# Subtracting two means and convert to %. What happens to the standard deviation

I have two sets of data to track the changes of my subject of analysis. I collected at two different time points, time = 0 and time = 10 min

At time = 0 min, the raw data are [12, 9, 10]. mean is 10.3 and SD is 1.5 At time = 10 min, the raw data are [5, 7, 6]. mean is 6.0 and SD is 1.0

I would like to calculate the changes from 0 to 10 min in terms of percentage.

For mean, i took [(10.3 - 6.0)/10.3]*100 = 44.6 %

What is the correct method to obtain the standard deviation in percentage?

• Same way you calculated the percentage change in means, as long as you are comparing the same concept while doing so (using estimates with the same units only). Although this has little to do with statistics, since this is not inferential but more descriptive in nature. – user2974951 Dec 26 '18 at 8:32

One way to create several of these estimates is to use bootstrapping. You resample your data with replacement and obtain several realizations, e.g. $$[12,9,10],[10,9,12],[10,10,9],...$$, record the mean of each of these, redo the same for the second set, calculate the percentage. After all, you'll have several percentages and you can directly estimate the deviation you ask for. But note that, this is a computational methodology.