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Warning: Slightly off topic; delete if not interested.

Not wanting to muddy the waters, but for those interested, here is a
link to an article on GPS precision and accuracy that appeared in my
GPS World column a few years ago:
http://gge.unb.ca/test/gpsworld.may10.pdf

There may be something of general use that could also be considered
when looking at the statistics of CN observations.

-- Richard Langley

On 5-Jan-13, at 6:24 AM, Marcel Tschudin wrote:

> ... when should I be using stdDevPop and when should I be using
> stdDevSamp?
>
> I try to explain the difference in a general understandable way.
>
> The calculation of the standard deviation requires to know the mean
> value. The difference between the two functions results from whether
> the mean value from the given data set represents the exact mean or
> is an estimated mean.
>
> If the given data represent all of them, i.e. they represent the
> complete population, then their mean value is exact and the standard
> deviation is calculated on the basis of an exact mean value.
> However, to have a complete population and know the exact mean is
> rather the exception. It is more likely that we have some selected
> (measured) values out of a greater population which is assumed
> infinite and where the exact mean value is unknown; the mean value
> of the given data set represents therefore an estimate, and the
> standard deviation is calculated on the basis that the mean value of
> the data set is an estimate.
>
> The difference between stdDevPop and stdDevSamp is therefore:
> stdDevPop() calculates the standard deviation understanding that the
> entered data are all of the population and that the mean value of
> the entered data is the exact mean value.
> stdDevSamp() calculates the standard deviation understanding that
> the entered data represent a sample from an infinite population and
> that the mean value of the entered data represents therefore an
> estimation for an infinite population.
>
> Now, what does the standard deviation mean? This is a measure for a
> probability that an other data (an other measurement taken under the
> same condition) will be within (or outside) certain limits. If we
> look at Greg's last data and designate with  the mean value  =
> 0.575' and with Sx = 0.159' the standard deviation of his sample
> with 20 measurements, then
>
>  +/- 1Sx (+/- one standard deviation)
> means that 68% or about 2 out of 3 other measurements of the same
> type are expected to be within (or about 1 out of 3 outside) the
> range between 0.416' and 0.734'.
>
> Generally the results provide the mean and one standard deviation as
> above. However, these values allow representing the result also
> related to other probabilities, like e.g.
>
>  +/- 2Sx (+/- two standard deviation)
> means that 95% other measurements of the same type are expected to
> be within (or about 1 out of 20 outside) the range between 0.257'
> and 0.893'.
>
>  +/- 3Sx (+/- three standard deviation)
> means that 99.7% other measurements of the same type are expected to
> be within (or 3 out of 1000 outside) the range between 0.098' and
> 1.052'.
>
> I hope it helps.
>
> To those of you who are familiar with the subject: Please feel free
> to improve or even correct these general explanations where
> necessary. Thank you.
>
> Marcel

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| Richard B. Langley                            E-mail:
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