## Question about chi^2

Interactive and automated data processing tools (PRIMUS, GNOM, AUTORG).
Scattering from simple bodies (BODIES), peak analysis (PEAK), data plotting (SASPLOT) etc.
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remba
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Joined: 2019.05.24 15:12

### Question about chi^2

Hello,

I'm fitting some data and I was wondering how do you calculate the scaling factor present in the formula for chi^2:

chi2=1/(k-1)sum((I0*nu-Iexp)/sgma)2

and also, I would like to understand the k-1 factor...IN your paper there is not any explanation about that factor...

thanks!

AL
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### reduced chi-squared

remba wrote:
2019.05.27 09:54
I'm fitting some data and I was wondering how do you calculate the scaling factor present in the formula for chi^2
The scaling factor minimizes chi-squared (least squares method).
remba wrote:
2019.05.27 09:54
and also, I would like to understand the k-1 factor...IN your paper there is not any explanation about that factor...
Not sure what paper you are referring to.
The 1/(k-1) factor comes from the reduced chi-squared definition.

remba
Member
Posts: 3
Joined: 2019.05.24 15:12

### Re: Question about chi^2

Thanks for the answer!

I was referring to Structural Characterization of Flexible Proteins Using Small-Angle X-ray Scattering Pau Bernado.

So it means that 1 is the parameter. Regarding this, I have a question too.
I tried to fit 2 theoretical curves obtained by 2 different 3d structures (say A and B). I'm creating with primus different theoretical curves with different population. (70% of A 30% of B, 60%A-40%B.50%A-50%B and so on). To create the 50-50 for example I load 1 A 1 B and I do the average and save the curve as the 50-50 curve.
How do I handle the parameters here? since I'm fitting always 1 curve, is it still 1 parameter or I have to take into account the number of structures I'm using to create the theoretical curve? (2 for the 50-50).

I'm asking also in order to think at some statistical test (as F-test) to prove that the curve 50-50 fits better then the 100%A or 100%B.

Thanks again!