I'm afraid this is a mere statistical question. But, as I worked with such data in GIS before, and if you have only one variable to study on ( canopy effect) a good way is to apply a fishnet in GIS and extract plot data. Afterward perform an ANOVA (if your canopy variable is a class variable) or regression analysis (if your canopy variable is a continuous variable).

Thank you, I have more than 20 varibles to do the kriging and analyse the influence of canopy. I have more or less clear how to analyse them (statiscally talking), the point is how to extract the data. The ideal will be extracting in R and obtain two databases per variable (one under canopy, one out canopy). Interesting the fishnet approach, I will try it in QGIS or R (but i do not know how to work with an *shp file in R)

I don't know that too ;)

you can try fishnet in GIS 10.1 from toolbox> Data management tools> feature class> create fishnet.

Using the "raster" and "rgdal" packages in R, maybe?

Here's a similar question I asked on ResearchGate:

http://tinyurl.com/qylsu3b

I advise to use ARCGIs or SAGA Gis (free). I don't know very well QGis, but in ARCGis and SAGA there's a command "Polygon statistics", where can you extract mean, median, standard deviation, variance, quantiles of the raster within your polygons. In Saga you can use more than one raster layer.

Though slower than dedicated GIS software, packages in R also allow extraction from a raster stack using a single line of code.

Finally I did the kriging and exported the data to a raster in R, and from that raster I extracted the data under canopy and out canopy in QGIS using the fishnet and the tools "interaction" (to select the fishnet points under and out canopy) and the "point sampling tool". I tried in R but I was not able to use a polygon shape, I tried with "readShapePoly" and "readShapeSpatial" but some errors were reported.

If you have access into ArcGIS software, then you can use Zonal Statistics as Table tool under Spatial Analyst toolbox to extract the data from the raster using your polygon or covert the polygon into points and then using the same tool you can extract the data.

or you can use Pythin script for ArcGIS to do that:

http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000w8000000.htm

There is another open source (free) option called Starspan. I have found it useful in the past for extracting raster data in various forms using vectors or shape files. It was developed at the University of California Davis, but it seems that the code has moved around a bit. This link should get you started.

http://code.google.com/p/starspan/

@Jane. Excellent resource. I wasn't aware of this. It looks to be very fast...very helpful for large rasters or layered rasters. I remember moving from GUI to command-line for my sound file processing (e.g. resampling 4GB sound files for bird song)...it took minutes instead of days. I'm a believer. Anyway, cool to know about this now.

I realize I am late to this but I just found something that would let you stay on QGIS (which for mac users is helpful). The Zonal Statistics plugin does exactly what it sounds like you want to do, and worked without a glitch when I used it. I had a polygon that was 1km buffers on a set of points, and it queried a DEM to give cell count, sum, and mean. Not that the "sum" of elevations is useful, but it could be for another data type.