Standard error

The standard error (SE) of a statistic is the standard deviation of its sampling distribution. It is the square root of the variance of an estimator of a parameter, as in the standard error of the mean. The standard error is often used in calculations of confidence intervals. The sampling distribution of a mean is generated by repeated sampling from the same population and recording the sample mean per sample. This forms a distribution of different sample means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. In regression analysis, the term "standard error" can also be used to refer to the square root of the reduced chi-squared statistic in addition to the more common use in describing the standard error for a particular regression coefficient as used in confidence intervals.