## Chi-Squared Values

Ab initio modelling: DAMMIF, DAMMIN, GASBOR, MONSA
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sazhns
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Joined: 2016.02.15 20:16

### Chi-Squared Values

Hi all,

I have a quick question on chi-squared values in programs such as CRYSOL and DAMMIN/F. In the literature associated with these papers, chi-squared is calculated as:

X2= (1/N-1) * sum [((( Iobs(s) - Icalc(s))2)/sigma(s)2]

therefore, this means if Iobs=Icalc, chi-squared should be zero. However, reading around, most posts on here suggest a chi-squared value of 1 is better. Where does this come from? Have I misinterpreted something?

ckerr
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Posts: 86
Joined: 2015.03.25 09:03
Location: EMBL Hamburg

### Re: Chi-Squared Values

Chi squared much less than one suggests that either you have been overfitting the data or your error estimates are too large.

sazhns
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Posts: 2
Joined: 2016.02.15 20:16

### Re: Chi-Squared Values

Is this quoted anywhere in the literature?

I understand that zero chi-squared is probably due to overfitting and large errors, but it would also be the result of perfect fitting to a curve of little errors (i.e correct solution), would it not?

ckerr
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Posts: 86
Joined: 2015.03.25 09:03
Location: EMBL Hamburg

### Re: Chi-Squared Values

The chi-square test compares the discrepancies between your theoretical and experimental curves with the expected errors. The null hypothesis is that the discrepancies are entirely due to random experimental errors. A reduced chi-squared value much less than one means that the discrepancies are much smaller than you expected, based on your estimate of what the experimental errors will be. Therefore either the discrepancies really are too small (i.e. overfitting) or the experimental errors are smaller than you estimated.

remba
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Joined: 2019.05.24 15:12

### Re: Chi-Squared Values

Hello, I have more general questions:

1) why is there the 1/(k-1) factor?

2) how is calculated the scale factor? can you give me the explicit formula?