Normal ranges
BMJ 2013; 346 doi: https://doi.org/10.1136/bmj.f1343 (Published 08 March 2013) Cite this as: BMJ 2013;346:f1343
All rapid responses
Rapid responses are electronic comments to the editor. They enable our users to debate issues raised in articles published on bmj.com. A rapid response is first posted online. If you need the URL (web address) of an individual response, simply click on the response headline and copy the URL from the browser window. A proportion of responses will, after editing, be published online and in the print journal as letters, which are indexed in PubMed. Rapid responses are not indexed in PubMed and they are not journal articles. The BMJ reserves the right to remove responses which are being wilfully misrepresented as published articles or when it is brought to our attention that a response spreads misinformation.
From March 2022, the word limit for rapid responses will be 600 words not including references and author details. We will no longer post responses that exceed this limit.
The word limit for letters selected from posted responses remains 300 words.
Dr. Sedgwick has written several Endgames (Normal Ranges; Standard deviation vs. standard error; Limits of agreement (Bland-Altman method)) which contain the statement that normal ranges of +/- one, two or three standard deviations can be calculated for any continuous variable, whether it follows a Normal distribution or not. This is misleading.
Of course, one may calculated whatever one chooses; but Dr. Sedgwick writes that these 'three ranges are typically derived that contain about 68%, 95% and 99% of the sample participants'. This will not always hold if the variable is not (approximately) normally distributed.
I would not have quibbled about this matter if it were not for the fact that Dr. Sedgwick includes this issue explicitly in two of the multiple choice questions (Normal ranges: statement c and Limits of agreement: statement c). In my opinion, the suggested answer is incorrect - or at least misleading!
Competing interests: No competing interests
"..if a patient’s measurement is outside the normal range it does not automatically mean the volume is abnormal (a is false)." This is clearly nonsense - the patient's measurement is abnormal by definition. Whether the definition is appropriate or not is another question.
Competing interests: No competing interests
Re: Normal ranges
I thank Schiff(1) and Franklin(2) for their rapid responses to my endgame on normal ranges(3).
Schiff has confused clinical and physical normality with the properties of the statistical normal distribution. Although a patient may have a physical measurement in the extremes of a statistical distribution, it does not mean the patient is “abnormal by definition”.
A previous question described how the sample standard deviation and mean can be used to calculate three ranges, containing approximate percentages of the sample members.(4) These ranges can be used to describe the variation in the measurements of a variable. The ranges are derived as one, two and three standard deviations from the mean (above and below), and will contain approximately 68%, 95%, and 99% of the sample participants. Obviously the derivation of these ranges is related to the theoretical properties of the statistical normal distribution. However, Franklin’s rapid response is misleading and out of context. It was incorrect of Franklin to suggest that these ranges will only hold true if the variable follows a normal distribution (if only approximately). The three ranges will apply to those distributions that are typically observed in clinical and biological studies, regardless of whether they have a normal distribution or not.
1. Schiff A. Re: Normal ranges. 1 April 2013.
2. Franklin J. Re: Normal ranges: distributional assumptions. 18 February 2014.
3. Sedgwick P. Normal ranges. BMJ 2013;346:f1343.
4. Sedgwick P. Standard deviation versus standard error. BMJ2011;343:d8010.
Competing interests: No competing interests