Dear Jesus Banda,

you should attach the data so that I can help your case

Dear Jesus Banda,

you should attach the data so that I can help your case

The problem will not work as stated.

So you have raw data, possibly treatments with replicates and subsamples within each replicate. You take the means of the subsamples. Then within each treatment you apply the scaling formula. In this case, just let the statistical software package calculate the mean and standard deviation of the transformed means. However, there is no going back -- so if you use the transformed means you cannot back transform the data to get the mean and standard deviation of the raw data. Of course you can use algebra to accomplish the task, but what algebra fails to do is to correct for how the distribution of the data has changed in the transformation. So if you take a set of 20 values randomly typed into Excel, you can take an average. You can then take the log(average). You can then take the log of every value. Take the average of these log transformed values. Log(average(raw data)) is not equal to average(log(raw data)). Now take the antilog of the average of the log transformed raw data. The outcome is closer to the median of the raw values than it is to the average of the raw values.

One might be tempted to try recalculating the standard deviation using the transformed mean (square root of the sum from g=1 to n the (xg-xi')2/(n-1)). Don't do this. The standard deviation will not have the same statistical properties that people will assume when you talk about the "standard deviation".

Thanks for your attention, Rusiadi!! Now I have attached the data in my post.

Thank you, Timothy!! Just to check if I understood correctly, and as a conclusion: In case I want to plot the normalized means (or averages), I should forget about standard deviations.