So I have been analyzing data a took in an experiment recently and have been using a chi squared as a "goodness of fit" test to against a linear model.(adsbygoogle = window.adsbygoogle || []).push({});

I am using excel and used the LINEST function (least square fitting method) to get an idea for a theoretical gradient and intercept for my data. Using these I found a series of normalized residuals:

R_{i}=[itex]\frac{obs-exp}{error}[/itex]

and my χ^{2}is the sum of these normalized residuals. I have then calculated my reduced χ^{2}by dividing this value by my number of degrees of freedom minus 2 (as i have a gradient and intercept).

However my reduced χ^{2}is much less than 1 (Specifically 0.007). I understand that this typically means I have over estimated my errors. I have checked these in great detail now, my errors are all in measurements which have very clearly defined uncertainty that I cant change. In light of this I am confused about how I should interpret this result. What does this test tell me?

I only have 8 data points for this particular set which I know is not a lot. Is it still reasonable to use chi square like this for such a small data set or might that be the reason I am not getting a very good result?

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# Interpreting a very small reduced chi squared value

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