Fusing measurement results

[ufechner7]

I have n measurements, statistically independant with n values x_i and n standard deviations \sigma_i. How can I combine them to get one value and one standard deviation?

[nilshg]

By “measurements” here you mean you only have the summary statistics of the measurements? (Otherwise you could just combine all the data)

Maybe this answers your question:

How do I combine standard deviations of two groups?

[wc4wc4wc4]

I personally like Barlow. On page 54, chapter 4 on errors, he writes:

[aplavin]

Just be careful and ensure you really believe the original individual errors. Otherwise, imagine you have measurements [1±0.01, 1±0.01, 2±0.01, 2±0.01], and the result will be 1.5±0.005. When you don’t believe original errors, better to do

using StatsBase
mean(vals) ± sem(vals)