Abstract
We propose that when individuals believe in fixed traits of personality (entity theorists), they are likely to expect a world of “uniformity.” As such, they easily infer a population statistic from a small sample of data with confidence. In contrast, individuals who believe in malleable traits of personality (incremental theorists) are likely to presume a world of “diversity,” such that they “hesitate” to infer a population statistic from a similarly sized sample. In four laboratory experiments, we found that compared to incremental theorists, entity theorists estimated a population mean from a sample with a greater level of confidence (Studies 1a and 1b), expected more homogeneity among the entities within a population (Study 2), and perceived an extreme value to be more indicative of an outlier (Study 3). These results suggest that individuals are likely to use their implicit self-theory orientations (entity theory versus incremental theory) to see a population in general as a constitution either of homogeneous or heterogeneous entities.
Highlights
Picture a little boy at an electronics store, badgering his mother to buy him a smart phone, insisting that everyone at his school has a smart phone
A 2 X 3 ANOVA on the midpoint of the range, did not yield any significant effect; the interaction effect did not approach significance (F(2,149) = 2.08, NS), nor did the main effects (F(1,149) = 1.00, NS, F(2,149) = .28, NS) (Fig 1). While both incremental and entity theorists estimated the same mean level of contribution, entity theorists were quicker to infer lower variance–as the sample size increased, entity theorists were quick to restrict the range while incremental theorists were more reluctant to do so
When the sample data included an extreme value, incremental theorists estimated a higher population mean than entity theorists across all standard deviation conditions. The magnitude of this difference between entity and incremental theorists became smaller as the SD of the sample data increased: under 1SD (F(1,35) = 36.60, p < .001, η2 = .52); under 2SD (F(1,36) = 15.01, p < .001, η2 = .30); and under 3SD (F(1,38) = 6.44, p = .016, η2 = .15). These results suggest that entity theorists were more likely to believe in a homogeneous population, such that they considered the extreme value in the sample dataset to be “an outlier”–most students would be closer to the sample average
Summary
Picture a little boy at an electronics store, badgering his mother to buy him a smart phone, insisting that everyone at his school has a smart phone. People of all ages collect small sizes of sample data and make statistical inferences from that sample to a population. When making an inference from a sample, people ought to begin with assessing the extent to which the sample is representative of the population. They do this to be confident (to some extent) about their estimates. One might assume that an assessment of the representativeness of sample data should be typically based on mathematical or statistical reasoning, using such notions as “a smaller variation among observations is more reliable information to infer the nature of a population,” or “a larger sample size would reduce the chance of the sample mean being significantly different from the population mean.”. Assuming that the boy was not lying to his PLOS ONE | DOI:10.1371/journal.pone.0168589 December 15, 2016
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