Naked Statistics: Stripping the Dread from the Data

by Charles Wheelan

1. If you draw large, random samples from any population, the means of those samples will be distributed normally around the population mean (regardless of what the distribution of the underlying population looks like). 2. Most sample means will lie reasonably close to the population mean; the standard error is what defines “reasonably close.” 3. The central limit theorem tells us the probability that a sample mean will lie within a certain distance of the population mean. It is relatively unlikely that a sample mean will lie more than two standard errors from the population mean, and extremely unlikely that it will lie three or more standard errors from the population mean. 4. The less likely it is that an outcome has been observed by chance, the more confident we can be in surmising that some other factor is in play.