In the last column we discussed the use of pooling to get a better estimate of the standard deviation of the measurement method, essentially the standard deviation of the raw data. But as the last column implied, most of the time individual measurements are averaged and decisions must take into account another standard deviation, the standard deviation of the mean, sometimes called the “standard error” of the mean. It’s helpful to explore this statistic in more detail: first, to understand why statisticians often recommend a “sledgehammer” approach to data collection methods; and, second, to see that there might be a better alternative to this crude tactic. We’ll also see how to answer the question, “How big should my sample size be?”

For the next few columns, we need to discuss in more detail the ways statisticians do their theoretical work and the ways we use their results.