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

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In summary, the conversation discusses finding the best fitting model for a background data set. The method suggested is to compare the values of their ##\chi^2/NDF## and see if they are close to 1. However, when two fits are very close, with values of 0.975 and 0.983, it becomes challenging to determine the better fit. The speaker believes that the exponential fit is physically better, but the statistics favor the polynomial fit. They plan to post figures and results for further analysis. Ultimately, both the polynomial and exponential fits are considered good, with the polynomial fit being slightly better according to the goodness of fit test.
  • #1
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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  • #2
Lies, damn lies, statistics !

Hard to say anything sensible without something to look at. Is there a significant difference between the .975 and .983 ?
 
  • #3
I will post some figures and the printed results tomorrow because I don't have them in this machine.
 
  • #4
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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Related to Goodness of Fit ##\chi^2/NDF##

1. What is the "Goodness of Fit ##\chi^2/NDF##" test?

The "Goodness of Fit ##\chi^2/NDF##" test is a statistical test used to determine how well a set of data fits a particular theoretical model or distribution. It compares the observed data with the expected data and calculates a value called the chi-square (##\chi^2##) statistic, which is then divided by the number of degrees of freedom (NDF) to get the "Goodness of Fit ##\chi^2/NDF##" value.

2. How is the "Goodness of Fit ##\chi^2/NDF##" test used in research?

The "Goodness of Fit ##\chi^2/NDF##" test is commonly used in research to assess the fit of a particular model or distribution to observed data. It can be used to determine if a model accurately represents the data or if there are significant differences between the observed and expected values. This test is used in a variety of fields, including biology, psychology, and economics.

3. What are the assumptions of the "Goodness of Fit ##\chi^2/NDF##" test?

The main assumptions of the "Goodness of Fit ##\chi^2/NDF##" test are that the data is independent, the sample size is large enough, and the expected values are greater than 5 for each category. Additionally, the data should be obtained through a random sampling method and the categories should be mutually exclusive and exhaustive.

4. How is the "Goodness of Fit ##\chi^2/NDF##" value interpreted?

The "Goodness of Fit ##\chi^2/NDF##" value is compared to a critical value from a chi-square distribution table. If the calculated value is greater than the critical value, it indicates that the observed data significantly deviates from the expected data and the null hypothesis (that the model fits the data) can be rejected. If the calculated value is less than the critical value, it suggests that the model fits the data well and the null hypothesis cannot be rejected.

5. What are the limitations of the "Goodness of Fit ##\chi^2/NDF##" test?

One limitation of the "Goodness of Fit ##\chi^2/NDF##" test is that it can only be used for discrete data and cannot be applied to continuous data. Additionally, the test assumes that the expected values are known and do not depend on any parameters estimated from the data. If this assumption is violated, a different test, such as the Kolmogorov-Smirnov test, may be more appropriate.

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