Suppose that I have a factor with three levels A, B, and C. If it
is used in a GLM model as a covariate, I will have two parameter
beta1 and beta2 (assuming they are for level B and C). To test a
statement "Any of the last two levels (either level B or level C)
has a different effect on the response variable than level A," a text
book says that the null hypothesis should be H0: beta1 + beta2 = 0.
However, I cannot figure out why this is the null hypothesis. I
thought the hypotheses should be H0: beta1=0 or beta2=0 vs
Ha: beta1!=0 and beta2!=0. If they are correct, how should I test
them using say Wald's test or the likelihood ratio test? Thanks
for any hints.
Paul.
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