I have field observations that are inherently binomial presence/absence, but here are the details: randomly placed quadrats are divided into 10 squares, then the field data recorded are the number of squares which have a subject present. This is repeated so that there are 30 quadrats at a reference site, and the greater of 30 or 10% of the area at a site of interest. Although the inherent basis is binomial presence/absence, what kind of data are my n=30 or n=30+ samples? What's the appropriate measure of central tendency - mean or median? What's the appropriate metric for standard error?
Plus, to test difference between the reference site and site of interest, I'm thinking a 2x2 Chi-Square test with either average or median present/absent from the 30 and 30+ observations. Is this the best or most appropriate test or should I consider another?
A binomial or Poisson GLM would be more aligned with your data and you may not need to do transformations to achieve normality. I suspect you'll have spatial dependency (ie presence of object at one square influences presence or absence in neighboring square) within your quadrant sampling, so you might need to take this into account. Also, how do you divide a quadrant into 10 squares - I presume a quadrant is also square?
How do you intent to model this? What is your response variable? What are your questions for the data?
Alexander,
First off, thank you so much for your assistance!!!
There definitely is spatial dependency, but maybe not what you're thinking; we are looking at growth of various species (mostly plants), and comparing between a restored/replanted injury area (i.e., "treatment") and a reference area (i.e., "control"). The sampling quadrats are 0.25 m2 PVC pipes squares evenly divided with wire into 10 sub-sections. The 10 subdivisions simply makes observation and counting easier and quicker. So the actual sampling unit is the entire quadrat, and the observation is the number of sub-sections with a species present (0-10). Essentially, this is a surrogate measure for density. Random locations are generated within the geometry of the restoration area. (They can be in close proximity, but are not allowed to overlap.) The number of samples is the greater of either 30 or enough to cover 10% of the restoration area. The reference area (an adjacent, undisturbed location) is always n=30.
The hypothesis for any given sampling event is the mean/median "density" of the restoration area = mean/median of the reference area.
This sampling is repeated maybe a half dozen times over several years at irregular intervals. We will want to look at trends over time to determine the trajectory of recovery
Thanks again for any advice.
Cheers,
Mike
Hi Mike, below an R (www.r-project.org) example that works on binomial presence/absence for a single sampling event. I am still unclear how you can divide a quadrant into 10 equal subquadrants as sqrt(10) gives 3.16...
require(MASS)
require(lattice)
require(ggplot2)
# create random data
set.seed(666666) # make it repeatable
d1
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