Which Fit Should Be Chosen When Goodness of Fit Values Are Close?

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Discussion Overview

The discussion revolves around the selection of fitting models for background data in a physics context, specifically comparing an exponential fit and a polynomial fit for a Higgs background. Participants explore the implications of goodness of fit values that are close to one and how to interpret these values in relation to physical motivations and statistical outcomes.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests comparing the goodness of fit values, ##\chi^2/NDF##, to determine the best fitting model when values are close to one.
  • Another participant questions the significance of the difference between the goodness of fit values of 0.975 for the exponential fit and 0.983 for the polynomial fit.
  • A later reply indicates that both fits yield similar goodness of fit values, with the polynomial fit appearing slightly better statistically, while the exponential fit is considered more physically motivated.
  • Participants express the need for visual data to better assess the differences between the fits.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the goodness of fit values and the physical relevance of the models. There is no consensus on which fit should be chosen, as both statistical and physical considerations are debated.

Contextual Notes

Limitations include the lack of visual data at the outset of the discussion, which may affect the assessment of the fits. The discussion also highlights the dependence on the definitions of goodness of fit and the subjective nature of model selection based on physical motivations.

Who May Find This Useful

This discussion may be useful for researchers and practitioners in physics and related fields who are involved in data fitting and model selection, particularly in contexts where statistical and physical considerations must be balanced.

ChrisVer
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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...?
 
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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 ?
 
I will post some figures and the printed results tomorrow because I don't have them in this machine.
 
So here I have the plots of the background fitted with Exponential p_0 e^{p_1 x} and Poly2 p_0 + p_1 x +p_2x^2

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

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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