Statistics Notes: Logarithms

doi:10.1136/bmj.312.7032.700

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J Martin Bland, professor of medical statisticsa,
Douglas G Altman, headb

^a Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
^b ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF

Correspondence to: Professor Bland.

Logarithms (or logs for short) are much used in statistics. We often analyse the logs of measurements rather than the measurements themselves, and some widely used methods of analysis, such as logistic and Cox regression, produce coefficients on a logarithmic scale. Here we shall give a brief summary of the properties of logarithms which make them so useful.

We shall start with logarithms to base 10. These are the common logarithms formerly widely used to do calculations for which we now use calculators and computers. The log to base 10 of a number …