Standard Error

The standard error (SE) is the standard deviation (標準差) of the sampling distribution — in plain words, the typical amount your estimate would differ from the true value just because of sampling luck. For a sample mean it equals the data’s standard deviation divided by the square root of the sample size, so quadrupling the sample size only halves the SE.

The standard error is the engine behind margins of error and confidence intervals: smaller SE means a sharper, more trustworthy estimate. A crucial caution: the standard error measures sampling noise, not measurement mistakes or bias — a biased survey can have a tiny standard error and still be confidently wrong.