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

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When comparing goodness of fit values that are close, such as 0.975 for an exponential fit and 0.983 for a polynomial fit, the choice can be challenging. The exponential fit is considered more physically motivated, while the polynomial fit shows slightly better statistical performance. The reported chi-squared values indicate both fits are acceptable, with the polynomial fit being marginally superior. However, the significance of the difference between the two values is questioned, suggesting that visual analysis of the fit plots is necessary for a more informed decision. Ultimately, the discussion highlights the tension between statistical metrics and physical reasoning in model selection.
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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