[time-nuts] Timelab error bars on xDEV traces

[Matthias Welwarsky]

On Samstag, 25. Juli 2020 14:16:23 CEST John Miles wrote:
> > 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.)

Indeed I noticed, I checked some matlab scripts that calculate adev and the 
error bars were practically nonexistent. Then I wondered what Timelab was 
doing differently.

Then, M = tau / tau0? So, for a time series with a measurement interval of 1s, 
M would be equal to tau, right?

> 
> 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.

I'll go with "pretty" and "informative".

Thanks!

> 
> -- john
> 
> 
> 
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