Bartlett Test in PCA Output: Exact Statistic and Degrees of Freedom in JMP

happy — Wed, 22 Apr 2026 09:33:53 GMT

Hi everyone,

I am trying to better understand the Bartlett test reported in the Principal Components output in JMP, specifically the one shown in the “Eigenvalues” table with Chi-square, DF, and p-values for each component.

From the documentation, I understand that this test is used to assess whether the remaining eigenvalues are equal (i.e., a test of homogeneity after extracting the first k principal components). However, I would like to clarify the exact form of the test used in JMP:

What is the exact test statistic used for this Bartlett test?
Is it based on a likelihood ratio involving the remaining eigenvalues (for example, using logarithms of ratios relative to their mean)?
In the correction term of the statistic, is the number of remaining components (m = p − k) used, or the total number of variables (p)?
The reported degrees of freedom are sometimes non-integers.
Does JMP apply an additional correction or approximation to the degrees of freedom?
Is this implementation directly based on Bartlett (1937, 1954), or are there JMP-specific modifications?

I would appreciate any clarification or references regarding the exact formulation used.

Thank you!

Re: Bartlett Test in PCA Output: Exact Statistic and Degrees of Freedom in JMP

Mark_Bailey — Wed, 22 Apr 2026 15:46:12 GMT

If the documentation and references there in are not sufficient, then you might reach out to JMP Technical Support (support@jmp.com) for further details. Keep in mind that some aspects of the implementation are proprietary and, therefore, confidential.

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Bartlett Test in PCA Output: Exact Statistic and Degrees of Freedom in JMP

Re: Bartlett Test in PCA Output: Exact Statistic and Degrees of Freedom in JMP