Saturday, January 12, 2008, 8:38:33 PM, Stephen Cole wrote: SC> I have a data set that is infested by a plague of zeros that is causing me SC> to violate all assumptions of classic parametric testing. ...
Stephen, if you're measuring density, abundance or such and you end up with many zeros and some non-zero values, then you should turn your analysis into something that is aimed at testing the independence of the "zero" response relative to some conditions, rather than testing the quantitative differences including zeros in the computations. For instance, assuming that you're interested in measuring changes in density of a copepod species in the upper layer of the water column between day and night, then the you can test whether differences between mean values (or median, in case you go for a non-parametric approch) during day and night are equal. That's more or less the rationale of the experimental design you mentioned, just a tad simpler. Now, imagine you realize that very often that species is absent (you might wonder whether you're collecting samples that are not large enough, or whether it is only a night vs day issue, but that's another story...): this means having too many zeros, that in turn means that info about variability is not reliable, so you already know that the methods you were planning to use (both parametric and non-parametric) won't work. In this case the real issue is changed: now the problem is "Are zero densities more frequent during the night?", i.e. H0: non-zero densities are independent of the time (day or night). Now you just need to build a 2x2 contingency table and a chi-square test will provide the answer to your question. Of course, you can also design something more complex, like a n-way design, or test whether a given frequency (e.g. zero density during the night) in your contingency table is significantly larger than the expected value or not. That's a sort of a posteriori test you can add to your basic procedure I hope I've been able to explain what I'm suggesting. As you probably guessed, English is not my first language... All the best, Michele -------------------------------- Michele Scardi Associate Professor of Ecology Department of Biology University of Rome "Tor Vergata" Via della Ricerca Scientifica 00133 Roma Italy http://www.mare-net.com/mscardi --------------------------------
