Uncertainty and the Mean, Standard Deviation

[e2m2a]

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?

 

[jbsteele]

Yes, you should include the absolute uncertainties of each measurement when calculating the mean and standard deviation. This will help to give you an accurate result for the t-test. You should also be sure to take into account any other factors that may affect the accuracy of your measurements such as random errors or systematic errors.

 

[tomcue]

I would advise you to include the absolute uncertainties of each measurement when calculating the mean and standard deviation. This will provide a more accurate representation of your data and allow for a more comprehensive analysis. The t-test formula you mentioned also requires the standard deviation to be calculated with the uncertainties included. This is because the standard deviation is a measure of how much the data points deviate from the mean, and including the uncertainties in the calculation will give a better understanding of the spread of the data. Additionally, including uncertainties in your calculations is a standard practice in scientific research and will ensure that your results are reliable and reproducible. Therefore, I recommend that you include the absolute uncertainties in both the mean and standard deviation when calculating the t-test and reporting your data.