SE vs SD vs SEM

Pete Lollar   (2005-11-28 16:01)  Emory University

The review by Whitley and Ball (Critical Care 2002, 6:143-148) adds further confusion to the distinction between a standard error and a standard deviation. They define the standard error as the population standard deviation divided by the square root of the sample size. This is what most statistics books call the standard error of the mean (SEM). In contrast, standard error is synonymous with standard deviation. The SEM is the standard deviation of the means of samples of size n. It is also possible to define standard errors of other population parameters (e.g., the standard error of the median and the standard error of the variance), although the SEM is the most widely used. It perhaps is unfortunate that the term standard error ever was introduced. It is important to make the distinction between standard error and SEM because so many research papers present their results as estimates of the SEM.

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