Beaman, C. Philip

Quarterly Journal of Experimental Psychology

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A little more learning: a re­analysis of ignorance­driven inference in Frosch, Beaman & McCloy (2007) Article Accepted Version Beaman, C. P. (2017) A little more learning: a re­analysis of ignorance­driven inference in Frosch, Beaman & McCloy (2007). Quarterly Journal of Experimental Psychology, 70 (3). pp. 592­595. ISSN 1747­0218 doi: https://doi.org/10.1080/17470218.2016.1209685 Available at http://centaur.reading.ac.uk/65998/ It is advisable to refer to the publisher’s version if you intend to cite from the work. To link to this article DOI: http://dx.doi.org/10.1080/17470218.2016.1209685 Publisher: Taylor & Francis All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement . www.reading.ac.uk/centaur CentAUR Central Archive at the University of Reading Reading’s research outputs online A Little More Learning     1   COMMENT  A little more learning:  A re-analysis of ignorance-driven inference in Frosch, Beaman & McCloy (2007)   C. Philip Beaman School of Psychology & Clinical Language Sciences, University of Reading  Earley Gate, Whiteknights, Reading RG6 6AL, UK  Email: c.p.beaman@reading.ac.uk Tel: +44 (0) 118 3787637 Fax: +44 (0) 118 3786715    Running Head: UPDATE ON IGNORANCE-DRIVEN INFERENCE  Keywords: Heuristics, Recognition, Multinomial Modelling  Word Count: 981 (excluding references and footnote).     A Little More Learning     2  In their study on ignorance-driven inference, Frosch, Beaman and McCloy (2007) reported a “less-is-more effect” (LiME) such that, when asked to judge the relative wealth of individuals, judgments were reliably more accurate when individuals did not recognise all of the names presented than when all the names were known. For example, participants might be more accurate when asked to compare the relative wealth of Mick Jagger and A.N. Unknown than when asked to compare the relative wealth of Mick Jagger and Keith Richards.   This outcome arose from the prediction that participants apply a recognition heuristic (RH; Goldstein & Gigerenzer, 2002) that is, they use fame as a surrogate for wealth without accessing any further information about the recognised individual. A LiME occurs if wealth and fame are positively correlated and recognition is a more accurate predictor of wealth (when contrasting a known with an unknown individual) than knowledge (when contrasting two known individuals). The RH is applicable across a variety of relative judgments (e.g., the size of cities, the profitability of shares, the infectiousness of diseases, the success of sports teams) and is the first step in a class of simple heuristic decision-making strategies in which the minimum information necessary to provide a basis for judgment is searched or employed (Gigerenzer, Hertwig & Pachur, 2011).  Frosch et al. (2007) concluded, in support of the RH, that “participants reliably use recognition as a basis for their judgments” (p. 1329) but, as an existence-proof, Beaman, Smith, Frosch and McCloy (2010) demonstrated how LiMEs might arise as a consequence of limited access to information about known items or individuals rather than choosing not to search for such information. Beaman et al. (2010) argued that many models with these properties would show similar behaviour but were unable to present empirical data to support this conjecture.  Relevant, but previously overlooked, data are however available in Frosch et al. (2007). Figure 1 shows the data from Frosch et al. (2007) for a comparison when participants were asked  “which of these two individuals is the richest?” presented in terms of the frequency of all choices rather than the percentage correct choices, and also breaks down the data into whether the choice was in  A Little More Learning     3  accordance with the RH. Viewing the data in this way reveals that the advantage for only recognising one of the individuals from the pair is apparent not only when participants’ choices are consistent with the RH but also when they seemingly disregard the RH and judge that the unrecognised individual is the wealthier of the two. Although this occurs only rarely (41 compared to 167 when the recognised individual was chosen) it is not predicted by the RH. This result was not obvious from the original analysis, which focussed on judgments in favour of the recognised option and the relative accuracy of judgments made when only one option was recognised. However a success rate which included these data-points where one option was recognised but the non-recognised option was chosen cannot ascribe all of this “ignorance-driven inference” advantage to RH usage. This is the first point to arise from this re-analysis.  FIGURE ONE ABOUT HERE  To determine the extent to which the RH is used, Hilbig, Erdfelder and Pohl (2010) introduced a measurement model, using multinomial processing tree techniques. The model consists of three decision trees which describe the possible decisions made given the recognition situations (recognise 0, 1 or 2 options) presented in Figure 1. The model is shown in Figure 2.   FIGURE TWO ABOUT HERE  Each branch of the tree is associated with a parameter which estimates the probability that branch is followed. The product of the parameters on a particular path gives the expected number of outcomes of that kind. So, if one option is recognised, the probability of using the RH is r, the  A Little More Learning     4  probability that the correct response is given is a. The probability that the RH is used successfully is therefore r a. Parameters are estimated given known constraints such as the total number of times exactly one item is recognised is known and the total number of times the correct response is given. The fact that a recognised option is chosen does not rule out the possibility that the RH is discarded and knowledge other than simple recognition is employed: Participants of a cautious nature might search for confirmatory evidence that Mick Jagger is sufficiently wealthy to choose over the unknown Fred Bloggs. A famous name for whom the information is available that s/he recently filed for bankruptcy might result in a deliberate choice against the RH. Applying Hilbig et al’s model  using multiTree software (Moshagen, 2010) the best-fitting set of parameters indicate that r, the estimated probability that the RH is employed is .571 The expected results of this model are shown in Figure 3 and these do not differ significantly from the observed data, G2 = 1.15, df = 1, p = .28.  FIGURE THREE ABOUT HERE   These results do not invalidate Frosch et al’s (2007) observation of a less is more effect, but they indicate that the reasons behind this effect may differ from those assumed. Previously, it was concluded that the RH was employed approximately 80% of the time in the situation considered here and the less-is-more effect was taken both as a consequence of participants using this heuristic and as further evidence for the widespread application of the heuristic. However, if the model is rerun with r=.80 then the results differ significantly from the data, G2 = 22.49, df = 2, p = .00001. The current analysis suggests instead, the heuristic was employed only a little over half the time and the less-is-more effect  therefore cannot be ascribed wholly to the use of the heuristic (indeed, Figure 1                                                           1 Other estimated parameter values are a (recognition validity) = .78, b (knowledge validity) = .58 and g (guessing validity) = .52. The fit is improved if g is not allowed to vary and set at a constant .5 (G2 = .1.43, df = 2, p = .49 but the other parameter values do not change and this version of the model is not significantly different from the original (G2 = .28, df = 1, p = .60)  A Little More Learning     5  implies a LiME for other strategies) and its appearance in any future data-set should not therefore be taken as unequivocal evidence that such a heuristic was universally employed.         A Little More Learning     6  References Beaman, C. P., Smith, P. T., Frosch, C. A., & McCloy, R. (2010). Less-is-more effects without the recognition heuristic. Judgment & Decision Making, 5, 258-271. Frosch, C., Beaman, C. P., & McCloy, R. (2007). A little learning is a dangerous thing: An experimental demonstration of ignorance-driven inference. Quarterly Journal of Experimental Psychology, 60, 1329–1336 Gigerenzer, D. G., Hertwig, R. & Pachur, T. (2011). Heuristics: The foundations of adaptive behavior. New York: Clarendon Press. Goldstein, D. G., & Gigerenzer, G. (2002). Models of ecological rationality: The recognition heuristic. Psychological Review, 109, 75–90. Hilbig, B. E., Erdfelder, E., & Pohl, R. F. (2010). One reason decision-making unveiled: A measurement model of the recognition heuristic. Journal of Experimental Psychology: Learning, Memory & Cognition, 36, 123–134. Moshagen, M. (2010). multiTree: A computer program for the analysis of multinomial processing tree models. Behavior Research Methods, 42, 42-54.      A Little More Learning     7  FIGURE LEGENDS Figure 1.: Data redrawn from the two-alternative forced choice task of Frosch et al. (2007) when participants are asked “Which of these two individuals is the wealthiest?” The frequency of different choices is broken down by the number of options recognised (out of a maximum of two), whether the choice was consistent with the recognition heuristic (RH) when applicable, and whether the choice was correct.  Figure 2: Graphical depiction of Hilbig et al.’s (2010) measurement model. The top decision tree represents the situation when neither of the options are recognised and g is the probability of a correct choice. The middle decision-tree represents the situation when only one option is recognised. In this situation, r is the probability of using the recognition heuristic (RH), a is the probability that the recognition heuristic gives the correct answer and b is the probability of a correct choice based upon knowledge. The bottom decision tree represents the situation when both options are recognised and b is once again the probability of a correct choice based upon knowledge.  Figure 3.: The expected results for the best-fitting model applied to the data presented in Figure 1 when all parameters are allowed to vary. The expected frequency of different choices is broken down by the number of options recognised (out of a maximum of two), whether the choice was consistent with the recognition heuristic (RH) when applicable, and whether the choice was correct.     A Little More Learning     8  FIGURE ONE      020406080100120140160Recog 0 Recog 1 RH Recog 1 ¬RH Recog 2Choice FrequencyConditionDataCorrectIncorrect A Little More Learning     9  FIGURE TWO                           Correct choice (Recog) False choice (Recog) Correct choice (Recog) Correct choice (¬Recog) False choice (¬Recog) False choice (Recog) Recognise 1 RH applied RH ¬applied RH valid RH ¬valid knowledge valid knowledge invalid RH valid RH ¬valid RH valid RH ¬valid r 1-r a 1-a a a 1-a 1-a b 1-b Correct choice (¬Recog) Recognise 0 False choice (¬Recog) g 1-g Correct choice (Recog) Recognise 2 False choice (Recog) b 1-b  A Little More Learning     10   FIGURE THREE            020406080100120140160Recog 0 Recog 1 RH Recog 1 ¬RH Recog 2Expected Choice FrequencyConditionModelCorrectIncorrect

A little more learning: a re-analysis of ignorance-driven inference in Frosch, Beaman & McCloy (2007)

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