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I am editing a report that has a table showing average treatment effects expressed as [log(kg/ha)] - its about growing maize. The authors have compared treatment and control values of 7.42 and 7.10 and calculated the difference as 0.32, which is 4.5% (7.42-7.10)/7.10 x 100 = 4.5% I want to convert this into real numbers. My question is, will the difference between these values expressed as real numbers be 4.5% or not? My gut instinct says not but its a long time since I did logs at school. Thanks for your help!

Keith
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  • Are the "7.42" and "7.10" values on the log-scale? If so, then (a) percentage differences on the log scale are *not* percentage differences on the original untransformed scale and (b) I would not be calculating percentage differences in the logs for this, but absolute differences. They are fairly easy to convert to percentage changes in the original variable. – Glen_b Mar 01 '22 at 02:03
  • Thanks! Here is my attempt to convert logs to original variables: – Keith Mar 02 '22 at 09:36
  • Here is my attempt to do this using https://ncalculators.com/number-conversion/anti-log-logarithm-calculator.htm Antiloge 7.42 = 1669 Antiloge 7.10 = 1212 Difference between the log values is 7.42-7.10 = 0.32/7.10 x 100 = 4.5% Difference between the equivalent ‘normal’ numbers (assuming I used the tool correctly – a big assumption): 1669-1212 = 457/1212 = 37.7% – Keith Mar 02 '22 at 09:36
  • No. Like this: Difference between the log values =0.32. $e^{0.32} = 1.377$, an increase of 37.7% – Glen_b Mar 02 '22 at 10:52
  • Great, many thanks – Keith Mar 02 '22 at 11:33
  • The report's author says 'Transforming log-converted values for percentage interpretation is sometimes a contentious issue in empirical research, so you may go ahead with the 37.7% yield increase. However, when submitting the paper to a journal, I will report the 4.5% yield difference' ....'we don’t usually convert the log-values back to real numbers before calculating the percentage effect, as this will lead to an erroneous interpretation due to an inequality concept in math called the arithmetic-geometric mean inequality'. Are these reasonable arguments? Can both 4.5 & 37.7% be correct! – Keith Mar 02 '22 at 17:18
  • I can't see any way to make any sense of the calculation by which 4.5 was obtained. Maybe I am missing something. – Glen_b Mar 05 '22 at 04:07

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