Is a Reduced Chi-Squared Value of 0.75 Acceptable for a Good Fit?

[Moham1287]

Hi all, just a quick query about data analysis:

Homework Statement

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!

 

[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.

 

[Architeuthis Dux]

I would suggest that the best way to determine if a reduced chi squared value of 0.75 is acceptable for your fit is to compare it to the expected value for your specific experiment or field. Different fields may have different accepted ranges for reduced chi squared values, so it is important to do some research and see what is considered a good fit in your particular area of study. Additionally, it is always a good idea to consult with your professor or colleagues for their input on the matter. Ultimately, the most important aspect of any data analysis is to accurately and honestly represent the results, so it is important to carefully consider the significance of your reduced chi squared value in relation to your experiment and its overall validity.