I am an independent researcher doing a physics experiment. I have collected data and want to report the data with the uncertainities included, etc. I have taken a set of readings and I know how to calculate the mean and standard deviation. What I don't know is do I include the absolute uncertainties of each measurement when calculating the mean and standard deviation? For example, I want to calculate a t-test defined as: |mean - expected value| t-test = -------------------------- standard deviation so that I can determine the number of standard deviations of the mean from the expected value. In this formula do I include the net absolute uncertainties for the mean and the standard deviation before I calculate the t-test?