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- W2181919103 abstract "Inferential statistics are used to decide whether two or more samples are from the same or different distributions, a decision that is generally difficult to make by visual inspection of sample frequency distributions. We investigate how children (8, 10, and 12 year old) and adults compare two sets of five vertical bars, similar in appearance to histograms, to determine which set represents a greater quantity or whether they were equal quantities. Our bars are conceptually simpler than histograms because only bar lengths matter, not their position. Participants of all ages correctly identified about 75% of the sets with greater quantity. Judgment accuracy was, however, strongly affected by age when sets contained equal quantities, increasing from 13% correct for 8 year olds to 61% for adults. Recognizing equality is difficult when integrating across multiple bars, and difficulty increases with variability. Implications for comparing statistical distributions are discussed. STATISTICAL REASONING AND THE EFFECT OF VARIABILITY Variability (i.e., dispersion of observed data) has a central role in statistics and in quantitative decisions in everyday life. Scientists must often decide whether two collections of measurements are samples from the same distribution or are from different distributions. A definitive answer to this problem is rarely possible because of sampling variability, and consequently scientists employ statistical inferential methods that yield probabilistic solutions. The mechanics of these statistical methods are relatively easy to learn and are commonly taught to undergraduate students in the social sciences, but the concepts that underlie statistical reasoning are difficult to learn (Garfield, 2003; Garfield & Ben-Zvi, 2008; Safran, 2010). Even students who complete a university statistics course and successfully demonstrate their mastery of these techniques may have little understanding of statistical reasoning (Garfield, delMas, & Chance, 2007)." @default.
- W2181919103 created "2016-06-24" @default.
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- W2181919103 date "2014-01-01" @default.
- W2181919103 modified "2023-10-18" @default.
- W2181919103 title "DEVELOPMENT OF INTEGRATED QUANTITY JUDGMENTS: MEANS OF DISTRIBUTIONS APPEAR MORE DIFFERENT THAN THEY ARE" @default.
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