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

[ChrisVer]

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...?

 

[BvU]

Lies, damn lies, statistics !

Hard to say anything sensible without something to look at. Is there a significant difference between the .975 and .983 ?

 

[ChrisVer]

I will post some figures and the printed results tomorrow because I don't have them in this machine.

 

[ChrisVer]

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.