Ok, so why do you get 559+-44 w/o cat.
and 509+-44 with cat.?

Or more detailed:
a) What happened to the other 50 events?
b) Why do you get the same error for 509 and 559 events?




On Mon, 29 Apr 2002, Daniele del Re wrote:

>
> Hi Oliver,
>
> > Now I am really confused.
> >
> > You are trying to make me believe that the total number of
> > measured events dependence on the categorization. Well, I
> > always thought that adding up the individual cat. should yield
> > the same number of events than making no categorization.
> > Apparently thats not the case ... why? If everything
> > is self consistent it should ... isn't it.
> > At this stage we do not have to care about eff. corrections.
>
> I don't want to make you believe anything, I am just saying that
>
> 1) I calcute how many events I have per category
> 2) I apply the efficiency per category to those numbers
> 3) I put together the numbers
>
> this is different from putting them together before and then dividing by
> the overall efficiency. The final number and the final error
> come out different (as I showed in the simple example in the previous
> mail).
>
> Cheers,
>
> Daniele
>
>
>
> >
> >
> > Oliver
> >
> > By the way,
> >
> > even in your simple example the total number of measured
> > events before eff. correction has to be the same. If you would have
> > a 10% discrepancy there;  at least one of the two results (with or w/o
> > cat.) has to be wrong.
> >
> >
> > On Mon, 29 Apr 2002, Daniele del Re wrote:
> >
> > >
> > > Hi,
> > >
> > > > Thanks Daniele, I will think about this eff. stuff a bit more.
> > > > However, in my last mail I was indicating a much more basic item only related to
> > > > the measurement of number of events. Your measurement is:
> > > >
> > > > 559+-44 w/o cat.
> > > > 509+-44 with cat.
> > > >
> > > > => same error but roughly 10% different yield (correct?)
> > >
> > > yes, this 10% less explains the difference but this effect will be
> > > enhanced once you apply the efficiency per category.
> > > You must get the same error if you put together the number before the
> > > efficiency correction.
> > >
> > > >
> > > > Even in your example
> > > > below you assume the same number of measured events ..isn't it.
> > > > This 10% might explain the difference between old and new results.
> > > >
> > > > The eff. stuff is the second step after you have already performed
> > > > the measurement. Hence not effecting your fit results and fit errors
> > > > (correct?!)
> > >
> > > This is not correct. Forget about 509 +- 44. You have to put together all
> > > numbers only after you will divide by each efficiency.
> > >
> > > Daniele
> > >
> > > >
> > > > Did you see my point?
> > > >
> > > >
> > > > Oliver
> > > >
> > > > On Mon, 29 Apr 2002, Daniele del Re wrote:
> > > >
> > > > >
> > > > > Hi,
> > > > >
> > > > >  each category has a different efficiency. If you correct by the
> > > > > efficiency before putting together the results you will get a larger
> > > > > error. For instance:
> > > > >
> > > > >  suppose to have just two categories
> > > > >
> > > > >  eff(1) = 90%
> > > > >  eff(2) = 10%
> > > > >
> > > > >  while
> > > > >
> > > > >  eff(overall) = 50%  (same amount of events in both categories at the
> > > > > origin)
> > > > >
> > > > >  Suppose to measure
> > > > >
> > > > >  N(1) = 900 +- 30
> > > > >  N(2) = 100 +- 10     =>
> > > > >
> > > > >  Then
> > > > >
> > > > >  N(1)_origin = 1000 +- 33
> > > > >  N(2)_origin = 1000 +- 100 => Ntot_origin = 2000 +- 105
> > > > >
> > > > >
> > > > >  while using just one category and one efficiency you get
> > > > >
> > > > >  N = 1000 +- 32  => (eff = 50%)
> > > > >
> > > > >  Ntot_origin = 2000 +- 64
> > > > >
> > > > >
> > > > >  The effect depends on the difference in the efficiencies and on the the
> > > > > number of events in each category.
> > > > >
> > > > >
> > > > >  Since in our categorization we have two "bad" categories (the last two,
> > > > > ch3ne1 and ch3ne2) with small efficiencies and containing a pretty
> > > > > large fraction of events at the origin, the final result can have a much
> > > > > different error.
> > > > >
> > > > >
> > > > >  Daniele
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > On Mon, 29 Apr 2002, Oliver Buchmueller wrote:
> > > > >
> > > > > >
> > > > > > Hi Daniele,
> > > > > >
> > > > > > thanks for the quick answer. This 20-30% difference was actually
> > > > > > the trigger for me to look more carefully to your results from the first
> > > > > > place. I just have difficulties to understand why a simple
> > > > > > (- assume statistically independent-) categorization can blow
> > > > > > up your fit error.
> > > > > > Looking at your numbers of fitted events and just adding the
> > > > > > the errors in quadrature I get 509+-44.3 events for the categorization
> > > > > > whereas you quote 559 +- 44 for no cat. . There is no 20-30% effect.
> > > > > > Are I am missing something (e.g. categories are not independent ..?)
> > > > > >
> > > > > >
> > > > > > Oliver
> > > > > >
> > > > > >
> > > > > > On Mon, 29 Apr 2002, Daniele del Re wrote:
> > > > > >
> > > > > > >
> > > > > > > Hi Oliver,
> > > > > > >
> > > > > > >  thanks for your good comment.
> > > > > > >
> > > > > > > >                         ^                      ^
> > > > > > > > Are the two BR results  |                      |
> > > > > > > > obtained from the same MC sample?
> > > > > > > > If yes, what has caused the shift?
> > > > > > > >
> > > > > > >
> > > > > > > As you see in general there is an increase of 20-30% in the error (due to
> > > > > > > categories with low statistics). This means that the two results can be
> > > > > > > different.
> > > > > > >
> > > > > > > In this particular case
> > > > > > >
> > > > > > > sqrt ( (sigma*1.3)^2 - sigma^2) ) ~ .8 sigma
> > > > > > >
> > > > > > > and 0.0179 - 0.0156 = .0023 = 1.6 * .0014(=sigma(ratio))
> > > > > > >
> > > > > > > So this result is 1.6 sigma off.
> > > > > > > Looking in detail
> > > > > > >
> > > > > > > * signal events from the fit w/o categories:
> > > > > > >
> > > > > > >  S = 559 +- 44
> > > > > > >
> > > > > > >
> > > > > > > * signal events from the fit with categories:
> > > > > > >
> > > > > > >          S       S from truth
> > > > > > >
> > > > > > >         32 +- 7        115
> > > > > > >         31 +- 12        93
> > > > > > >        220 +- 20       662
> > > > > > >        190 +- 28       594
> > > > > > >         15 +- 15       108
> > > > > > >         21 +- 19       144
> > > > > > >
> > > > > > > total     509         1716
> > > > > > >
> > > > > > >
> > > > > > > The lack comes from the last two categories and they weight more since
> > > > > > > they have a small efficiency. I don't see a fitting problem in these fits
> > > > > > >
> > > > > > > http://www.slac.stanford.edu/~daniele/vub/MCmulti/newMCshapech3ne1fitresults.eps
> > > > > > > http://www.slac.stanford.edu/~daniele/vub/MCmulti/newMCshapech3ne2fitresults.eps
> > > > > > >
> > > > > > > BTW I will look into the problem more in detail.
> > > > > > >
> > > > > > > Thanks a lot,
> > > > > > >
> > > > > > >  Daniele
> > > > > > >
> > > > > > >
> > > > > > >
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