Bronx Baseball Bat & Ball Set

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Johnson ED, Tubau E, & De Neys W (2016). The Doubting System 1: Evidence for automatic substitution sensitivity. Acta Psychologica, 164, 56–64. doi: 10.1016/j.actpsy.2015.12.008 [ PubMed] [ CrossRef] [ Google Scholar]

Bourgeois-Gironde S, & Vanderhenst J-B (2009). How to open the door to System 2: Debiasing the Bat and Ball problem. In Watanabe S, Bloisdell AP, Huber L, & Young A (Eds.), Rational animals, irrational humans (pp. 235–252). Tokyo: Keio University Press. [ Google Scholar]Newell BR, & Shanks DR (2014). Unconscious influences on decision making: A critical review. Behavioral and Brain Sciences, 37, 1–19. doi: 10.1017/S0140525X12003214 [ PubMed] [ CrossRef] [ Google Scholar] Campitelli G, & Gerrans P (2014). Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach. Memory & Cognition, 42, 434–447. doi: 10.3758/s13421-013-0367-9 [ PubMed] [ CrossRef] [ Google Scholar] Finally, latency responses to both the standard and control versions were collected. Correlations between response time and response confidence were expected, in line with previous work (e.g., Johnson et al., 2016; Kelley & Lindsay, 1993; Thompson, Prowse Turner, & Pennycook, 2011; Thompson et al., 2013).

De Neys W (2012). Bias and conflict: A case for logical intuitions. Perspectives on Psychological Science, 7, 28–38. doi: 10.1177/1745691611429354 [ PubMed] [ CrossRef] [ Google Scholar] B. T., & Stanovich KE (2013). Dual-process theories of higher cognition: Advancing the debate. Perspectives on Psychological Science, 8, 223–241. doi: 10.1177/1745691612460685 [ PubMed] [ CrossRef] [ Google Scholar] Szollosi A, Bago B, Szaszi B, & Aczel B (2017). Exploring the determinants of confidence in the bat-and-ball problem. Acta Psychologica, 180, 1–7. doi: 10.1016/j.actpsy.2017.08.003 [ PubMed] [ CrossRef] [ Google Scholar] The body of work on conflict detection in decision-making provides the theoretical framework for explaining the findings outlined above (e.g., Aczel, Szollosi, & Bago, 2016; De Neys, 2012; Pennycook, Fugelsang, & Koehler, 2012). In this line of theorizing, reasoning errors arise from an inability to inhibit prepotent intuitive responses that, importantly, cannot be explained solely due to miserly cognition because incorrect reasoners demonstrate that they are unsure their reasoning was accurate. Indeed, there is a rich body of research in support of error sensitivity in particular and logical intuitions more generally (e.g., Bago & De Neys, 2017; De Neys, 2012, 2014; De Neys & Bonnefon, 2013; De Neys & Glumicic, 2008; De Neys et al., 2013; Gangemi, Bourgeois-Gironde, & Mancini, 2015; Mata, Schubert, & Ferreira, 2014; but see Singmann, Klauer, & Kellen, 2014, for some caveats regarding this literature). Furthermore, sensitivity to error processing has been demonstrated though converging evidence in latency response investigations ( De Neys & Glumicic, 2008; Frey, Johnson, & De Neys, 2017; Johnson, Tubau, & De Neys, 2016) neuroimaging ( De Neys, Vartanian, & Goel, 2008), and alternative measurements of confidence ( De Neys, Cromheeke, & Osman, 2011). However, sensitivity effects were not obtained by indexing reasoner’s mouse-movements ( Travers, Rolison, & Feeney, 2016) nor their eye-movements ( Mata, Ferreira, Voss, & Kollei, 2017; see the subsequent debate concerning the studies by Mata et al. and Frey et al. discussed by Mata & Ferreira, 2018). On a more general level, unconscious processes have not been found to have much (if any) explanatory power (for a review, see Newell & Shanks, 2014).

As for the response confidence scores, the opinion judgments are reported here as proportions rather than percentages. There was a positive relationship between standard question confidence and standard question opinion judgments for incorrect reasoners, r(225) = .480, p< .001, such that incorrect reasoners who were less confident in their response were also less likely to think other reasoners could answer the standard question correctly. This strong relationship lends support to the notion that opinion judgments and response confidence scores are reflecting similar cognitive processes. Scherer LD, Yates JF, Baker SG, & Valentine KD (2017). The influence of effortful thought and cognitive proficiencies on the conjunction fallacy: Implications for dual-process theories of reasoning and judgment. Personality and Social Psychology Bulletin, 43, 874–887. doi: 10.1177/0146167217700607 [ PubMed] [ CrossRef] [ Google Scholar]

For the recall response, a mixed effects logistic regression (with subject as the random variable) was conducted due to the dichotomous dependent variable (with or without “more than”), considering only those participants who wrote down an answer that could be coded as with or without the “more than” phrase (e.g., “don’t know” responses were excluded). Incorrect reasoners usually recalled the standard problem, but not the control, as containing “more than” (see Table 1), with this effect of condition significant, b = 3.02, odds ratio ( OR) = 20.44, χ 2 = 21.69, p< .001, 95% confidence interval ( CI) [5.74, 72.75].

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De Neys W, & Bonnefon J-F (2013). The ‘whys’ and ‘whens’ of individual differences in thinking biases. Trends in Cognitive Sciences, 17, 172–178. doi: 10.1016/j.tics.2013.02.001 [ PubMed] [ CrossRef] [ Google Scholar] Baron J, Scott S, Fincher K, & Metz SE (2015). Why does the Cognitive Reflection Test (sometimes) predict utilitarian moral judgment (and other things)? Journal of Applied Research in Memory and Cognition, 4, 265–284. doi: 10.1016/j.jarmac.2014.09.003 [ CrossRef] [ Google Scholar] De Neys W, Cromheeke S, & Osman M (2011). Biased but in doubt: Conflict and decision confidence. PloS one, 6( 1), e15954. [ PMC free article] [ PubMed] [ Google Scholar]