How to compare two quantities with uncertainties? I've got two instruments that measure one quantity. One of them is regarded to be more precise, therefore, I use this measurement as a reference. Then, I take two measurements of the same quantity using completely different method.
I want to compare my measurements and the reference and find how good my estimates and method are. I assume the uncertainites are gaussian and they are the standard deviations.
Quantitatively:
reference:     2.00 +/- 0.20
measurement 1: 1.99 +/- 0.02
measurement 2: 1.86 +/- 0.10

I tried simply finding how many standard deviations my measurements are away from the mean of the reference. That is, I calculated $0.5\sigma$ and $1.4\sigma$.
I feel, however, that there is more to it than that. I have not been educated in this aspect by my university and don't know where to look for answers.

The right way to compare between the measurement and the reference is using statistical test. The only thing that is missing is that we don't know the number of observations, but in your example i don't think it matters much.
Example using t-test:
from scipy.stats import ttest_ind_from_stats
ttest_ind_from_stats(mean1=2.0, std1=0.2, nobs1=13,
...:                      mean2=1.86, std2=0.1, nobs2=13)
Out[11]: Ttest_indResult(statistic=2.257432169523592, pvalue=0.0333559253888411)
vs:
In [12]: ttest_ind_from_stats(mean1=2.0, std1=0.2, nobs1=13,
...:                      mean2=1.99, std2=0.02, nobs2=13)
Out[12]: Ttest_indResult(statistic=0.17938288051478665, pvalue=0.8591429265656996)
you can see that the pvalue in the first is much smaller, which means that the second one is much closer. Changing the number of observations will not changed much the results.
