Sympercents: symmetric percentage differences on the 100 log(e) scale simplify the presentation of log transformed data.
The results of analyses on log transformed data are usually back-transformed and interpreted on the original scale. Yet if natural logs are used this is not necessary--the log scale can be interpreted as it stands. A difference of natural logs corresponds to a fractional difference on the original scale. The agreement is exact if the fractional difference is based on the logarithmic mean. The transform y = 100 log(e)x leads to differences, standard deviations and regression coefficients of y that are equivalent to symmetric percentage differences, standard deviations and regression coefficients of x. Several simple clinical examples show that the 100 log(e) scale is the natural scale on which to express percentage differences. The term sympercent or s% is proposed for them. Sympercents should improve the presentation of log transformed data and lead to a wider understanding of the natural log transformation.
Cole
T J
TJ
Department of Paediatric Epidemiology and Biostatistics, Institute of Child Health, London WC1N 1EH, UK. Tim.Cole@ich.ucl.ac.uk
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