Two studies investigated the reliability and predictive validity of commonly used measures and mo... more Two studies investigated the reliability and predictive validity of commonly used measures and models of Approximate Number System acuity (ANS). Study 1 investigated reliability by both an empirical approach and a simulation of maximum obtainable reliability under ideal conditions. Results showed that common measures of the Weber fraction (w) are reliable only when using a substantial number of trials, even under ideal conditions. Study 2 compared different purported measures of ANS acuity as for convergent and predictive validity in a within-subjects design and evaluated an adaptive test using the ZEST algorithm. Results showed that the adaptive measure can reduce the number of trials needed to reach acceptable reliability. Only direct tests with non-symbolic numerosity discriminations of stimuli presented simultaneously were related to arithmetic fluency. This correlation remained when controlling for general cognitive ability and perceptual speed. Further, the purported indirect measure of ANS acuity in terms of the Numeric Distance Effect (NDE) was not reliable and showed no sign of predictive validity. The non-symbolic NDE for reaction time was significantly related to direct w estimates in a direction contrary to the expected. Easier stimuli were found to be more reliable, but only harder (7:8 ratio) stimuli contributed to predictive validity.
The perspective of the naïve intuitive statistician is outlined and applied to explain overconfid... more The perspective of the naïve intuitive statistician is outlined and applied to explain overconfidence when people produce intuitive confidence intervals and why this format leads to more overconfidence than other formally equivalent formats. The naïve sampling model implies that people accurately describe the sample information they have but are naïve in the sense that they uncritically take sample properties as estimates of population properties. A review demonstrates that the naïve sampling model accounts for the robust and important findings in previous research, as well as provides novel predictions that are confirmed, including a way to minimize the overconfidence with interval production. The authors discuss the NSM as a representative of models inspired by the naïve intuitive statistician.
Http Dx Doi Org 10 1080 20445911 2013 841170, Oct 7, 2013
Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy... more Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy of estimates of central tendency and variability. In this paper, we investigate two hypothesised cognitive processes by which people make judgements of distribution shape. The first claims that people spontaneously induce abstract representations of distribution properties from experience, including about distribution shape. The second process claims that people construct beliefs about distribution properties post hoc by retrieval from long-term memory of small samples from the distribution, implying format dependence with accuracy that differs depending on judgement format. Results from two experiments confirm the predicted format dependence, suggesting that people are often constrained by the post hoc assessment of distribution properties by sampling from long-term memory. The results, however, also suggest that, although post hoc sampling from memory seems to be the default process, under certain predictable circumstances people do induce abstract representations of distribution shape.
Journal of Experimental Psychology General, Nov 1, 2009
This article explores the configural weighted average (CWA) hypothesis suggesting that extension ... more This article explores the configural weighted average (CWA) hypothesis suggesting that extension biases, like conjunction and disjunction errors, occur because people estimate compound probabilities by taking a CWA of the constituent probabilities. The hypothesis suggests a process consistent with well-known cognitive constraints, which nonetheless achieves high robustness and bounded rationality in noisy real-life environments. Predictions by the CWA hypothesis are that in error-free data, conjunction and disjunction errors should be the rule rather than the exception when pairs of statements are randomly sampled from an environment, the rate of extension errors should increase when noise in data is decreased, and that adding a likely component should increase the probability of a conjunction. Four experiments generally verify the predictions by the hypothesis, demonstrating that extension errors are frequent also when tasks are selected according to representative design.
Costello and Watts (2014) present a model assuming that people's knowledge of probabilities a... more Costello and Watts (2014) present a model assuming that people's knowledge of probabilities adheres to probability theory, but that their probability judgments are perturbed by a random noise in the retrieval from memory. Predictions for the relationships between probability judgments for constituent events and their disjunctions and conjunctions, as well as for sums of such judgments were derived from probability theory. Costello and Watts (2014) report behavioral data showing that subjective probability judgments accord with these predictions. Based on the finding that subjective probability judgments follow probability theory, Costello and Watts (2014) conclude that the results imply that people's probability judgments embody the rules of probability theory and thereby refute theories of heuristic processing. Here, we demonstrate the invalidity of this conclusion by showing that all of the tested predictions follow straightforwardly from an account assuming heuristic prob...
Are human contingency judgments based on associationistic principles such as cue competition or o... more Are human contingency judgments based on associationistic principles such as cue competition or on normative principles as specified by rational-cognitive models? In this study, participants learned to predict an outcome from several simultaneously presented cues. They were asked to judge the cues in regard to causal power or statistical concepts such as probability or relative frequency. Uniform application of associationistic principles implies cue-interaction effects of blocking (Experiment 1) and conditioned inhibition (Experiment 2) for all judgments. A rational-cognitive framework predicts cueinteraction effects for causality judgments, but not for probability and relative frequency judgments. The results support the rational-cognitive framework on all accounts.
Organizational Behavior and Human Decision Processes, Feb 1, 2003
Predictions for probability judgments in a general knowledge task were derived from the combined ... more Predictions for probability judgments in a general knowledge task were derived from the combined error model and predictions for probability judgments in a sensory discrimination task were derived from the sensory sampling model . As predicted, an experiment suggested: (a) good calibration with full-range probability assessments for general knowledge tasks, but underconfidence for sensory discrimination, (b) more deviations from additivity in sensory discrimination, and (c) a preference to bet specifically on general knowledge or sensory tasks depending on the assessed probability, violating source-independence. The quantitative fit of the two models appropriately distinguished between the two task contents, but both models substantially under-predicted the overconfidence observed with interval estimation.
Previous data suggest that probability judgments can often be fairly realistic, but production of... more Previous data suggest that probability judgments can often be fairly realistic, but production of probability intervals pro-motes extreme overconfidence bias (Juslin & Persson 2002; Juslin, Wennerholm, & Olsson, 1999; Klayman, Soll, Gon-zález-Vallejo, & Barlas, 1999). We present a novel explana-tion of this format-dependence effect in terms of a naïve sam-pling model. The model assumes that people process distribu-tional information in an unbiased manner, but they are naïve in the sense that they uncritically take sample properties as es-timates of population properties. A Monte Carlo simulation demonstrates that the model predicts format dependence, with extreme overconfidence bias for interval production that prac-tically disappears for probability assessments for the same in-tervals. In the last section this novel prediction is empirically verified by data from human participants.
Two studies investigated the reliability and predictive validity of commonly used measures and mo... more Two studies investigated the reliability and predictive validity of commonly used measures and models of Approximate Number System acuity (ANS). Study 1 investigated reliability by both an empirical approach and a simulation of maximum obtainable reliability under ideal conditions. Results showed that common measures of the Weber fraction (w) are reliable only when using a substantial number of trials, even under ideal conditions. Study 2 compared different purported measures of ANS acuity as for convergent and predictive validity in a within-subjects design and evaluated an adaptive test using the ZEST algorithm. Results showed that the adaptive measure can reduce the number of trials needed to reach acceptable reliability. Only direct tests with non-symbolic numerosity discriminations of stimuli presented simultaneously were related to arithmetic fluency. This correlation remained when controlling for general cognitive ability and perceptual speed. Further, the purported indirect measure of ANS acuity in terms of the Numeric Distance Effect (NDE) was not reliable and showed no sign of predictive validity. The non-symbolic NDE for reaction time was significantly related to direct w estimates in a direction contrary to the expected. Easier stimuli were found to be more reliable, but only harder (7:8 ratio) stimuli contributed to predictive validity.
The perspective of the naïve intuitive statistician is outlined and applied to explain overconfid... more The perspective of the naïve intuitive statistician is outlined and applied to explain overconfidence when people produce intuitive confidence intervals and why this format leads to more overconfidence than other formally equivalent formats. The naïve sampling model implies that people accurately describe the sample information they have but are naïve in the sense that they uncritically take sample properties as estimates of population properties. A review demonstrates that the naïve sampling model accounts for the robust and important findings in previous research, as well as provides novel predictions that are confirmed, including a way to minimize the overconfidence with interval production. The authors discuss the NSM as a representative of models inspired by the naïve intuitive statistician.
Http Dx Doi Org 10 1080 20445911 2013 841170, Oct 7, 2013
Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy... more Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy of estimates of central tendency and variability. In this paper, we investigate two hypothesised cognitive processes by which people make judgements of distribution shape. The first claims that people spontaneously induce abstract representations of distribution properties from experience, including about distribution shape. The second process claims that people construct beliefs about distribution properties post hoc by retrieval from long-term memory of small samples from the distribution, implying format dependence with accuracy that differs depending on judgement format. Results from two experiments confirm the predicted format dependence, suggesting that people are often constrained by the post hoc assessment of distribution properties by sampling from long-term memory. The results, however, also suggest that, although post hoc sampling from memory seems to be the default process, under certain predictable circumstances people do induce abstract representations of distribution shape.
Journal of Experimental Psychology General, Nov 1, 2009
This article explores the configural weighted average (CWA) hypothesis suggesting that extension ... more This article explores the configural weighted average (CWA) hypothesis suggesting that extension biases, like conjunction and disjunction errors, occur because people estimate compound probabilities by taking a CWA of the constituent probabilities. The hypothesis suggests a process consistent with well-known cognitive constraints, which nonetheless achieves high robustness and bounded rationality in noisy real-life environments. Predictions by the CWA hypothesis are that in error-free data, conjunction and disjunction errors should be the rule rather than the exception when pairs of statements are randomly sampled from an environment, the rate of extension errors should increase when noise in data is decreased, and that adding a likely component should increase the probability of a conjunction. Four experiments generally verify the predictions by the hypothesis, demonstrating that extension errors are frequent also when tasks are selected according to representative design.
Costello and Watts (2014) present a model assuming that people's knowledge of probabilities a... more Costello and Watts (2014) present a model assuming that people's knowledge of probabilities adheres to probability theory, but that their probability judgments are perturbed by a random noise in the retrieval from memory. Predictions for the relationships between probability judgments for constituent events and their disjunctions and conjunctions, as well as for sums of such judgments were derived from probability theory. Costello and Watts (2014) report behavioral data showing that subjective probability judgments accord with these predictions. Based on the finding that subjective probability judgments follow probability theory, Costello and Watts (2014) conclude that the results imply that people's probability judgments embody the rules of probability theory and thereby refute theories of heuristic processing. Here, we demonstrate the invalidity of this conclusion by showing that all of the tested predictions follow straightforwardly from an account assuming heuristic prob...
Are human contingency judgments based on associationistic principles such as cue competition or o... more Are human contingency judgments based on associationistic principles such as cue competition or on normative principles as specified by rational-cognitive models? In this study, participants learned to predict an outcome from several simultaneously presented cues. They were asked to judge the cues in regard to causal power or statistical concepts such as probability or relative frequency. Uniform application of associationistic principles implies cue-interaction effects of blocking (Experiment 1) and conditioned inhibition (Experiment 2) for all judgments. A rational-cognitive framework predicts cueinteraction effects for causality judgments, but not for probability and relative frequency judgments. The results support the rational-cognitive framework on all accounts.
Organizational Behavior and Human Decision Processes, Feb 1, 2003
Predictions for probability judgments in a general knowledge task were derived from the combined ... more Predictions for probability judgments in a general knowledge task were derived from the combined error model and predictions for probability judgments in a sensory discrimination task were derived from the sensory sampling model . As predicted, an experiment suggested: (a) good calibration with full-range probability assessments for general knowledge tasks, but underconfidence for sensory discrimination, (b) more deviations from additivity in sensory discrimination, and (c) a preference to bet specifically on general knowledge or sensory tasks depending on the assessed probability, violating source-independence. The quantitative fit of the two models appropriately distinguished between the two task contents, but both models substantially under-predicted the overconfidence observed with interval estimation.
Previous data suggest that probability judgments can often be fairly realistic, but production of... more Previous data suggest that probability judgments can often be fairly realistic, but production of probability intervals pro-motes extreme overconfidence bias (Juslin & Persson 2002; Juslin, Wennerholm, & Olsson, 1999; Klayman, Soll, Gon-zález-Vallejo, & Barlas, 1999). We present a novel explana-tion of this format-dependence effect in terms of a naïve sam-pling model. The model assumes that people process distribu-tional information in an unbiased manner, but they are naïve in the sense that they uncritically take sample properties as es-timates of population properties. A Monte Carlo simulation demonstrates that the model predicts format dependence, with extreme overconfidence bias for interval production that prac-tically disappears for probability assessments for the same in-tervals. In the last section this novel prediction is empirically verified by data from human participants.
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Papers by Anders Winman