
06649331
j
2016f.01306
Lane, David M.
Simulations of the sampling distribution of the mean do not necessarily mislead and can facilitate learning.
J. Stat. Educ. 23, No. 2, 7 p., electronic only (2015).
2015
Taylor \& Francis, Abingdon, Oxfordshire; American Statistical Association (ASA), Alexandria, VA
EN
K90
K70
stochastics
statistics
university teaching
sampling distribution simulations
variance of means
effectiveness of simulations
central limit theorem
large number of samples
using simulations effectively
sampling distribution of the mean
simulation
sampling variability
variance of variances
estimated mean
estimated standard deviation
ME 2016f.01283
http://ww2.amstat.org/publications/jse/v23n2/lane.pdf
Summary: Recently {\it A. E. Watkins} et al. [ibid. 22, No. 3, 21 p. (2014; ME 2016f.01283)] discovered that simulations of the sampling distribution of the mean can mislead students into concluding that the mean of the sampling distribution of the mean depends on sample size. This potential error arises from the fact that the mean of a simulated sampling distribution will tend to be closer to the population mean with large sample sizes than it will with small sample sizes. Although this pattern does not change as a function of the number of samples, the size of the difference between simulated sampling distribution means does and can be made invisible to observers by using a very large number of samples. It is now practical for simulations to use these very large numbers of samples since the speed of computers and even mobile devices is sufficient to simulate a sampling distribution based on 1,000,000 samples in just a few seconds. Research on the effectiveness of sampling distribution simulations is briefly reviewed and it is concluded that they are effective as long as they are used in a pedagogically sound manner.