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Letters to the Editor: Letters & Announcements

Let's End the Error of the Standard Error

Tighe, Patrick MD; Gravenstein, Nikolaus MD; Rice, Mark J. MD

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doi: 10.1213/ANE.0b013e3181f2c0cd
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To the Editor

In a study presenting evidence that preventative hypothermia may be useful to attenuate pulmonary inflammation, vascular permeability, and neutrophil activation stemming from air embolism, Peng et al.1 chose to report their results using mean ± standard error of the mean (SEM). Given the understandably limited sample size (7), this would generally not be the preferred approach, because this study did not seek to infer how the sample means related to means found in the target population. Instead, the data are the type for which the distribution about the mean would be much better and more correctly described using standard deviation (SD).

The SD and the SEM are mathematically related despite yielding different types of information. Because SD = SEM · ✓n (where n is the sample size), SD must be larger than the SEM for any study involving greater than 1 sample. Increases in the SD suggest wider distributions of data around the mean, which minimize the ability to distinguish differences between 2 groups.

This is a persistently common error in our literature, as has been pointed out previously.2 We do not write this to impugn the work of Peng et al. Instead, we want to remind readers, reviewers, and authors alike that though often mistakenly used interchangeably, SEM and SD are in fact quite different. In this report the presentation of the descriptive data would have been better served by calculation of the SD instead of the SEM to have provided the readers the greatest confidence in the statistical conclusions.

Patrick Tighe, MD

Nikolaus Gravenstein, MD

Mark J. Rice, MD

University of Florida College of Medicine

Gainesville, Florida

[email protected]


1. Peng CK, Huang KL, Wu CP, Li MH, Lin HI, Hsu CW, Tsai SH, Chu SJ. The role of mild hypothermia in air embolism-induced acute lung injury. Anesth Analg 2010;110:1336–42
2. Nagele P. Misuse of standard error of the mean (SEM) when reporting variability of a sample. A critical evaluation of four anaesthesia journals. Br J Anaesth 2001;90:514–16
© 2011 International Anesthesia Research Society