# Calculating percentiles on log transformed data

I am trying to replicate results from a research paper that has the calculated 2.5 percentile and 97.5 percentile for a dataset, both with log10 transformed and untransformed versions. I can match their results for the untransformed data but not for the log10 transformed data. Is there a different approach needed when working with transformed data?

The dataset is:

data = c(1.0798,0.6047,1.2799,0.7581,0.6652,0.9692,1.1422)


They also define the 2.5 and 97.5 percentile as:

mean+- 1.96*sd


For their results they get the following:

| Stat          | Value  |
|---------------|--------|
|Geomean        | -0.047 |
|s.d. (logmean) |  0.125 |
|Mean           |  0.897 |
|2.5 percentile |  0.510 |
|97.5 percentile|  1.578 |


Unfortunately, they do not provide more information on how they define each statistic in the table above.

My understanding of geomeans with log transformed data might be wrong, but when I calculate the mean and geomean I get the values around the other way (i.e. my geomean = the paper's mean).

I have done my calculations both in R and excel and I cannot get their percentiles using their formula. The dataset might be too small to really calculate these percentiles (?) but I would still like to replicate their results so I can make sure I am applying it appropriately to my work.

Am I missing something or is there a mistake in the paper? Any help would be greatly appreciated! Thank you.

• your transformed variable's 97.5 percentile is $$-0.047+1.96*0.125\approx 0.198$$
• exponentiate it to get the answer $$10^{0.198}\approx 1.578$$