1. ## chi-square post-hoc tests?

Hi there, I've been searching the forum and elsewhere to figure out how to interpret my chi-square results and I can't find anything that relates to what I've got.

Here's the deal:
I have a contingency table that looks like this:
Year 2-eggs 1-egg
2002 19.0000 6.0000
2003 23.0000 2.0000
2004 18.0000 2.0000
2005 22.0000 3.0000
2006 14.0000 1.0000
2007 199.0000 65.0000
2008 266.0000 48.0000
2009 48.0000 44.0000
2010 58.0000 55.0000

I ran a chi-square for contingency table (using SigmaPlot 11), which came out significant, as I expected. However, I don't know what to do next... are there post-hoc tests I can run to figure out which years are different from others?

Similarly, I tried running a GLM in R with a poisson family, but the resulting qqplot is terrible. Binomial family doesn't work, since the numbers are not between 1 and 0. ANd besides, I really don't know what I'm looking at. I understand model-reduction in GLMs in R, but I can't figure out how to apply it to my above data.

Essentially, what I'm trying to do is figure out if clutch size is different among years. I can see from looking at the raw counts and a graph of the clutch sizes that 2009 and 2010 are different from all the rest, but can't figure out how to test that statistically.

I'm familiar with ANOVAs and their post-hoc comparisons, and I think this sort of thing is what I'll need to do next.

I'm at my wits end with stats and am so ready to give up.

2. ## Re: chi-square post-hoc tests?

Essentially, what I'm trying to do is figure out if clutch size is different among years. I can see from looking at the raw counts and a graph of the clutch sizes that 2009 and 2010 are different from all the rest, but can't figure out how to test that statistically.
Did you mean all possible pairwise comparisons? AFAIK there is no other "post
hoc" procedure than to perform the tests and use Bonferroni correction (alpha/36),
but that will make the test very conservative.

Regards

K.

3. ## Re: chi-square post-hoc tests?

I suppose I'm not sure if I need to run ALL pairwise comparisons. Looking at my barchart, it looks like I only need to compare 2009 vs 2010 and both of those against all other years. So I'd need to look at:

2009 vs 2010
2009 vs 2002
2009 vs 2003
2009 vs 2004
2009 vs 2005
2009 vs 2006
2009 vs 2007
2009 vs 2008

and the same for 2010, making it alpha/15. Still conservative, but not so bad as /36

What about looking at overlapping 95%CI? Is that valid for this too?

4. ## Re: chi-square post-hoc tests?

You do not have to perform all possible 36 tests, but you have to correct
by 1/36 anayway. The reason is, you haven't selected which comparisons you
want to make beforehand, but only after inspection of the data. Or at least
it seems so. And while inspecting the data, you perfomed test-like
differences for formal Chi² testing.

Maybe inspection of adjusted standardized cell residuals is an alternative,
though I am not too familiar with this approach. Residuals > |2| indicate an
important deviation of the cell frequency from what is expected under the Null.
The resuidual diagnostics does not substitute formal tests, though.
Haberman, S (1973): The Analysis of Residuals in Cross-Classified Tables. Biometrics 29: 205-220.
Agresti A (1996): An Introduction to Categorical Data Analysis. New York: John Wiley & Sons.

5. ## Re: chi-square post-hoc tests?

Ok, I understand what you mean about still using alpha/36...ugh, that's too bad.

Interesting about the other suggestions...thanks for the references, I'll take a look!

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