English language

G*Power 3 covers statistical power analyses for many different statistical tests of the
* F test,
* t test,
* χ2-test and
* z test families and some
* exact tests.
G*Power 3 offers five different types of statistical power analysis:
* A priori (sample size N is computed as a function of power level 1-β, significance level α, and the to-be-detected population effect size)
* Compromise (both α and 1-β are computed as functions of effect size, N, and an error probability ratio q = β/α)
* Criterion (α and the associated decision criterion are computed as a function of 1-β, the effect size, and N)
* Post-hoc (1-β is computed as a function of α, the population effect size, and N)
* Sensitivity (population effect size is computed as a function of α, 1-β, and N)
G*Power 3 provides improved effect size calculators and graphics options. It supports both a distribution-based and a design-based input mode.
G*Power 3 is available for Mac OS X 10.4 and Windows XP/Vista.
G*Power 3 is free.

R is a language and environment for statistical computing and graphics. It is a GNU project. R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, ...) and graphical techniques, and is highly extensible. One of R's strengths is the ease with which well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed.
R is available in many different languages.

PSPP is a program for statistical analysis of sampled data. It is a Free replacement for the proprietary program SPSS, and appears very similar to it with a few exceptions.
The most important of these exceptions are, that there are no “time bombs”; your copy of PSPP will not “expire” or deliberately stop working in the future. Neither are there any artificial limits on the number of cases or variables which you can use. There are no additional packages to purchase in order to get “advanced” functions; all functionality that PSPP currently supports is in the core package.
PSPP can perform descriptive statistics, T-tests, linear regression and non-parametric tests. Its backend is designed to perform its analyses as fast as possible, regardless of the size of the input data.
You can use PSPP with its graphical interface or the more traditional syntax commands.

OpenStat by Bill Miller contains a large variety of parametric, nonparametric, multivariate, measurement, statistical process control, financial and other procedures. One can also simulate a variety of data for tests, theoretical distributions, multivariate data, etc.
It was originally written as an aid in the teaching of statistics to the students enrolled in a social science program. It has been expanded to provide procedures useful in a wide variety of disciplines.

RStudio is an integrated development environment (IDE) for R which works with the standard version of R available from CRAN. Like R, RStudio is available under a free software license. Our goal is to develop a powerful tool that supports the practices and techniques required for creating trustworthy, high quality analysis. At the same time, we want RStudio to be as straightforward and intuitive as possible to provide a friendly environment for new and experienced R users alike.

Instat is a general statistical package, maintained by the Statistical Services Centre, University of Reading.
It is simple enough to be useful in teaching statistical ideas, yet has the power to assist research in any discipline that requires the analysis of data.
Instat began life on a BBC microcomputer. It was first used on a training course on 'statistics in agriculture' held in Sri Lanka during 1983. The BBC micro version was marketed commercially from mid-1985, with the DOS version for PCs becoming available in 1987. From 1994 Instat was free-of-charge. Updated DOS versions were released in 1996 and 1997.
Instat has been used widely in the UK and elsewhere by a range of companies, research institutes, schools, colleges, universities and private individuals. At Reading it has been used extensively on training courses run by the SSC. It has also been used in many countries on statistics courses and on courses related to health, agriculture and climatology.
Instat is free of charge for individual, non-commercial use.

SOFA is a user-friendly statistics, analysis, & reporting program. It is free, with an emphasis on ease of use, learn as you go, and beautiful output.
SOFA lets you display results in an attractive format ready to share. And SOFA will help you learn as you go.

MYSTAT- the Free SYSTAT Statistical Analysis Product for Student Use.
MYSTAT is a free, streamlined, student-oriented variation of the SYSTAT flagship product, featuring statistical routines that are covered in undergraduate-level statistics, science, and social science courses.

WinIDAMS is a free software package for the validation, manipulation and statistical analysis of data, developed by the UNESCO Secretariat in co-operation with experts from various countries.
It offers:
- modern graphical user interface and on-line Reference Manual,
- possibility to customize the environment for an application,
- facilities for editing/creating data files and data description files,
- interactive data import/export,
- editor for creating/updating files with instructions for program execution,
- viewer for displaying and quick navigation through results,
- advanced text editing facilities,
- facilities for sorting and merging files, data editing, checking of codes and consistencies, correcting, listing, subsetting, aggregating, merging and transforming data, including construction of new variables,
- wide range of data analysis techniques such as: table building, regression analysis, one-way analysis of variance, discriminant analysis, cluster analysis, principal components factor analysis and analysis of correspondences, partial order scoring, rank ordering of alternatives, segmentation and iterative typology,
- interactive components for construction of multidimensional tables and their graphical presentation, for graphical exploration of data and for times series analysis.
WinIDAMS and a self-teaching module "How to work with WinIDAMS" are available in English, French, Portuguese and Spanish.
It seems that UNESCO is no longer supporting or updateing WinIDAMS. Latest version is WinIDAMS 1.3, available since May 2008.

MicrOsiris is a comprehensive statistical and data management package for Windows. Derived from OSIRIS IV, a statistical and data management package developed and used at the University of Michigan, MicrOsiris includes special techniques for data mining (SEARCH) and analysis of nominal- and ordinal-scaled data (MNA, MCA) and an interface to IVEware, the Michigan Survey Research Center's imputation software.
The MicrOsiris IVEware interface command, IVEWARE, invokes the Srcware version of IVEware (installed with MicrOsiris) that can:
- Perform single or multiple imputations of missing values using the Sequential Regression Imputation Method.
- Perform a variety of descriptive and model based analyses accounting for such complex design features as clustering, stratification and weighting.
- Perform multiple imputation analyses for both descriptive and model-based survey statistics.
- Returns an imputed data set for further analysis in MicrOsiris.
MicrOsiris accepts data from SPSS, SAS, STATA, and Excel as well as from other sources, including UNESCO IDAMS datasets and older OSIRIS datasets from ICPSR.
It's free and it's speed and small disk footprint makes it excellent for students and student labs as well as large-scale research projects.