It seems as if the term 'standard error' was first used by Yule in 1897 in relation to the standard error of a residual. The term is only about a century old but the underlying concepts are considerably older. Like many ideas in the history of statistics, it's not as simple as that the standard error of the mean doesn't burst sui generis from a single mind. (2000) Asymptotics in Statistics: Some Basic Concepts (second ed.). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm (in Latin) One of the main arguments was that De Moivre lacked the notion of probability density function.ĭe Moivre, A. However, this history subsection of the Wikipedia page on the concept of normal distribution provides some compelling reasons challenging such an alternative view. Some believe that he should be credited with the introduction of normal distribution rather than Gauss (Johnson, Kotz & Balakrishnan.

If you want to be extra technical when it comes to attributing the notion of normal distribution to Gauss, you may want to say a couple of sentences about De Moivre (1738) and his book the Doctrine of Chances. Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm (in Latin).

Hence, I would use the following citation: And, when we are talking about the distribution of sample means in the population, the standard deviation is the standard error. The square root of the variance is the standard deviation. This is because normal distribution is defined by two parameters: the mean and variance. If that is the case, then you would not go entirely wrong by even citing Gauss (1809) when he first introduced the normal distribution in his monograph. Suppose you are talking about the standard error of the mean in the context of normal distribution. See this Wikipedia page for more details. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

Standard error of the mean