- #1

patric44

- 296

- 39

- 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

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