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BMJ. 1996 Nov 9;313(7066):1200.

Detecting skewness from summary information.

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ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, Oxford.



Many statistical methods of analysis assume that the data have a normal distribution. When the data do not, they can often be changed to make them more normal. However, readers of published papers may wish to be certain that the authors have conducted a proper analysis. One can clearly see whether the distributional assumption is met when data are presented in the form of a histogram or scatter diagram. However, when only summary statistics are presented, the task becomes far more difficult. An idea of the distribution can be gleaned if the summary statistics include the range of the data. For example, a range from 7 to 41 around a mean of 15 suggests that the data are positively skewed. Belief in that assumption may be unreliable because the range is based upon the two most extreme, and atypical, values. Similar asymmetry affecting the lower and upper quartiles would better indicate a skewed distribution. it is suggested that for measurements which must be positive, if the mean is smaller than twice the standard deviation, the data are likely to be skewed. A second indicator of skewness can be used when there are data for several groups of individuals. Deviations from the normal distribution and a relation between the standard deviation and mean across groups often go together. A standard deviation which increases as the mean increases is a strong indication of positively skewed data, and specifically that a log transformation may be needed.

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