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

 

[hutchphd]

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]

I think the formula with the m is appropriate. Very often m=1 when the the mean value is taken as a "fitted" parameter from the data. I have no idea about the names and categories of these things sorry.