The short answer to your question is that either ArcGIS/QGIS or the R statistical package would allow you to accomplish your task. Of course, each of the different software packages have advantages/disadvantages for your particular use case, and I will try to summarize some of what I expect may be relevant for your work.
I will start with R,
- Good community to ask questions and get really quick feedback (R-Help, Stack Overflow & R). Some R questions get asked on this specific community as well, but the R community over on SO is much more mature. The amount of contributions Roger Bivand makes to the R-help spatial list-serve is difficult to describe (epic?)
- Roger Bivand's book, Applied spatial data analysis with R, is nearly a one stop shop/how-to on whatever spatial analysis/mapping you can/need to do. Also given your field of research I suspect the spatstat package for spatial point pattern analysis and all of its documentation will be of interest. (Although I will note on Bivand's book, I suspect the community is developing so fast that the book will be outdated in a few years)
- Everything is accomplished through syntax & scripts, so reproducing the same product 33 times tends to be a fairly trivial task.
- The world of statisical methodology at your fingure tips.
- Non-map statistical graphics are hard to beat (such as the
- IMO takes more work to make a nice looking map (although nice maps are definately possible in the software, see this map competition in R).
- Editing spatial data is very difficult, and it is not uncommon to have difficulty reading in second hand spatial data. This may be a small concern though, as it sounds like your spatial data is not likely to be very complicated (mostly points for beds?). The same goes for creating the data in the first place.
- The variety in packages/objects makes it difficult to navigate at first. It is unlikely you would stop at the
sp package, and will need to rely on different packages and maybe need to worry about transforming different spatial objects.
- Data manipulation and spatial operations are much more difficult than in traditional GIS software and are scattered in a variety of packages. (hopefully
rgeos helps with that somewhat)
- lacks ability to directly interact with the map (e.g. can't pan/zoom a produced image)
Now onto, ArcMap/QGIS
I am not going to be so formal in describing the advantages/disadvantages of desktop GIS's, but some of the areas that are lacking in R are more easily accomplished in ArcMap/QGIS. In particular creating/editing data tends to be much simpler, and obviously interacting with the map can be accomplished in these programs. Also since these packages tend to be mainly used by the GUI, I think the introduction to the programs is gentler than that of R, although the reliance on the GUI makes it more difficult to accomplish repetitive tasks (although they frequently can be accomplished, and this community is perhaps the best place to ask such questions). You can probably reproduce a statistical graphic 33 times in some type of automated fashion in either ArcMap or QGIS, but I would suspect it is much more difficult and your hands are tied in the types/options in the graphic compared to what can be accomplished in R.
Long story short, while R and desktop GIS's may have alot of overlapping cababilities, they really excel at accomplishing different tasks. While migrating back and forth between different environments is a pain, I find it hard to imagine that at some point it would not be necessary to have a desktop GIS. When you develop a more specific question, this community can give more useful advice about implementation (and that would make comparisons between the work flow in the two different software more easy to differentiate).
A note on other statistical packages that have capabilities of importing spatial data & conducting analysis. I can't speak directly of SAS, but what you can do in Stata is quite pathetic compared to what you can do in R (and on its face it looks to me like the capabilities of SAS is pretty much the same as Stata). If you plan on doing anything more than producing choropleth maps or conducting regression with spatial weights, these programs aren't going to cut it. I think SPSS recently re-added similar functionality with its most recent release, but I doubt it is any more impressive than SAS or Stata.