How to calculate error of a percentage difference?

Question

I calculated a percentage and I need to find out the error of that percentage.
Example: Percentage difference is 10%. How do I find out the plus or minus error? So get something like this "0.41 ± 0.03%

Answer 1

Hi Noor:

You cannot answer this question with just the information given. For example, there might be a 10% difference between sets of results from a physics lab that are very precise, and the error could be very small. A sociologist might see a 10% difference on survey results, but since the survey results cover a broad range, the error could be very large. Such a calculation must include the variance of the data. In simple terms, how widely do the individual results vary from the mean that was used to calculate the percentage difference.