Re: Likelihood ratio, Pearson Chisquare, Linear-by-Linear Association in crosstabs

Posted by Rich Ulrich on Feb 23, 2011; 9:14pm
URL: http://spssx-discussion.165.s1.nabble.com/Likelihood-ratio-Pearson-Chisquare-Linear-by-Linear-Association-in-crosstabs-tp3397257p3397719.html

Following what Bruce posted,
Agresti's books are great reading and great references.

You may also gather from Agresti that, contrary to what
some people expect, the two versions of the test do *not*
become equivalent for large samples.  They test slightly
different versions of the hypothesis of heterogeneity. 

The overall difference is such that, in an R x K table, one cell with
a very discrepant expectation may out-weigh several moderate
discrepances; or vice-versa.   The Pearson test is more likely to
reject for a single cell that is off, whereas the Likelihood test is
more likely to reject for several cells.  (I think I didn't get that
backwards.)   So, the nature of what you expect can determine
the choice of your test -- And there is a rational explanation for
why the two tests may lead to different decisions, if you are
'rejecting'  at a particular alpha.

--
Rich Ulrich