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 Confused about reduced chi-squared fit		  New Topic  Reply to Topic
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ghostyblop

5 Posts
Posted - 11/23/2024 :  5:01:00 PM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Hello,

I've been fitting a 2D gaussian to some of my data. My reported reduced chi-squared fit is 0.000144 which is very small.

I have read on a previous forum https://my.originlab.com/forum/topic.asp?TOPIC_ID=4058
that the reported chi-squared fit will be small in a perfect fit since chi^2 = 0 (and then this is subsequently divided by DOF). However, online I am reading if a chi-sqaured fit is < 1 than this indicates an overfit.

As a result, I am confused as to whether a very small value below 1 is an indication of a good fit.

Any help on this topic would be great, Thanks

YimingChen

1613 Posts
Posted - 11/25/2024 :  3:43:32 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
"a very small value below 1 is an indication of a good fit."
This is true only if the measurement error is well-defined and incorporated as weights in the fitting. For more details, please refer to the discussion section of the Wiki page and the Origin webpage on how weights are included in fitting.

https://en.wikipedia.org/wiki/Reduced_chi-squared_statistic
https://www.originlab.com/doc/origin-help/nlfit-theory#Weighted_Fitting

Thank you
James
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