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Sympercents: symmetric percentage differences on the 100 log e scale simplify the presentation of log transformed data
Author(s) -
Cole T. J.
Publication year - 2000
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/1097-0258(20001130)19:22<3109::aid-sim558>3.0.co;2-f
Subject(s) - scale (ratio) , mathematics , statistics , transformation (genetics) , logarithm , simple (philosophy) , logarithmic scale , regression , standard deviation , regression analysis , combinatorics , mathematical analysis , physics , biochemistry , philosophy , epistemology , quantum mechanics , acoustics , gene , chemistry
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. Copyright © 2000 John Wiley & Sons, Ltd.