooled the data from Hoffrage et al (2015) and the data from Study 1 of Gigerenzer and Hoffrage (1995) . Our pooled data set consists of 19 different tasks (4 tasks from Hoffrage et al, 2015 and 15 tasks from Gigerenzer and Hoffrage, 1995 ), presented to a total of 500 different participants who provided 1,773 responses. Table 1 gives an overview of these tasks and how they score on various quantitative and qualitative dimensions (which will be introduced in more detail below).…”

“…Tasks 13, 15, 17, and 18 have been taken from Hoffrage et al (2015 ; for the full descriptions, see their introduction, their Table 1, and their Appendix). The 440 participants who worked on these tasks were 259 undergraduate students of a business school and 181 managers in their role as students in an Executive MBA program.…”

“…Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates (see Hoffrage et al, 2002 and Gigerenzer and Hoffrage, 2007 ; for an example of how probability information can be translated into natural frequencies, see the caption of Table 1 ). Natural Frequencies have proven to facilitate diagnostic inferences in laypeople ( Gigerenzer and Hoffrage, 1995 ), advanced medical students and advanced law students ( Hoffrage et al, 2000 ), patients ( Garcia-Retamero and Hoffrage, 2013 ), physicians ( Hoffrage and Gigerenzer, 1998 ), and managers and management students ( Hoffrage et al, 2015 ). For a discussion about when and why natural frequencies are effective, see Gigerenzer and Hoffrage (2007) , Brase (2008) , Hill and Brase (2012) , Brase and Hill (2015) , and Johnson and Tubau (2015) .…”

Comprehension and computation in Bayesian problem solving

“…It has been argued that the wide variability reported with natural frequency problems can be attributed to individual differences in ability or motivation (Brase et al, 2006 ; Barbey and Sloman, 2007 ). In line with this suggestion (and summarized in Table 2 ), better performance with natural frequencies has been observed by individuals higher in cognitive reflection (Sirota and Juanchich, 2011 ; Lesage et al, 2013 ; Sirota et al, 2014a ; measured with the CRT); fluid intelligence (Sirota et al, 2014a ; measured with Raven's matrices); preference for rational thinking (Sirota et al, 2014a ; measured with the REI), education level (Brase et al, 2006 ; Siegrist and Keller, 2011 ; though see Hoffrage et al, 2015 ), and numeracy (Chapman and Liu, 2009 ; Sirota and Juanchich, 2011 ; Hill and Brase, 2012 ; Garcia-Retamero and Hoffrage, 2013 ; Johnson and Tubau, 2013 ; Garcia-Retamero et al, 2015 ; McNair and Feeney, 2015 ). These higher ability individuals often perform quite well, although the success of even these more capable individuals varies widely across studies.…”