[time-nuts] σ vs s in ADEV

Attila Kinali attila at kinali.ch
Mon Jan 9 13:28:41 EST 2017

Hoi Tom,

On Wed, 4 Jan 2017 16:26:22 -0800
"Tom Van Baak" <tvb at LeapSecond.com> wrote:

> I've never quite understood the pedantic separation of "sample" and
> "population" mean that statistic textbooks and academics love to discuss.

For me it's a matter of being exact. If there is one thing I've learned
in the last two years during my PhD then it is that we engineers are
way too often too sloppy about our notation and about the assumption
under which the used model/formulas hold.

> They clearly have never measured oscillators. In my experience if you think
> there's an important difference between N and N-1, then that's nature's way
> of telling you to go back to sleep and wait until tomorrow when you have
> more data. If your N is too small your ADEV wanders all over the place
> (TimeLab is good at displaying this in real-time) -- meaning that the
> distinction between sample (n-1) and population (n) mean is beyond
> ridiculous; even if there's a "correct" textbook answer.

Not really. If you are looking at very long taus, then letting it run
for another day will not do. You'd have to run for weeks or months
to get enough samples. And no, overlapping ADEV does not necessarily
help as for the longer taus the dominating noise is not white phase noise
anymore and thus has some long term correlation. I.e. oADEV will not work
as expected as two samples that are close time-wise will also have a large
correlation between them.

I have not had a look at the formula used to estimate the error bars for
ADEV in TimeLab, but I wouldn't be surprised if it underestimates the error
for certain kind of noise processes. There are a lot of assumptions about
the type of noise from atomic clocks and I am not sure anymore that even
the most basic one (that the noise is Gaussian, even for the 1/f^a noise)
holds in all cases.

				Attila Kinali

Malek's Law:
        Any simple idea will be worded in the most complicated way.

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