id: 06649331
dt: j
an: 2016f.01306
au: Lane, David M.
ti: Simulations of the sampling distribution of the mean do not necessarily
mislead and can facilitate learning.
so: J. Stat. Educ. 23, No. 2, 7 p., electronic only (2015).
py: 2015
pu: Taylor \& Francis, Abingdon, Oxfordshire; American Statistical Association
(ASA), Alexandria, VA
la: EN
cc: K90 K70
ut: 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
ci: ME 2016f.01283
li: http://ww2.amstat.org/publications/jse/v23n2/lane.pdf
ab: 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.
rv: