[time-nuts] uncertainty calculations

jimlux jimlux at earthlink.net
Fri Apr 14 11:49:07 EDT 2017


On 4/14/17 8:37 AM, jimlux wrote:
> If one is counting an unknown 1pps source with a counter that runs at 10
> MHz (e.g. the error in any one measurement is uniformly distributed over
> 1 ppm) and you collect 100 samples,
> is the (1 sigma) measurement uncertainty 0.1ppm * sqrt(100)/sqrt(12)
>
> (standard deviation of a uniform distribution is 1/sqrt(12) )
>
> (assuming for the moment that both sources have no underlying
> variability - we're talking about the *measurement uncertainty*)
>

Oops..
0.1 ppm * 1/sqrt(N) * 1/sqrt(12)

That is, the standard  deviation goes down as sqrt(N)


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