How does JMP adjust for p-value of Pearson Chi-Squared Value

zimmerj

I'm doing a discrete fit between an observed count distribution and a Gamma-Poisson mixture.  However the Pearson Chi-Squared Goodness-of-fit statistics is returning a very high value for X2, but indicating an acceptable p-value.

In the example provided, X2 is 1222.58, which if inserted into a Chi Squared distribution would return a p-value of 7.552193e-268.

JMP returns a p-value of 0.1021.

Is there some adjustment that is done in JMP's calculation that would increase the value so much over a direct calculation?

tonya_mauldin

The expected Chi Square under the null hypothesis is equal to the degrees of freedom.  Your degrees of freedom are high for this example, you have an N of 1162.  Therefore I am not surprised by the results.

Most issues with the Pearson Goodness of Fit tests comes from the bin sizes.

The Pearson Goodness of Fit test has changed for Version 15.  The problem with this test is that the bin size it not well defined.  For version 15, JMP makes sure there are at least 5 expected observations in each bin.  This way we satisfy that rule of thumb (the assumptions are towards the bottom).  https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test 

The last bin is the exception.  If it's expected count is less than 5, JMP does not worry about it.

Previously, JMP treated every integer between the min and max as a bin.  This means there can be bins with zero observations and expections essentially zero.