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- Lindskog, Marcus, 1980-, et al.
(författare)
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Are all Data Created Equal? : Exploring Some Boundary Conditions for a Lazy Intuitive Statistician
- 2014
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Ingår i: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 9:5, s. e97686-
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Tidskriftsartikel (refereegranskat)abstract
- The study investigated potential effects of the presentation order of numeric information on retrospective subjective judgments of descriptive statistics of this information. The studies were theoretically motivated by the assumption in the naive sampling model of independence between temporal encoding order of data in long-term memory and retrieval probability (i.e. as implied by a "random sampling'' from memory metaphor). In Experiment 1, participants experienced Arabic numbers that varied in distribution shape/variability between the first and the second half of the information sequence. Results showed no effects of order on judgments of mean, variability or distribution shape. To strengthen the interpretation of these results, Experiment 2 used a repeated judgment procedure, with an initial judgment occurring prior to the change in distribution shape of the information half-way through data presentation. The results of Experiment 2 were in line with those from Experiment 1, and in addition showed that the act of making explicit judgments did not impair accuracy of later judgments, as would be suggested by an anchoring and insufficient adjustment strategy. Overall, the results indicated that participants were very responsive to the properties of the data while at the same time being more or less immune to order effects. The results were interpreted as being in line with the naive sampling models in which values are stored as exemplars and sampled randomly from long-term memory.
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| 2. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Calculate or wait : Is man an eager or a lazy intuitive statistician?
- 2013
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Ingår i: Journal of Cognitive Psychology. - : Informa UK Limited. - 2044-5911 .- 2044-592X. ; 25:8, s. 994-1014
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Effects of Response and Presentation Format on Measures of Approximate Number System Acuity
- 2013
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Ingår i: Proceedings of the 35th Annual Conference of the Cognitive Science Society. - Austin, TX : Cognitive Science Society, Inc.. - 9780976831891 ; , s. 2908-2913
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Konferensbidrag (refereegranskat)abstract
- Human adults, infants, and non-human animals are believed to be equipped with an Approximate Number System (ANS) supporting non-symbolic representations of numerical magnitudes. Recent research has questioned both the validity and reliability of tasks intended to measure acuity in the ANS. Issues with validity and reliability might be due to differences in methodology. In the present study, we compare four tasks designed to measure ANS acuity, using a within-subjects design. The tasks are compared with respect to response and presentation format effects previously studied in the psychophysics literature, but largely ignored in the ANS literature. We find a presentation format effect and show that when non-symbolic numerical stimuli are presented sequentially the magnitude of the second stimulus is overestimated. Further, the results indicate that people’s sensitivity to differentiate between non-symbolic numerosities is dependent on response format. The implications of the results to measures of ANS acuity are discussed.
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| 7. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Is it possible to train the approximate number system?
- 2012
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Ingår i: Proceedings of the 34th Annual Meeting of theCognitive Science Society. - Austin, TX : Cognitive Science Society, Inc.. ; , s. 2760-
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Konferensbidrag (refereegranskat)
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| 8. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Is it Time Bayes went Fishing? : Bayesian Probabilistic Reasoning in a Category Learning Task
- 2013
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Ingår i: Proceedings of the 35th Annual Conference of the Cognitive Science Society. - Austin, TX : Cognitive Science Society, Inc.. - 9780976831891 ; , s. 906-911
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Konferensbidrag (refereegranskat)abstract
- People have generally been considered poor at probabilistic reasoning, producing subjective probability estimates that far from accord to normative rules. Features of the typical probabilistic reasoning task, however, make strong conclusions difficult. The present study, therefore, combines research on probabilistic reasoning with research on category learning where participants learn base rates and likelihoods in a category-learning task. Later they produce estimates of posterior probability based on the learnt probabilities. The results show that our participants can produce subjective probability estimates that are well calibrated against the normative Bayesian probability and are sensitive to base rates. Further, they have accurate knowledge of both base rate and means of the categories encountered during learning. This indicates that under some conditions people might be better at probabilistic reaso
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| 9. |
- Lindskog, Marcus, 1980-
(författare)
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Is the Intuitive Statistician Eager or Lazy? : Exploring the Cognitive Processes of Intuitive Statistical Judgments
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Numerical information is ubiquitous and people are continuously engaged in evaluating it by means of intuitive statistical judgments. Much research has evaluated if people’s judgments live up to the norms of statistical theory but directed far less attention to the cognitive processes that underlie the judgments.The present thesis outlines, compares, and tests two cognitive models for intuitive statistical judgments, summarized in the metaphors of the lazy and eager intuitive statistician. In short, the lazy statistician postpones judgments to the time of a query when the properties of a small sample of values retrieved from memory serve as proxies for population properties. In contrast, the eager statistician abstracts summary representations of population properties online from incoming data.Four empirical studies were conducted. Study I outlined the two models and investigated whether an eager or a lazy statistician best describes how people make intuitive statistical judgments. In general the results supported the notion that people spontaneously engage in a lazy process. Under certain specific conditions, however, participants were able to induce abstract representations of the experienced data. Study II and Study III extended the models to describe naive point estimates (Study II) and inference about a generating distribution (Study III). The results indicated that both the former and the latter type of judgment was better described by a lazy than an eager model. Finally, Study IV, building on the support in Studies I-III, investigated boundary conditions for a lazy model by exploring if statistical judgments are influenced by common memory effects (primacy and recency). The results indicated no such effects, suggesting that the sampling from long-term memory in a lazy process is not conditional on when the data is encountered.The present thesis makes two major contributions. First, the lazy and eager models are first attempts at outlining a process model that could possibly be applied for a large variety of statistical judgments. Second, because a lazy process imposes boundary conditions on the accuracy of statistical judgments, the results suggest that the limitations of a lazy intuitive statistician would need to be taken into consideration in a variety of situations.
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| 11. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Measuring acuity of the approximate number system reliably and validly : the evaluation of an adaptive test procedure
- 2013
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Ingår i: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 4, s. 510-
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 12. |
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| 13. |
- Lindskog, Marcus, 1980-, et al.
(författare)
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Naïve Point Estimation
- 2013
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Ingår i: Journal of Experimental Psychology. Learning, Memory and Cognition. - : American Psychological Association (APA). - 0278-7393 .- 1939-1285. ; 39:3, s. 782-800
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Tidskriftsartikel (refereegranskat)abstract
- The capacity of short-term memory is a key constraint when people make online judgments requiringthem to rely on samples retrieved from memory (e.g., Dougherty & Hunter, 2003). In this article, theauthors compare 2 accounts of how people use knowledge of statistical distributions to make pointestimates: either by retrieving precomputed large-sample representations or by retrieving small samplesof similar observations post hoc at the time of judgment, as constrained by short-term memory capacity(the naı¨ve sampling model: Juslin, Winman, & Hansson, 2007). Results from four experiments supportthe predictions by the naı¨ve sampling model, including that participants sometimes guess values thatthey, when probed, demonstrably know have the lowest probability of occurring. Experiment 1 alsodemonstrated the operations of an unpredicted recognition-based inference. Computational modeling alsoincorporating this process demonstrated that the data from all 4 experiments were better predicted byassuming a post hoc sampling process constrained by short-term memory capacity than by assumingabstraction of large-sample representations of the distribution.
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| 14. |
- Lindskog, Marcus, 1980-
(författare)
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The Lazy Intuitive Statistician : Influence of Data Representation and Retrieval Processes on Intuitive Statistical Judgment
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Intuitive statistical judgments are an integral part of people’s everyday life and a long line of research has investigated the extent to which man lives up to the norms of statistical theory when performing such judgments. A recent account of intuitive statistical judgments, summarized in the metaphor of the naïve intuitive statistician (K. Fiedler & P. Juslin, 2006), has suggested that people base judgments on small samples, which they have an ability to veridically record but an inability to evaluate the representativeness of. The present thesis builds on research concerning the naïve intuitive statistician and investigates how representation and memory retrieval of numerical information influences intuitive statistical judgments. Two studies were conducted. Study I introduced two possible accounts of how numerical information is represented and retrieved. The first possibility suggests that information is stored as exemplars and that estimates of statistical properties are calculated on small samples drawn from memory at the time of a query. The second possibility suggests that numerical information is stored as abstract summary statistics calculated at the time of exposure. The distinction was summarized in the metaphor of a lazy vs. an eager intuitive statistician. Study II extended the findings of Study I by investigating how point estimates of unknown quantities are formed from knowledge of statistical properties of a numerical variable. More specifically, a model of naïve point estimation based on the naïve sampling model (P., Juslin, A., Winman, & P., Hansson, 2007) was introduced to predict participants’ distribution of point estimates. In general, the results from both studies support the idea that people spontaneously act as lazy intuitive statisticians that record numerical information in a raw format during exposure and postpone evaluation of statistical properties until they are requested to do so. Under certain fairly predictable and limited circumstances, however, participants were able to form abstract representations of statistical properties. The results of Study II support the predictions by the model of naïve point estimation, including a novel phenomenon where participants give point estimates which they know, when probed otherwise, have a low probability of occurring. The findings of the two studies extend previous research concerning people’s ability to be intuitive statisticians by not only measuring how accurate the knowledge of properties of numerical variable is but by also describing how such knowledge is represented. The model of naïve point estimation contributes to the existing body of research by describing how people perform one type of intuitive statistical inference, point estimation, and shows how statistical properties of the underlying distribution influences the pattern of responses. The model also suggests novel explanations to results showing that people seem to have implicit expectations that distributions are normal.
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