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    Re: Standard Deviation Question
    From: Richard B. Langley
    Date: 2013 Jan 5, 10:10 -0400

    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
    
    -----------------------------------------------------------------------------
    | Richard B. Langley                            E-mail:
    lang---.ca         |
    | Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
      |
    | Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506
    453-5142   |
    | University of New Brunswick                   Fax:      +1 506
    453-4943   |
    | Fredericton, N.B., Canada  E3B
    5A3                                        |
    |        Fredericton?  Where's that?  See: http://
    www.fredericton.ca/       |
    -----------------------------------------------------------------------------
    
    
    
    
    

       
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