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The question and answer here suggest that the answer is “yes,” but my own analysis in SPSS suggests otherwise:

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Note: I understand that the likelihood ratio chi-square and chi-square test are expected to yield different non-simulated (non-Monte Carlo) p-values simply because they have different statistical bases.

Edit: Also, if degrees of freedom are inapplicable when applying a Monte Carlo simulation, why is SPSS returning them here?

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Short answers:

  1. The two test statistics (and thus the p-values) converge when the sample size approaches infinity. That is not what's happening in the MC simulation, and so the p-values are not the same (nor are the CIs).
  2. The ${df}$ values are there for the ordinary test statistics and don't apply to the simulated values.
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