A Tutorial on Standard Errors

A Tutorial on Standard Errors E. Garcia admin@miislita.com Published on: June 25, 2010; Last Modified: June 25, 2010 © 2010 E. Garcia Keywords: tutorial, standard errors, correlation coefficients, Fisher Transformation Abstract: This is a tutorial on standard errors. Every statistic from a sample distribution has a standard error that is specific to that statistic. Using the incorrect definition for a standard error invalidates any research study. Introduction The standard deviation of the sampling distribution of a statistic is known as the standard error of that statistic (1). A standard error, denoted by stderr or SE, measures the accuracy of a statistic. According to Arsham (2): “To express the accuracy of the estimates of population characteristics, one must also compute the standard errors of the estimates. These are measures of accuracy that determine the possible errors arising from the fact that the estimates are based on random samples from the entire population, and not on a complete population census. “ In general, SE values are computed in different ways depending on the statistic used. A comprehensive list of SE definitions is provided elsewhere (2, 3). This tutorial covers a limited number of these. The Standard Error of the Mean This is probably the best known standard error. The standard error of the mean is the standard deviation of the sample mean estimate of a population mean (1); i.e. ...