For mathematicians who are pathological liars:
SAS: Huge dinosaur stats and data manipulation package, tries to be everything, only partially succeeds. Steep learning curve, Steep price. Lots of expensive add-ins.
R: Like SAS, but free. Lots of free but questionably coded add-ins. Caveat emptor.
SPSS, MiniTAB: Clicky stats. Get the job done, if you don't need much.OpenEpi
is cool if you need to do some basic stats from a strange computer.
My overwhelming favorite:
Stata: A bit of a learning curve (can replace 30 lines of SAS code with a single line). Excellent handling of complex survey weights. Small, fast, and powerful, leaves data manipulation to database programs that are good at that sort of thing. Has a peer-reviewed database of new procedures and papers, the online help/journal is amazing. Pisses SAS users off.
To quote a STATA rep's remix of Baby Got Back
: "So they teach Stata in class, but the real world uses SAS..."
My take on the many and sundry statistics packages out there:
SAS: The 800 pound gorilla of the stats world, it does a tremendous amount of stuff, and does it well. A very active community means there are code snippits for almost anything out there, and when it comes down to it, chances are your collaborators are using it. Very good at data manipulation. Cons: Wicked pricey, a substantial learning curve, and without some serious know-how, it can't graph its way out of a paper bag, temptation to punch Stata users.
JMP: SAS's graphical cousin - I'm convinced one day its just going to be repackaged as the GUI and data visualization arm of the main SAS package. Decent stats, good integration with SAS for data manipulation needs, very good data visualization. It makes some decisions essentially for you, which can be good for the beginning statistics types, but occasionally gets annoying.
SPSS/MiniTab/SysStat etc.: Pretty lightweight programs that can get the job done if you're talking about t-tests, ANOVA and linear regression. For anything more complex, SAS/Stata/R users will look at you like you're damaged.
R: Free, rockstar visualization, active community. Very good package, can do nigh everything SAS or Stata can do. On the other hand, at least one major paper has had to be retracted due to coding errors - open source is only as good as the community, and every module needs to be looked over with a critical eye.
Stata: Very good program, way cheaper than SAS, but with somewhat less market penetration. Can do much better visualization than SAS, but that's like beating a cripple in a foot race. Tends, in my experience, to not be the program of choice for the hardcore stats types, who favor SAS or R/S+, but very popular with applied folks. Does meta-analysis way better than SAS. Slightly less "there's a book on how to do that" than SAS because they're lacking the publication might of the SAS Press. My major hangup is the language itself tends to encourage letting you not specify certain choices or let the program take care of it in the background - I prefer having to expressly code things.