Geometric means ± SD [🇷 for BE/BA]

posted by Ben – 2016-11-08 22:20 (2696 d 23:43 ago) – Posting: # 16789
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Dear Helmut,

❝ I suggest to plot geometric means* ± backtransformed standard deviations. Concentrations likely follow a log-normal distribution.


We should bear in mind that when we back transform to the original scale we end up with asymmetry with respect to +/-. Therefore, it is IMHO not appropriate to do +/- back transformed standard deviation. Symmetry is however obtained with respect to * and /. So the error bars should be such that lower end = gMean / gSD and upper end = gMean * gSD, where gSD = exp(standard deviation from log-transformed values).
[Mathematical rationale: exp(m - s) = exp(m)/exp(s) = gMean / gSD and exp(m + s) = exp(m) * exp(s) = gMean * gSD), where m and s are mean and sd on log scale, respectively]

Best regards,
Ben.

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