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Simulation of the sampling distribution of the mean can mislead. (English)
J. Stat. Educ. 22, No. 3, 21 p., electronic only (2014).
Summary: Although the use of simulation to teach the sampling distribution of the mean is meant to provide students with sound conceptual understanding, it may lead them astray. We discuss a misunderstanding that can be introduced or reinforced when students who intuitively understand that “bigger samples are better" conduct a simulation to explore the effect of sample size on the properties of the sampling distribution of the mean. From observing the patterns in a typical series of simulated sampling distributions constructed with increasing sample sizes, students reasonably ‒ but incorrectly ‒ conclude that, as the sample size, $n$, increases, the mean of the (exact) sampling distribution tends to get closer to the population mean and its variance tends to get closer to $σ^2$/$n$, where $σ^2$ is the population variance. We show that the patterns students observe are a consequence of the fact that both the variability in the mean and the variability in the variance of simulated sampling distributions constructed from the means of $N$ random samples are inversely related, not only to $N$, but also to the size of each sample, $n$. Further, asking students to increase the number of repetitions, $N$, in the simulation does not change the patterns.
Classification: K70 K90
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