Standard Error

The standard error (s sub x-bar) is a measure of the variability among the sample means () of repeated samples taken from the same population. The standard error is a measure of precision, and reflects how certain we are in the results from our sampling. A small standard error indicates that we expect to get the same result from repeated samples, whereas a large standard error suggests that repeated samples produce highly divergent results.

The standard error is calculated as

s sub x-bar = s / square root of n

If we sample a highly variable population (i.e., the value of s in the formula is large) we would expect a large standard error, which demonstrates a low level of repeatability among samples and indicates we should be cautious about how well our sample actually represents the population. By including more members of the population in each sample (i.e., increasing the value of n in the formula), we should reduce the standard error and improve the repeatability among samples

References and Further Reading

Bonham, C.D. 1989. Measurements for terrestrial vegetation. John Wiley Son, New York, NY. p 8.

Cook, C.W., and J. Stubbendieck. (eds). 1986. Range research: Basic problems and techniques. Society for Range Management, Denver, CO. pp 217-219.