The distribution matters: two types of sample-size tasks

Sedlmeier, Peter

doi:10.1002/(sici)1099-0771(1998120)11:4<281::aid-bdm302>3.0.co;2-u

Cited by 22 publications

(17 citation statements)

References 17 publications

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“…However, the solution rates for both types of problem are lower than the average solution rate found among adult test persons (Sedlmeier & Gigerenzer, 1997). The comparatively low solution rate may hint at problems in understanding the task properly (Sedlmeier, 1998). Does the students' sensitivity to the effects of the sample size increase with the number of years of school attendance?…”

Section: Comprehension Of Planar Uniform Distributionmentioning

confidence: 92%

“…Kahneman & Tversky, 1972;Piattelli-Palmarini, 1994). A closer look, however, reveals that in judgment research two different types of tasks have been used (Sedlmeier, 1998;Sedlmeier & Gigerenzer, 1997): on the one hand, the tasks were frequency distributions tasks, where confidence judgments about proportions or means from a sample (a frequency distribution) were asked for. On the other hand sampling distribution tasks were used, where the variation of empirical sampling distributions has to be judged.…”

Section: Empirical Law Of Large Numbersmentioning

confidence: 99%

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On middle-school students' comprehension of randomness and chance variability in data

Engel

2005

Zentralblatt für Didaktik der Mathematik

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Understanding variability in empirical data is at the core of statistical reasoning and thinking. Of particular interest is how students' comprehension of chance and variability develops over time. This article reports the results of a crosssectional study that examined how students' statistical literacy evolves with increasing age. Our results are discussed and related to earlier studies with children by Fischbein and Green and with adults by Sedlmeier. Our study replicates in a modified form earlier investigations in other countries and confirms for German students conclusions from earlier studies. In particular, there are no indications of an improvement with increasing age. Our findings are consistent with findings in judgment research.

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Section: Comprehension Of Planar Uniform Distributionmentioning

confidence: 92%

Section: Empirical Law Of Large Numbersmentioning

confidence: 99%

On middle-school students' comprehension of randomness and chance variability in data

Engel

2005

Zentralblatt für Didaktik der Mathematik

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“…However, a substantial body of research suggests that people are naïve with respect to several aspects of the processes that shape samples. For example, even though people under some conditions acknowledge that larger samples contain more information than smaller samples (Bar-Hillel, 1979;Chesney & Obrecht, 2012;Evans & Dusoir, 1977;Obrecht, Chapman, & Gelman, 2007;Obrecht & Chesney, 2013;Sedlmeier, 1998;Sedlmeier & Gigerenzer, 1997), they do not always integrate this information in their decisions (Evans & Pollard, 1985;Kahneman & Tversky, 1972;Obrecht et al, 2007). In addition, people seem to be naïve with respect to the conclusions that can be drawn from a sample (Fiedler, 2000;Fiedler & Juslin, 2006;Kareev et al, 2002;Lindskog et al, 2013b).…”

Section: Judgements and Decisions Informed By Samplesmentioning

confidence: 99%

Where did that come from?—Identifying the source of a sample

Lindskog

2015

Quarterly Journal of Experimental Psychology

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People's ability to summarize their knowledge of an observed numerical variable has been extensively studied. However, many real-life situations require people to go beyond summary statistics and infer which process or distribution has generated a sample. The present study investigates the extent to which people can make such inferences when the experienced variable is continuous and when they have had previous experience with instances of the variable. It also tests specific predictions derived from three possible cognitive processes of how inferences about a generating distribution are made. The results indicate that participants are efficient and flexible intuitive statisticians, requiring only as little as four observations in a sample to successfully infer which distribution it came from. Further, the results indicate that the cognitive process supporting the inference uses statistical properties of both an experienced distribution and a presented test sample, as suggested by the Naïve Sampling Model (NSM).

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“…Furthermore, competing factors such as anecdotal descriptions and encounter frequency may lead to sample size being overlooked (Nisbett et al, 1983;Obrecht, Chapman & Gelman, 2009;Ubel, Jepson & Baron, 2001). Additionally, as illustrated by Kahneman and Tversky's (1972) classic "hospital problem," many people fail to recognize that larger sample sizes will reduce the chance that sample means will differ from a population mean (but see Evans & Dusior, 1977;Sedlmeier, 1998).…”

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confidence: 99%

Statistical judgments are influenced by the implied likelihood that samples represent the same population

Chesney

Obrecht

2011

Mem Cogn

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When sample information is combined, it is generally considered normative to weight information based on larger samples more heavily than information based on smaller samples. However, if samples appear likely to have been drawn from different subpopulations, it is reasonable to combine estimates of these subpopulation means (typically, the sample means) without weighting these estimates by sample size. This study investigated whether laypeople are influenced by the likelihood of samples coming from the same population when determining how to combine information. In two experiments we show that (1) implied binomial variability affected participants' judgments of the likelihood that a sample was drawn from a given population, (2) participants' judgments were more affected by sample size when samples were implied to be drawn randomly from a general population, compared to when they were implied to be drawn from different subpopulations, and (3) people higher in numeracy gave more normative responses. We conclude that when determining how to weight and combine samples, laypeople use not only the provided data, but also information about likelihood and sampling processes that these data imply.

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The distribution matters: two types of sample-size tasks

Cited by 22 publications

References 17 publications

On middle-school students' comprehension of randomness and chance variability in data

On middle-school students' comprehension of randomness and chance variability in data

Where did that come from?—Identifying the source of a sample

Statistical judgments are influenced by the implied likelihood that samples represent the same population

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