# Precision – Allan Variance (two sample variance)

The quality of data / stability of an instrument is characterized by the accuracy (shift from true value) and the precision (statistical distribution of values and drift due to external influence). A good measure is the Allan variance/Allan deviation which chops the time course of data into equaliy spaced intervals τ and compares these intervals, generating the Allan variance σ:
- σ
^{2}_{y(t)} = ½ <(y_{k+1} – y_{k})^{2}>, where y_{k+1} and y_{k} are successive mean values and t_{k+1} = t_{k} + τ.
- The brackets <...> denote the expectation value.
- The Allan deviation is the square root of the Allan variance.

### Simulated data

Signal noise in ppm
^{13}CO_{2} = 0.1
^{12}CO_{2} = 1

Signal drift (linear) in ppm
^{13}CO_{2} = 0.1
^{12}CO_{2} = 2