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EDUCATION AND DEBATE: Douglas G Altman and J Martin Bland Standard deviations and standard errors BMJ 2005; 331: 903 [Full text]

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A standard error?

Stephen J Senn   (18 October 2005)

Usually it is advisible to avoid "usually" in statistics

Jo R Goedhuys   (21 October 2005)

Standard error refers to standard error of mean

Dr.Girish Singh   (25 October 2005)

A standard error? 18 October 2005
Stephen J Senn, Professor of statistics University of Glasgow, Glasgow, G12 8QQ Send response to journal: Re: A standard error?	Doug Altman and Martin Bland’s clear and useful description of the difference between a standard deviation and a standard error nevertheless omits one important point. The formula for deriving the standard error of a mean as the standard deviation divided by the square root of the sample size is only valid if the observations are independently sampled from a population of interest. Now it is commonly the case in medical applications that to the extent that the observations are independently sampled from a population this is not the population of interest and to the extent that they are sampled from a population of interest they are not independent1-3. Consider for simplicity a small clinical trial in asthma in a single centre. If we regard the centre as being representative of the population of centres treating asthmatics, then the patients are not independently sampled from this population. On the other hand, the patients might be regarded as independent observations of some hypothetical population of patients attending this centre but that is of little interest. It turns out, however, that the standard error of a treatment effect, the difference between two means, can be reasonably estimated for a randomised clinical trial and given a useful causal interpretation, even if the standard errors of the individual group means could not1 3. Thus, for clinical trials I would go even further than Altman and Bland. Only standard deviations should be produced for individual groups and in my view to quote a standard error of a mean for a clinical trial is, in fact, an error, albeit a standard one. References 1. Senn SJ, Auclair P. The graphical representation of clinical trials with particular reference to measurements over time [published erratum appears in Statistics in Medicine 1991 Mar;10(3):487]. Statistics in Medicine 1990;9(11):1287-302. 2. Ludbrook J, Dudley H. Issues in Biomedical Statistics - Statistical- Inference. Australian and New Zealand Journal of Surgery 1994;64(9):630- 636. 3. Senn SJ. Statistical Issues in Drug Development. Chichester: John Wiley, 1997. Competing interests: My academic career is furthered by publication. I consult regularly for the pharmaceutical industry.
Usually it is advisible to avoid "usually" in statistics 21 October 2005
Jo R Goedhuys, Lecturer at the Catholic University of Leuven, Belgium Catholic University Leuven, Faculty of Medicine, Kapucijnenvoer 33J, 3000 Leuven, Belgium Send response to journal: Re: Usually it is advisible to avoid "usually" in statistics	Altman and Bland state that "about 95% of observations of any distribution usually fall within the 2 standard deviation limits". However, using the Chebyshev Inequality, we know that only 75% (or more) of observations fall between these limits. To be sure of 95% or more of the observations we need 4.5 standard deviations. In line with the attempt to explain difficult statistics in a simple way, as the authors always do in an excellent manner, I see no problem with the following sentence. "If you don't know what your distribution really looks like, whether it is unimodal or not, symmetric or not, ... you can use the following rule: there is always at least 1-(1/k square) percent of observations between k standard deviation limits. Thus for values of k = 2, 3 and 4 we know that at least 1 - 1/4 = 75%, 1 - 1/9 = 89% and 1 - 1/16 = 93% of observations respectively, can be found in the area between 2, 3 and 4 standard deviation limits." Competing interests: None declared
Standard error refers to standard error of mean 25 October 2005
Dr.Girish Singh, Scientific Assistant Biostatistics Unit, Dept. of Basic Principles, Inst. of Medical Sciences,BHU, Varanasi 221005 India Send response to journal: Re: Standard error refers to standard error of mean	The term standard error(SE) refers to standard error of mean(SEM) unless specified otherwise. Those who understand the meaning of the term standard deviation(SD) may see SE as the SD of sample mean. In even more simple words it may be statd that SD measures the variation in the observations of a given sample wheareas SE measures the variation in the means of possible samples. SD comes under descriptive statistics while SE clearly belongs to inferential statistics. Competing interests: None declared