75  Estimation

Metric Equation Description Example
Standard Error of the Mean (SEM) \(SEM_{\overline{x}}=\frac{s}{\sqrt{n}}\)
95% Confidence Interval_ (95% CI) \(1.96(\frac{s}{\sqrt{n}})=1.96(SEM_{\overline{x}})\)
or ideally, \(t_{n-1}(SEM_{\overline{x}})\)

Inferential statistics (\(SEM\) and \(95\%\ CI\)) are popular for error bars, since they can be much smaller than the standard deviation. The SEM is, by definition, always smaller than the \(95\%\ CI\). The \(95\%\ CI\) is the range that covers the true population parameter with a \(95\%\) probability. The \(SEM\) is the standard deviation of the random variable \(\bar{X}\), i.e. of many sample means, and is primarily used because it is so small, not because it is a useful measure of spread of a single sample.