[time-nuts] Timelab error bars on xDEV traces

[John Miles]

> I've been trying to figure out how the error estimates (error bars) in the
> XDEV traces in TimeLab are computed. The status bar says " +/- sigma /
sqrt(n/
> m)", obviously "n" is the number of values in the bin for the computed
tau,
> but what is "m"? It cannot be smaller than "n" as the error estimate would
> then become larger than the actual value, right?
> 

Hi, Matthias --

There's a bit more detail on page 94 at
http://www.miles.io/PhaseStation_53100A_user_manual.pdf .  This method is
based on the "simple confidence intervals" described on page 37 of
https://www.nist.gov/publications/handbook-frequency-stability-analysis . 

The denominator (m) used by TimeLab is the tau multiple for the bin.  The
division is necessary because the sqrt(n) subexpression assumes
non-overlapped calculations, while TimeLab always uses overlapping.  If you
use sqrt(n) for overlapped calculations, the resulting error bars are
unrealistically small (almost invisible.)  

In reality the confidence interval at any given bin is influenced by other
factors such as the dominant noise type.  For applications that require
mathematically-defensible confidence intervals, it's best to export the data
to Stable32 and crunch it there. 

-- john