So what is that parameter. When I make a non-linear fit, the program gives me a value χ2/doF. What is it?

I know some statistics and I know those χ2 distributions are used for non-parametric contrasts, like how good a fit is to a data, knowing that λ⇝χ2n−1 (that's supposed to mean the pearson parameter behaves like that distribution). I suspect it's totally related to that, telling me how good the fit is actually making the contrast, I don't know though, how to relate that value, as I'm not giving aconfidence level, so I guess it's a general number something independent of that so you decide if it's good or not, what is it exactly? Why is it divided by the degrees of freedom?


  • 2
    $\begingroup$ Because there are many ways to "make a nonlinear fit," please provide some details of what you are doing, including what program you are using. (Doesn't the program's documentation explain its output?) $\endgroup$
    – whuber
    Mar 21, 2013 at 17:47
  • $\begingroup$ @whuber I'm using SciDavies. And I'm fitting to an arbritary function (not linear) to a set of points. I searched the documentation and didn't find anything. The algorithm it says it's using is Levenberg-Marquardt $\endgroup$ Mar 21, 2013 at 18:47

1 Answer 1


It is the reduced Chi-Square statistic, used for testing how 'useful' a model is for the data. You divide the chi-square statistic by the degrees of freedom to get a scaled measure of variance (it equals sum of squares divided by degrees of freedom). The ratio of two reduced Chi-Square statistics is the F statistic (used for testing variance between the two).

See this wikipedia article for information on interpreting the resulting value: http://en.wikipedia.org/wiki/Goodness_of_fit

  • $\begingroup$ But what is that value. I know it must provide some information about that chi-square distribution. What I want to know is what is that value. $\endgroup$ Mar 21, 2013 at 18:46
  • $\begingroup$ In your case it is a test statistic for how 'useful' the model is. This wiki article should answer your questions: en.wikipedia.org/wiki/Goodness_of_fit $\endgroup$
    – TLJ
    Mar 21, 2013 at 19:27
  • $\begingroup$ I edited my answer to include the additional info. Please mark as answered if it helped you! $\endgroup$
    – TLJ
    Mar 21, 2013 at 19:51
  • $\begingroup$ I already did... thanks for the info, I finally understood what that was, I had never seen that called as Chi-Square, but RSS. $\endgroup$ Mar 21, 2013 at 19:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.