在scipy找到卡方检验的自由度？

Question

I have a maxwellian distribution observation that I fit to expected maxwellian distribution. Then I run a chi square test to find out the goodness of the fit. I get excellent results however, I also want to find out the degrees of freedom that the chi square test uses. To quote the documentation chisquare

: The p-value is computed using a chi-squared distribution with k - 1 - ddof degrees of freedom, where k is the number of observed frequencies. The default value of ddof is 0.

What is k exactly here? Is it the total number of data points (41000) that I have? Or is it the frequency per bin?

Answer 1

k is the size of f_obs , the first argument of chisquare . It is the number of bins.

For example, in the following example from the docstring,

>>> chisquare([16, 18, 16, 14, 12, 12])
(2.0, 0.84914503608460956)

f_obs is [16, 18, 16, 14, 12, 12] , and k is len(f_obs) , or 6.

Answer 2

The docs follow typical statistical variable names. K-1 is the degrees of freedom. K represents the amount of samples of each size n. So in your words, frequency per bin.

Last paragraph of http://statistics.about.com/od/Inferential-Statistics/a/What-Is-A-Degree-Of-Freedom.htm reads:

Another example of a different way to count the degrees of freedom comes with an F test. In conducting an F test we have k samples each of size n. The degrees of freedom in the numerator is k - 1 and in the denominator is k(n - 1).