Misuse of standard error of the mean (SEM) when reporting variability of a sample. A critical evaluation of four anaesthesia journals

Abstract

Background. In biomedical research papers, authors often use descriptive statistics to describe the study sample. The standard deviation (SD) describes the variability between individuals in a sample; the standard error of the mean (SEM) describes the uncertainty of how the sample mean represents the population mean. Authors often, inappropriately, report the SEM when describing the sample. As the SEM is always less than the SD, it misleads the reader into underestimating the variability between individuals within the study sample. Methods. The aim of this study was to evaluate the frequency of inappropriate use of the SEM in four leading anaesthesia journals in 2001. The journals were searched manually for descriptive statistics reporting either the mean (SD) or the mean (SEM), and inappropriate use of the SEM was noted. Results. In 2001, all four anaesthesia journals published articles that used the SEM incorrectly: Anesthesia & Analgesia 27.7%, British Journal of Anaesthesia 22.6%, Anesthesiology 18.7% and European Journal of Anaesthesiology 11.5%. Laboratory reports and clinical studies were equally affected, except for Anesthesiology where 90% were basic science reports. Conclusions. One in four articles (n=198/860, 23%) published in four anaesthesia journals in 2001 inappropriately used the SEM in descriptive statistics to describe the variability of the study sample. Anaesthesia journals are encouraged to provide clearer statistical guidelines on how to report data variability in descriptive statistics.