Specifically, the term standard error refers to a group of statistics that provide information about the dispersion of the values within a set. Standard error statistics are a class of statistics that are provided as output in many inferential statistics, but function as descriptive statistics. Taken together with such measures as effect size, p-value and sample size, the effect size can be a useful tool to the researcher who seeks to understand the accuracy of statistics calculated on random samples. The standard error is an important indicator of how precise an estimate of the population parameter the sample statistic is. The computations derived from the r and the standard error of the estimate can be used to determine how precise an estimate of the population correlation is the sample correlation statistic. It can allow the researcher to construct a confidence interval within which the true population correlation will fall. This statistic is used with the correlation measure, the Pearson R.
The Standard Error of the estimate is the other standard error statistic most commonly used by researchers. The formula, (1-P) (most often P < 0.05) is the probability that the population mean will fall in the calculated interval (usually 95%).
The standard error of the mean permits the researcher to construct a confidence interval in which the population mean is likely to fall. The two most commonly used standard error statistics are the standard error of the mean and the standard error of the estimate. The confidence interval so constructed provides an estimate of the interval in which the population parameter will fall. Standard error statistics are a class of inferential statistics that function somewhat like descriptive statistics in that they permit the researcher to construct confidence intervals about the obtained sample statistic.
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