# What is the correct formula for the reduced Chi square?

patric44
Homework Statement:
what is the correct formula of reduced Chi square
Relevant Equations:
\Chi^2
Hi all
I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD :
$$\chi=\sqrt{\frac{1}{N}\sum_{i}^{N}\left(\frac{(y_{i}-\tilde{y}_{i})}{\delta y_{i}}\right)^{2}}$$
and in some books the same formula with little modification (instead of ##N## they put the degrees of freedom) as :
$$\chi=\sqrt{\frac{1}{N-m}\sum_{i}^{N}\left(\frac{(y_{i}-\tilde{y}_{i})}{\delta y_{i}}\right)^{2}}$$
which one is reduced ##\chi^{2}## and which is RMSD if any of them?!
another question why i read that we need to minimize the value of reduced ##\chi^{2}## to get the best fit, isn't the optimum value is 1 ?! , shouldn't we minimize 1-##\chi^{2}## or what?
I will appreciate any help, thanks in advance

Homework Helper
2022 Award
Please carefully define the elements in these formulae, particularly ##\tilde{y}_{i}## and
##\delta y_i ## and what is m?)

patric44
Please carefully define the elements in these formulae, particularly ##\tilde{y}_{i}## and
##\delta y_i ## and what is m?)
##y## is the measured data
##\tilde{y}## is the calculated data from a specific model
##\delta y_i ## is the error in measuring ##y##
##m## the number of parameters of the model
I am not talking about the so called category chi2. I mean the other one

• hutchphd
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