Instrument Error or Standard Deviation

[no_face]

I had a question about how to properly perform error analysis on a series of distance measurements. I need to find the relative error in the distance. I was wondering, should I use the instrument uncertainty divided by the measurement (in this case, it would be 0.005m / (mean measurement)). Or, should I be using the formula that relates absolute error to standard deviation: σ_x=s_x/(N^1/2), then use this value to find relative error. Or, should I use whichever one is larger to account for the largest possible error?

 

[Dr. Courtney]

I had a question about how to properly perform error analysis on a series of distance measurements. I need to find the relative error in the distance. I was wondering, should I use the instrument uncertainty divided by the measurement (in this case, it would be 0.005m / (mean measurement)). Or, should I be using the formula that relates absolute error to standard deviation: σ_x=s_x/(N^1/2), then use this value to find relative error. Or, should I use whichever one is larger to account for the largest possible error?

Both are reasonable ball park estimates, and using the larger one is a common approach. There are subtleties regarding random and systematic errors which prevent either from being rigorous.

 

[Student100]

I had a question about how to properly perform error analysis on a series of distance measurements. I need to find the relative error in the distance. I was wondering, should I use the instrument uncertainty divided by the measurement (in this case, it would be 0.005m / (mean measurement)). Or, should I be using the formula that relates absolute error to standard deviation: σ_x=s_x/(N^1/2), then use this value to find relative error. Or, should I use whichever one is larger to account for the largest possible error?

If you have a data set I always recommend calculating error from it directly. You should find $\alpha = \frac{σ_{n-1}}{{n^{1/2}}}$, remember to calculate the standard deviation as n-1, you lose a degree of freedom when working from the set. You can then analyze the data, apply Chauvenet's criterion, relative error, etc.