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I am trying to calculate a p-value after fitting a distribution to some data. In one way, I use the Pearson's chi-square test and get a p-value=0.369. I then use the log-likelihood ratio method and get a p-value=0.97. Is it reasonable to get such different numbers? I tried taking the exponent of the log-likelihood ratio chi-square statistic, but then my p-value=0.79, which is still much higher than from the Pearson's chi-square test. Are the p-values supposed to be the same?

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  • $\begingroup$ I think you need to explain exactly what you have done. For instance, if you conducted the chi-squared test improperly (without reflecting that you fit the distribution to the data and accounting correctly for how you did the fitting and the number of parameters you used) then that alone will explain any difference. The same goes for the other test. $\endgroup$ – whuber May 7 at 16:58
  • $\begingroup$ For each test, I fit a discrete Weibull distribution to the data and found the parameters (2 parameters). I used the MLE method and then used the Pearson chi-square test using the fit parameters. The other method I used the -2 log likelihood ratio to find the parameters of the discrete Weibull and plugged that statistic into the chi square cdf to get that p-value. $\endgroup$ – user1414 May 7 at 17:02
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    $\begingroup$ The approach to the chi-squared test sounds like it was not quite correct: see stats.stackexchange.com/a/17148/919 for an explanation. Regardless, the two approaches will rarely yield exactly the same p-values, but they should be close unless your dataset is tiny. $\endgroup$ – whuber May 7 at 17:06

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