Standard error of the mean or standard deviation?

EDITORIAL Standard error of the mean or standard deviation?

Referees continue to be presented with papers containing confusing statistical statements. One source of ambiguity, which may also indicate a certain misunderstanding, is the use of the f symbol to attach an ill-defined measure of variability or precision to a quoted mean. Variability

between

individuals in the sample may wel1 be summarised

by the descriptive

measure srundurd

deviation (SD)whilst precision of an estimate of the population mean may wel1 be expressed in terms of the sfundurd error ofthe meun (SEM).As an example, a recent study of flexion of the lumbar spine for schoolchildren suggested

that the mean is 76.1” with a standard deviation of 9.4”. However because there were many subjects in the study the mean itself had a stundurd error of only 0.7”. Thus the referee may receive either: mean = 76.1” k 9.4” or mean = 76.1” f 0.7”. Clearly this is confusing. The ambiguity can be removed if the format, mean 76.1” (SD,9.4”) or mean 76.1” (SEM, 0.7”) is used. A similar problem arises when plots of means over, say, time have ‘error bars’ added. It must be made clear in the legend whether the error bars are of one sfundurd deviution length, to give an impression of the variability in the sample, or one stundard error, to give an impression of the precision of the estimate of the population mean. Malcolm Tillotson MIS

School of Computing and Mathematics Huddersfield Polytechnic HD13DH UK