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model selection vs. H0 based testing

Hello,

I wish to thank Douglas Bates very much for clarification and pointing 
me to the MCMC simulation method to get p values even for cases where 
Wald tests are inappropriate.

One question however remains when publishing statistical results: does 
it help readers if we combine both,

- AIC based model selection
*and*
- null hypothesis based tests statistics

or should we focus on model selection only and try to reduce the amount 
of tables provided?

Apologies if this is question is too much off-topic, so you may decide 
to answer off-list. I will give a short summary at the end.

Thomas P.

An article explaining the background:

Johnson, J. & Omland, K.S., Model Selection in Ecology and Evolution. 
Trends in Ecology and Evolution, 2004, 19 , 101-108