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STATISTICAL SOFTWARE
Almost all serious statistical analysis is done in one of the following packages: R (S-PLUS), Matlab, SAS, SPSS and Stata. I have expertise in each of those packages but it does not mean that each of those packages is good for a specific type of analysis. In fact, for most advanced areas only 2-3 packages will be suitable, providing enough functionality or enough tools to implement this functionality easily. For example, a very important area of Markov Chain Monte Carlo is doable in R, Matlab and SAS only, unless you want to rely on convoluted macros written by random users on the web. The table at the end of this page compares the five packages in great detail.
R & MATLAB
R and Matlab are the richest systems by far. They contain an impressive collection of libraries, which is growing every day. Even if a desired specific model is not part of the standard functionality you can implement the model yourself, because R and Matlab are really programming languages with relatively simple syntaxes. As "languages" they allow you to express any idea. The question is whether you are a good writer or not. In terms of modern applied statistics tools, R libraries are somewhat richer than those of Matlab. Also R is free. On the flip side, Matlab has much better graphics, which you will not be ashamed to put in a paper or a presentation.
SPSS
On the other end of the spectrum is a package like SPSS. SPSS is quite narrow in its capabilities and allows you to do only about half of the mainstream statistics. It is quite useless for ambitious modeling and estimation procedures which are part of kernel smoothing, pattern recognition or signal processing. Nonetheless, SPSS is very popular among the practitioners because it does not require almost any training. All you have to do is hit several buttons and SPSS does all the calculations for you. In those cases when you need something standard, SPSS may have it implemented fully. The SPSS output will be quite detailed and visually pleasing. It will contain all the major tests and diagnostic tools associated with the method and will allow you to write an informative statistics section of your empirical analysis. In short, when the method is there, it is faster to run than a similar functionality in R or Matlab. So I use SPSS often for standard requests from my clients, like linear regression, ANOVA or principal components analysis. SPSS gives you the ability to program macros but that feature is quite inflexible.
SAS & STATA
Somewhere in-between R, Matlab and SPSS lie SAS and Stata. SAS is more extensive analytics than Stata. It is composed of dozens of procedures with massive, massive output, often covering more than ten pages. The idea of SAS is not to listen to you that much. It is like an old grandfather, whom you approach with a simple question but instead he tells you the story of his life. Many procedures contain three times more than what you need to know about that segment. So some time has to be spent on filtering in the relevant output. SAS procedures are invoked using simple scripts. Stata procedures can be invoked by clicking buttons in the menu or by running simple scripts. In the menu part, Stata resembles SPSS. Both SAS and Stata are programming languages, so they allow you to build analytics around standard procedures. Stata is somewhat more flexible than SAS. Still, in terms of programming flexibility, Stata and SAS do not come even close to R or Matlab. Selected strengths of SAS compared to all other packages: large data sets, speed, beautiful graphics, flexibility in formatting the output, time series procedures, counting processes. Selected strengths of Stata compared to all other packages: manipulation of survey data (stratified samples, clustering), robust estimation and tests, longitudinal data methods, multivariate time series.
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