How to properly calculate Chi Square

John will likely add something but have a look at:

DisplayHelptopic "Overview of Curve Fitting"

You can manually calculate ChiSquare using something like

I believe if you do not specify an uncertainty of yy, it is taken to be 1. If the uncertainty of yy is given the numeric values of chisquare can be drastically different.

As already noted by ChrLie, the ChiSquare value takes the error or standard deviation into account for the calculation. Naturally, if you provide an error yourself instead of the default value your result will be very different. By the way, your 'model' does not seem to fit your data very well. This makes the ChiSquare a bit meaningless either way, since obviously your 'hypothesis' is far off from the start.

Armoh-

Both ChrLie and chozo are correct. When Igor computes chi-square during a fit, the equation is this:

chi-square = sum_over_i( ((y_hat_i - y_i)/sigma_i)^2 )

y_hat_i is the model value for data point i

y_i is data point i

sigma_i is either 1.0 or your weighting value in standard deviation terms

So, as you can see here, if you provide weighting, the chi-square can be quite different from what it is if you don't. Note also that in both cases, there is no division by N or degrees of freedom. That is a bit different from some other applications like Excel. It is pretty easy to compute that yourself :)

When the uncertainties for the coefficients are computed, Igor takes into account whether you provided weighting values. If you do, a rule of thumb is that chi-square should be about the number of data points. If it is much larger than that, then you are underestimating the uncertainty or your model doesn't fit very well.