Variances

The standard error is a measure of the variability of an estimate due to sampling. It indicates the variability of a sample estimate that would be obtained from all possible samples of a given design and size. Standard errors are used as a measure of the precision expected from a particular sample. If all possible samples were surveyed under similar conditions, intervals of 1.96 standard errors below to 1.96 standard errors above a particular statistic would include the true population parameter being estimated in about 95 percent of the samples. This is a 95 percent confidence interval. For example, the estimated percentage of institutions reporting that they offered any distance education courses in 2000–2001 is 56.3 percent, and the estimated standard error is 1.2 percent. The 95 percent confidence interval for the statistic extends from [56.3 - (1.2 times 1.96)] to [56.3 + (1.2 times 1.96)], or from 53.9 to 58.7 percent.