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I am doing a chi squared goodness of fit test. I have found the chi squared test statistic to be 1.88. From what I understand, if the test statistic is lower than the critical values given in the tables, then we conclude that the model is a good fit for the data. But when I looked at the table of critical values I realised I didn’t understand quite what the values meant.

Instead of 1.88, say I got a value of 13.

I have 6 degrees of freedom. Looking at the tables, I see that at the 95% level the value given is 12.59. From what I understand this would mean I would conclude the model was not a good fit at the 95% significance level as 13 is greater than 12.59. However, at 99%, the value given is 16.81. By my logic, since 13 < 16.81 that would mean I would conclude that the model was a good fit at the 99% significance level.

But the idea of rejecting the null hypothesisthat the model was a good fit at a 95% significance level but accepting it at a 99% significance level makes no sense.

What have I done wrong?

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