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ERIC Number: EJ1046365
Record Type: Journal
Publication Date: 2014
Pages: 21
Abstractor: As Provided
Reference Count: 21
ISBN: N/A
ISSN: EISSN-1069-1898
Simulation of the Sampling Distribution of the Mean Can Mislead
Watkins, Ann E.; Bargagliotti, Anna; Franklin, Christine
Journal of Statistics Education, v22 n3 2014
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 s[superscript 2]/n, where s[superscript 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.
American Statistical Association. 732 North Washington Street, Alexandria, VA 22314. Tel: 703-684-1221; Tel: 888-231-3473; Fax: 703-684-2037; e-mail: asainfo@amstat.org; Web site: http://www.amstat.org/publications/jse
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: National Science Foundation
Authoring Institution: N/A
IES Grant or Contract Numbers: 1119016