Comparing counts between two groups with replicates I hope you can help me. I need to compare count data (number of grazed plants among plants previously marked inside a plot) recorded in 4 different sites (considered replicates), each of them receiving 2 different treatments (different grazing practices). Treatments were the same in all 4 sites as well as the number of marked plants was the same across sites and treatments (200 plants per site, 100 each treatment, 800 plants in total). Below an example of the dataset and of the resulting table. I'm interested to see if the number of grazed plants differs between treatments (grazing practice). We considered each site as a replicate. I'm more interested in comparing the treatments than the sites but I have to take them into account in the analysis. I was thinking to use the Chi-Square Test for Homogeneity of Proportions (which should be like a 2x2 contingency table, right?), but I'm not sure it is appropriate since "site" was set as a replicate and not a factor. This test would give the same importance to site and grazing but we assumed that site was a replicate and not a factor (despite the results). In case, is there any alternative to compare count data by using a categorical variable (grazing) and replicates (sites)? Any advice? Thanks!!! P.S. I've been using SPSS, not R!

 A: Is grazing method 1 consistently different than grazing method 2?
Pretty clearly not: At sites A, B, and C more plants were grazed with
method 1, but the reverse is true at site D.
If you need a test to show that sites are not homogeneous for grazing counts,
then a chi-squared test of homogeneity will suffice. The P-value (whether you
do it in R, as below, or in SPSS, or by hand) gives a P-value near $0,$ strongly
rejecting the null hypothesis of homogeneity. [However, this computation assumes
that there was equal opportunity for grazing in all eight cells of the table.
This seems in some doubt with 78 plants grazed at site B and only 30 at site D.]
g1= c(19,55,37,10)
g2= c(10,23,30,20)
TBL = rbind(g1,g2)
TBL
   [,1] [,2] [,3] [,4]
g1   19   55   37   10
g2   10   23   30   20
chisq.test(TBL)

        Pearson's Chi-squared test

data:  TBL
X-squared = 13.372, df = 3, p-value = 0.003898

You say you are not interested in the differences among the four plots.
In that case, I wonder why you bothered to use four different plots in
your experiment.
It seems true that across the four sites 121 plants were
grazed under method 1 and 82 were grazed under method 2. That's considerably
more than half under method 1, but not knowing the numbers of 'marked'
plants that went ungrazed, I don't see a valid way to test whether that turns out to be 'significantly'
more than half. (It certainly doesn't appear that a hungry animal ever has a chance
to choose whether to 'graze' a plant under method 1 or under method 2.)
If you have crucial information necessary for various tests, please edit your
Question so that information is available.
