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Goodness of Fit ##\chi^2/NDF##

  1. Aug 27, 2015 #1


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    Suppose I want to find a model for a background from the data of it...
    One way is to try different fittings and compare the values of their ##\chi^2/NDF## if they're close to 1 or not.

    However what happens when two fits are really close to one? For example if I take a ##M_{\gamma \gamma}## background for a Higgs, and apply an exponential drop fit or a polynomial of deg=2 fit, I am getting values: 0.975(expon) and 0.983 (polynomial)...
    Physically I think the exponential is a better fitting function, but the statistics is telling me that the polynomial fits best...?
  2. jcsd
  3. Aug 27, 2015 #2


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    Lies, damn lies, statistics !

    Hard to say anything sensible without something to look at. Is there a significant difference between the .975 and .983 ?
  4. Aug 27, 2015 #3


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    I will post some figures and the printed results tomorrow because I don't have them in this machine.
  5. Aug 28, 2015 #4


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    So here I have the plots of the background fitted with Exponential [itex] p_0 e^{p_1 x}[/itex] and Poly2 [itex]p_0 + p_1 x +p_2x^2[/itex]

    The [itex](\chi^2/NDF)_{exp}=102.4/118 \approx 0.868[/itex]
    And [itex](\chi^2/NDF)_{pol2}=104.2/117 \approx 0.8905[/itex]

    Typically I would say that the goodness of fit test tells me that both pol2 and expo are good to fit the data (compared to other tests I tried)....with pol2 being a little better , but expo being the physically motivated one.

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    Last edited: Aug 28, 2015
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