Causal model and sampling approaches to reducing base rate neglect

Causal model and sampling approaches to reducing base rate neglect Brett K. Hayes (B.Hayes@unsw.edu.au) Ben R. Newell (Ben.Newell@unsw.edu.au) Guy E. Hawkins (G.Hawkins@unsw.edu.au) School of Psychology, University of New South Wales Sydney, 2052, Australia such an explanation was supplied (see the causal version in Figure 1) there was a marked increase in the accuracy of probability estimates. Alternately Hogarth and Soyer (2011) suggest that people are less likely to neglect relevant statistics when they have had “experience” with the relevant sample. Specifically, they suggest that trial-by-trial sampling of the frequency of an event from the relevant probability distribution can lead to more accurate estimates in problems involving low base rates (cf. Lejarraga, 2010; Sedlmeier, 1999). Hence, Hogarth and Soyer (2011) allowed some participants to draw sequential samples of women with a positive mammogram from a distribution with a low base rate of cancer. Sampling led to more accurate probability estimates than when only a description of the base rate was provided. Abstract Two studies examined how sampling of base rate information and causal explanation of false positives facilitate intuitive probability judgments. Experiment 1a varied these two manipulations factorially. Each had an additive effect on reducing base rate neglect and increasing choice of the normatively correct solution. Experiment 1b showed that description of relevant distributional information produced similar facilitation to sequential sampling. These results indicate that causal and sampling approaches impact on different components of probability judgment. Keywords: Causal reasoning, Sequential sampling, Base rate neglect, Bayesian judgment, Belief updating Introduction One of the most commonly observed biases in human judgment is neglect of relevant base rate information (Eddy, 1982; Gigerenzer & Hoffrage, 1995; Tversky & Kahneman, 1974). For example, when people attempt to solve intuitive probability problems like that in Figure 1 (standard version), they typically ignore the low base rate (p(Cancer) = . 01), generating probability estimates that are much higher than the normative Bayesian solution (p(Cancer|Mammogram+) ≈ 0.051, see Appendix for a derivation) . Previous work has suggested a number of solutions to the problem of base rate neglect. These include the use of frequency rather than probability formats for relevant statistics (Gigerenzer & Hoffrage, 1995), and instructions that clarify set relations between the relevant samples (Barbey & Sloman, 2007; Evans, Handley, Perham, Over, & Thompson, 2000). Two novel approaches to explaining and reducing base rate neglect have recently been proposed. The first involves consideration of the intuitive causal models that people construct when solving probability problems. Krynski and Tenenbaum (2007) outline a “causal-Bayes” account of probability judgments which assumes that errors arise when the statistics in a given problem do not readily map onto an intuitive causal model. In the standard mammogram problem for example, no causal explanation for the false positive rate (the probability of a positive mammogram in the absence of cancer) is given. According to Krynski and Tenenbaum (2007) this makes it difficult to integrate the false positive rate into Bayesian calculations, leading to inflated probability estimates. The problem can be overcome by providing a causal explanation for the relevant statistics. Krynski and Tenenbaum (2007) found that when Mammogram problem Doctors often encourage women at age 50 to participate in a routine mammography screening for breast cancer. From past statistics, the following is known: 1% of women had breast cancer at the time of the screening Of those with breast cancer, 80% received a positive result on the mammogram [Standard version] Of those without breast cancer, 15% received a positive result on the mammogram [Causal version] 30% of the women had a benign cyst at the time of screening. Of those with a benign cyst, 50% received a positive test on the mammogram All others received a negative result Suppose a woman gets a positive result during a routine mammogram screening. Without knowing any other symptoms, what are the chances she has breast cancer? ___% Figure 1. The mammogram problem Combining causal model and sampling approaches A key motivation for the current work was that the causal model and sampling approaches appear to address different components of intuitive probability problems. Krynski and Tenenbaum (2007), focused on incorporating information about false positive rates into a causal model of the problem. In contrast, Hogarth and Soyer’s (2011) sequential sampling approach aimed at improving sensitivity to the low base