Definition

Standard error

The standard deviation of an estimate across hypothetical repeated samples — how precisely you know a mean, proportion, or coefficient.

The standard error (SE) shrinks as the sample grows (SE of the mean = SD/√n): more data pins the estimate down more tightly. It is the building block of confidence intervals (estimate ± ~2 SE for 95%) and test statistics.

Report SD when describing people ("scores varied, SD = 12"); report SE or a confidence interval when describing an estimate’s precision. They answer different questions and differ by a factor of √n.