Difference and errors on the differences for the default error option and the option "s"

If a cell has N data points all with the same value Z (especially
    possible when dealing with integers), the spread in Z for that cell
    is zero, and the uncertainty assigned is also zero, and the cell is
    ignored in making subsequent fits. If SQRT(Z) was the correct error
    in the case above, then SQRT(Z)/SQRT(N) would be the correct error here.
    In fact, any cell with non-zero number of entries N but with zero spread
    should have an uncertainty SQRT(Z)/SQRT(N).

    Now, is SQRT(Z)/SQRT(N) really the correct uncertainty?
    that it is only in the case where the Z variable is some sort
    of counting statistics, following a Poisson distribution. This should
    probably be set as the default case. However, Z can be any variable
    from an original NTUPLE, not necessarily distributed "Poissonly".
    The computation of errors is based on the parameter option:
     ' '  (Default) Errors are Spread/SQRT(N) for Spread.ne.0. ,
                      "     "  SQRT(Z)/SQRT(N) for Spread.eq.0,N.gt.0 ,
                      "     "  0.  for N.eq.0
     's'            Errors are Spread  for Spread.ne.0. ,
                      "     "  SQRT(Z)  for Spread.eq.0,N.gt.0 ,
                      "     "  0.  for N.eq.0

Find the explanation for the different options in detail here.

Basically, the difference lies in the fact, that for the default option there is an additional factor of 1/sqrt(N), which reduces the error.

As here, the difference between two weight tables was calculated, the error from the individual TProfile2Ds from each weight table was taken and used to calculate the propagating error according to error = Sqrt ( (error_weighttable1)^2 + (error_weighttable2)^2 )

For the s option, the error seems to be larger than the differences. This is however not the case for the default option, so which one is the right one??


Fig. 1.2.1a: weight table difference


Fig. 1.2.1b: errors on the weight differences for the option "s"


Fig. 1.2.1c: Errors for the default error option

-- Main.kristin - 18 Dec 2006

Topic attachments
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JPEGjpg weight_table_diff_version_default.jpg r1 manage 26.4 K 2006-12-18 - 18:30 UnknownUser  
JPEGjpg weight_table_diff_version_error_default.jpg r1 manage 23.2 K 2006-12-18 - 18:31 UnknownUser  
JPEGjpg weight_table_diff_version_error_s.jpg r1 manage 25.5 K 2006-12-18 - 18:30 UnknownUser  
JPEGjpg weight_table_diff_version_s.jpg r1 manage 26.4 K 2006-12-18 - 18:29 UnknownUser  
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