# Chi Squared Analysis help?

1. Nov 14, 2007

### Moham1287

Hi all, just a quick query about data analysis:

1. The problem statement, all variables and given/known data

Having been asked to use Chi Squared analysis to test the validity of a fit, I have calculated my data to have a reduced chi squared of ~ 0.75 to 2 dp. I know that a reduced chi squared (chi squared / number of degrees of freedom) much lower than 1 suggests that the errors have been overestimated, but I can't find what the "accepted" value for <<1 is; i.e. is 0.75 too far from one to be considered alright for a fit? My course notes only say

"For a good fit, reduced chi-squared will be about 1.
A value << 1 suggests you overestimated the uncertainties.
For a value > 1, the probability that the fit is reasonable drops accordingly."

Thanks in advance for any help!

2. Nov 16, 2007

### EnumaElish

Firstly, an alternative def. of the reduced C.S. stat is "Chi-Sq./Variance" (see http://en.wikipedia.org/wiki/Goodness_of_fit)

Going with your def, if the predicted data fit reasonably well to the actual, then Chi-Sq. will be a small number (e.g., < 1). For a moderate fit, it may be somewhat large, but not too large (e.g., < 2). Note that the deg. of frdm > 1. So for a good fit, Chi-Sq./DOF will be < 1. For a moderate fit, Chi-Sq./DOF might be around 1 or slightly higher than 1. If Chi-Sq./DOF >> 1 then the fit must be poor. Which gives you a quick rule of thumb for evaluating the fit.