🚀 go-pugleaf

I have a two sample problem with quantal responses, e.g.

Group A				Group B
xa (dead)			xb (dead)
ya (live)				yb (live)

ta (total)      tb (total)

I wish to test the hypothesis that (xa/ta) = (xb/tb) against a one sided
alternative that (xa/ta) > (xb/tb).

Standard references give the Fisher's exact procedure for this, however
this is cumbersome if the numbers get large.  Also given in standard
references is the usual normal approximation to the binomial followed by
a two sample z - test.  However this latter case is not really good if
the proportion of responses is small (since the normal approximation to
the binomial fails in this case).

It seems to me, however, that an alternative approach would be a
likelihood ratio statistic to test whether the two groups were drawn from
a population with a single (versus two distinct) values of the population
proportion.  However I have not seen this described.  I wonder if anyone
has a reference to the approach I suggest, along with any comments
(power, robustness, etc.) versus either the Fisher exact test or the
normal approximation test.

I shall endeavor to summarize responses that are sent via e-mail to me.

Charles N. Haas
Professor, Environmental Engineering
Drexel University, Philadelphia PA 19104
======================================
CHaas@COE.Drexel.Edu