In article ,
eric gisse writes:
I'm somewhat confused as what you said reinforces my point. The reduced
chi squared, in my understanding, takes into account the differences in
degrees of freedom.

Yes. Think of it this way: if the model is a good description and
has no free parameters, each data point will contribute about 1 to
the total chi-square. Of course this is only an average. Some data
points will agree perfectly with the model (and thus contribute
zero), but others will be off by one or two sigma (or more if you
have a lot of data points). But _on average_, each data point
contributes about one to the total chi-square, so the _reduced_
chi-square will be about one if the model is a good description.

If your model has free parameters, each of them reduces the total
chi-square by about 1. That's why "degrees of freedom" is the number
of data points minus the number of free model parameters.

Of course this is approximate. If you want to calculate probability,
there are tables or formulas for any given number of degrees of
freedom and chi-square. I've seen tables that use chi-square and
others that use reduced chi-square, so just be sure you know which
you have.

If I use the bins of 0.145 M_sun as the degrees of freedom, I have 25
degrees of freedom. Reduced chi squared is 98.4

If I use the actual amount of stars, I have 185 degrees of freedom.
Reduced chi squared is 13.3.

Are you calculating the number of stars per bin (expected minus
actual)? Or the distance of each star from the nearest "predicted"
mass value? In the latter case, I don't see why you need bins at
all. Either way, the explanation I've given should tell you how to
figure degrees of freedom.

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