Recently Watkins, Bargagliotti, and Franklin (2014) 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.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education