(SAS, SPSS, S-PLUS, R, Stata, JMP, Minitab, SYSTAT, UNISTAT, STATISTICA, ...)
Widely used for more than a decade as a high-powered statistical system, Mathematica's capabilities in statistics-related areas have steadily grown. Mathematica includes industrial-strength versions of the usual statistics and visualization capabilities, together with many important unique capabilities, made possible by its broad overall scope and extensibility, immense interconnected web of algorithms and integrated programming language and interface framework.
Mathematica dramatically raises the bar for statistical computation—making possible a vastly higher level of integration of the complete analysis workflow, as well as providing major extensibility beyond the specific functions implemented in particular statistical systems.
Mathematica uses its unique core architecture to provide convenient import of the world's broadest range of data formats. Then, Mathematica's well-developed symbolic language makes it easy to specify arbitrarily extensible statistical models and data analysis methods. With its unique approach to computational aesthetics, Mathematica automates the generation of compelling visualizations—and allows any output or computation to immediately become interactive and dynamic.
An important feature of Mathematica is its integrated notebook mechanism, in which a single document can store a complete, formatted, editable, executable history of an analysis, complete with live graphics, interactive controls and arbitrary typeset tabular, mathematical and other material. Mathematica allows notebooks to be built up interactively, or generated programmatically, then immediately exported in a wide range of online, print and web formats.
Most existing statistical packages have gradually evolved from specific libraries of functions. Mathematica's broader overall conception, vastly greater range of capabilities and integration with the latest computing technologies allows it easily to incorporate the latest developments in statistics and data analysis that would be difficult or impossible for narrowly defined statistics systems.