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    Re: Standard Deviation Question
    From: Richard B. Langley
    Date: 2013 Jan 5, 12:27 -0400

    ;-) There's also Inside GNSS, whose editor is the former editor of GPS
    World:
    http://www.insidegnss.com/
    
    On 5-Jan-13, at 12:14 PM, Thomas Sult wrote:
    
    > The thing of general use to me is ... WOW there is a GPS world
    > magazine!
    >
    > Tom Sult
    > Sent from my iPhone
    >
    > On Jan 5, 2013, at 8:10, "Richard B. Langley"  wrote:
    >
    >> 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/       |
    >> -----------------------------------------------------------------------------
    >>
    >>
    >>
    >>
    >
    >
    >
    
    -----------------------------------------------------------------------------
    | 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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