Fractional uncertainties (Data analysis)

[superwolf]

I've been trying to determine the Boltzmann constant by observation of Brownian motion. I undertook four experiments and hence got four different estimated values for kB. To analyse the data, I estimated the mean value and the standard deviation. This is maybe not the best way to analyze the data since there are so few data points. I've heard of a method called "fractional uncertainties", but I was unable to find anything relevant by googling.

What does the method consist of, and should I use it?

 

[lippyka]

Fractional uncertainties is a statistical method used to estimate the precision of a measurement. It involves dividing the absolute uncertainty of a measurement by its value, giving an uncertainty expressed as a fraction or percentage. This allows for more accurate comparisons between measurements with different absolute uncertainties. For example, if two measurements have the same absolute uncertainty, but one has a larger value than the other, then the fractional uncertainty of the larger value will be lower. When analyzing the data from your experiments, you can use fractional uncertainties to compare the precision of each measurement and determine which ones are most reliable. It is likely a better method than just taking the mean value and standard deviation since it takes into account both the absolute uncertainty and the actual value of each measurement.