Explorations in statistics: standard deviations and standard errors

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This series in Advances in Physiology Education provides an opportunity to do just that: we will investigate basic concepts in statistics using the free software package R. Because this series uses R solely as a vehicle with which to explore basic concepts in statistics, I provide the requisite R commands. In this inaugural paper we explore the essential distinction between standard deviation and standard error: a standard deviation estimates the variability among sample observations whereas a standard error of the mean estimates the variability among theoretical sample means. If we fail to report the standard deviation, then we fail to fully report our data. Because it incorporates information about sample size, the standard error of the mean is a misguided estimate of variability among observations. Instead, the standard error of the mean provides an estimate of the uncertainty of the true value of the population mean.