Curve fitting question (OT) Message #1 Posted by Walter B on 29 July 2009, 9:30 a.m.
Hi experts,
So far, I thought I know some statistical data analysis, but here's something strange leaving me confused:
Fitting a model curve to measured data points, i.e. data with errors > 0 , reduced chi square (RC2) is one method to assess the goodness of fit. Browsing some textbooks and the net, I find just one-sided tests for RC2. I.e. it is said to be a good fit model if RC2 is less than or approximately equal to 1, and a bad fit model if RC2 >> 1. Why isn't this a two-sided test?
Reasoning: The model curve hitting all data points right in the middle is very improbable for physical data. So it should be a two-sided test for RC2, excluding very low values of RC2, too. OTOH, fitting is done minimizing the sum of squared distances from all data points to the curve, so zero would be optimum.
You see me confused. What's wrong? Help is appreciated.
Walter
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