Chi-square test with 2 bins, why do I get P = nan ?

I would like to use chi-square statistical test with just two bins. Everything seems fine in the table, but the p value is nana and degree of freedom is 0. p value is different from nan when the number of bins is hgher than 3. For bins=4 degree of freedom is 1. Why is it so?

e.g. [h,p,stats] = chi2gof(rand(1,1000),'nbins',2)

    chi2stat: 0.0130
          df: 0
       edges: [0.0012 0.5003 0.9995]
           O: [489 511]
           E: [490.8038 509.1962]

thanks

Answer 1

[Tom Lane]

The default for chi2gof is to test against the normal distribution, estimate the parameters, and deduct the number of estimated parameters from the degrees of freedom.

Compare these:

x = randn(100,1);
[h,p,stats] = chi2gof(x,'nbins',2)
[h,p,stats] = chi2gof(x,'nbins',2,'cdf',@normcdf)

The first is what you tried. The second tests against the standard normal distribution (parameters fixed at mu=0 and sigma=1), so it doesn't lose any degrees of freedom by estimating the parameters. You will probably see that the chi-square statistic is higher for the latter, because the estimation process tends to reduce the statistic compared with pre-specified values.