Simulations of the Sampling Distribution of the Mean Do Not Necessarily Mislead and Can Facilitate Learning

Abstract

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.

• Sampling distribution simulations
• Variance of means
• Effectiveness of simulations
• Central Limit theorem