P value value for a large number of degree of freedom in lmer

For the record, I have to register my disagreement.  In the
experimental sciences, the name of the game is to design a
well-controlled experiment, which means that the null hypothesis will
be true if the alternative hypothesis is false.  People who say what
is below, which includes almost everyone who responded to this post,
have something else in mind.  What they say is true in most
disciplines.  But when I hear this sort of thing, it is like someone
is telling me that my research career as an EXPERIMENTAL psychologist
has been some sort of delusion.

If you have a very large sample and you are doing a correlational
study, yes, everything will be significant.  But if you do the kind of
experiment we struggle to design, with perfect control conditions, you
won't get significant results (except by chance) if your hypothesis is
wrong.

Jon

It is well known amongst statisticians that having a large enough data set will
result in the rejection of *any* null hypothesis, i.e. will result in a small
p-value.  There is no ``bias'' involved.

Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)