evaluate goodness of fit

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Hi there,

I have a few sets of data similar to the attached one. i have fit the same set of data with both a linear function and a single exponential function. I would like to find out which of the two functions have a better goodness of fit. How can I do it easily in Igor? I know it might be a stupid question but how can I compare the two fit in a quantitative and statistically relevant way?

Thanks a lot Wavemetrics_fits.pxp (109.27 KB)
When you use curve fit, it gives the goodness of fit results in V_chisq. I use this to evaluate which fit is best. In your case however, the value is very large and almost the same for both fits. My interpretation would be that linear and single exponential function are pretty poor fits for your data and that neither one is better than the other. Sorry if that sounds a bit negative - that's just how I see it.

January 25, 2015 at 12:07 pm - Permalink

A comment to comparing fits:
You should rather think of a good scientific model than testing functions to match your data.
("8 peaks fit an elephant - 20 a dancing elephant")
Your data is noisy (a fact - no offense :-) ). If you want to decide between two models you need better data.
Comparing the two fits in a quantitative and statistically relevant way would be checking the reliability of your model.
To address your "stupid" question (there are no stupid questions anyway): Maybe you want to have a look at http://en.wikipedia.org/wiki/Confidence_interval .

HJ

January 26, 2015 at 02:54 pm - Permalink

Does it bother you at all that the standard deviation of the tau coefficient is larger than the coefficient value?

My eye tells me that your data don't support any interpretation beyond the simply mean of the data. That is, a constant value.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

January 26, 2015 at 09:22 am - Permalink

HJDrescher wrote:
...
("8 peaks fit an elephant - 20 a dancing elephant")


I thought it was, seven parameters fit an elephant, and eight makes it tail wag.

The quote from von Neumann is however apparently stated as "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk".

http://en.wikiquote.org/wiki/John_von_Neumann

http://www.nature.com/nature/journal/v427/n6972/full/427297a.html

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville

January 26, 2015 at 05:16 pm - Permalink

Off topic:
I got it from a "in house" fitting package with these numbers and I was too lazy too look up the original citation -- my apologies!
It might have been modified since sulfur oxidation on platinum was investigated by XPS: S, SO, SO2, SO3, and SO4 each a doublet. That makes 10 well motivated peaks.

On topic:
My condensed message was: A good fit does not make a correct model and a poor fit is (almost) useless.

HJ

January 27, 2015 at 02:04 am - Permalink