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I understand how the p-values are calculated for the coefficients in a GLM with known dispersion parameter. I can find rough estimates for the p-values using the Z table. However, when the GLM has estimated parameter, we perform a t-test. It seems that the p-values can again be found in the Z table. Why is this? Why do we not use the t table?

Also, we use a critical value from the t table to see whether our variable is significant for a t-test. I understand this, but then I don't understand why we switch to a Z table for the p-value.

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