Standard Error

The standard error of a sample statistic is the standard deviation of the sampling distribution of that particular statistic. Since the sample statistic most commonly used is the mean, this is often referred to as the standard error of the mean. The sampling distribution of a sample statistic is its frequency distribution, which is obtained from repeated random samples of size n from a normal population. Because the sampling distribution is derived from many samples drawn from the population, there will be some error in the estimate of the population parameter. Therefore, the standard error is the standard deviation for the distribution of errors, or random statistical fluctuations, that occur when using a sample statistic to estimate a parameter. It represents the variability of a sample statistic, quantifies sampling error, and enables researchers to determine the probability that their sample measures are valid representations of the population, allowing them to make predictions about the population from the sample, particularly since drawing more than one sample from a population is time- and resource-intensive and usually unavailable to many researchers. Standard error statistics are frequently used to estimate the interval in which population parameters are likely to be found.

Standard error and standard deviation are similar concepts that describe dispersion. However, the standard deviation is a measure of variability in a sample while standard error is a measure of variability in a sampling distribution. Standard error is a fundamental concept in statistics and is the basis of significance testing and computing confidence intervals. This concept builds on a basic understanding of descriptive statistics, primarily standard deviation and variance.

This entry defines standard error and explains how to calculate it, both manually (though this is rarely done) and using computer software. The entry then clarifies the confusion between terms that are similar to standard error of a sample statistic, primarily standard error of measurement and standard error of estimate.