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Re: Standard Deviation Question
From: Richard B. Langley
Date: 2013 Jan 5, 10:10 -0400
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 withthe 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@unb.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/ | -----------------------------------------------------------------------------