Teorie, tecniche ed esperienze nei processi di verifica e valutazione dei Servizi e Progetti Immateriali
Free Statistical Software

General Packages: No package does everything, but these programs support a wide variety of statistical analyses.
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
ViSta -- a Visual Statistics program for Win3.1, Win 95/NT, Mac and Unix, featuring a Structured Desktop, with features designed to structure and assist the statistical analyst.

OpenStat -- a general stats package for Win 95/98/NT, developed by Bill Miller of Iowa State U, with a very broad range of data manipulation and analysis capabilities and an SPSS-like user interface. Bill also has provided an excellent downloadable textbook in the form of Adobe Acrobat files.

Instat Plus -- from the University of Reading, in the UK. (Not to be confused with Instat from GraphPad Software.) An interactive statistics package for Windows or DOS.

WinIDAMS -- from UNESCO -- for numerical information processing and statistical analysis. Provides data manipulation and validation facilities classical and advanced statistical techniques, including interactive construction of multidimensional tables, graphical exploration of data (3D scattergram spinning, etc.), time series analysis, and a large number of multivariate techniques.

SSP (Smith's Statistical Package) -- a simple, user-friendly package for Mac and Windows that can enter/edit/transform/import/export data, calculate basic summaries, prepare charts, evaluate distribution function probabilities, perform simulations, compare means & proportions, do ANOVA's, Chi Square tests, simple & multiple regressions.

Also, check out R and Ox, described in the Programming Languages section below.

NCSS 6.0 Junior -- a free, stripped-down version of NCSS 6.0 for Win 3.1. Has data entry, descriptive statistics, t-tests, multiple regression, tests on proportions, cross tabs, one-way ANOVA, exponential smoothing, histograms, scatter plots, and box plots.

Dataplot -- (Unix, Linux, PC-DOS, Windows) for scientific visualization, statistical analysis, and non-linear modeling. Has extensive mathematical and graphical capabilities. Closely integrated with the NIST/SEMATECH Engineering Statistics Handbook.

WebStat -- A Java-based statistical computing environment for the World Wide Web. Needs a browser, but can be downloaded and run offline.

EasyStat -- Simple program for Windows and Mac for t-tests, F-tests, simple ANOVA, contingency table, Mantel-Haenszel

Regress+ -- A professional package (Macintosh only) for univariate mathematical modeling (equations and distributions). The most powerful software of its kind available anywhere, with state-of-the-art functionality and user-friendliness. Too many features to even begin to list here.

Scilab -- a scientific software package for numerical computations in a user-friendly environment. Available for Windows, Mac and Unix computers, this is a sophisticated programming language with a MatLab-like syntax, hundreds of built-in functions and libraries, 3-d graphics, and symbolic capabilities through a Maple interface.

SISA -- Simple Interactive Statistical Analysis for PC (DOS) from Daan Uitenbroek. An excellent collection of individual DOS modules for several statistical calculations, including some analyses not readily available elsewhere.

Statistical Software by Paul W. Mielke Jr. -- a large collection of executable DOS programs (and Fortran source). Includes: Matrix occupancy, exact g-sample empirical coverage test, interactions of exact analyses, spectral decomposition analysis, exact mrbp (randomized block) analyses, exact multi-response permutation procedure, Fisher's Exact for cross-classfication and goodness-of-fit, Fisher's combined p-values (meta analysis), largest part's proportion, Pearson-Zelterman, Greenwood-Moran and Kendall-Sherman goodness-of-fit, runs tests, multivariate Hotelling's test, least-absolute-deviation regression, sequential permutation procedures, LAD regression, principal component analysis, matched pair permutation, r by c contingency tables, r-way contingency tables, and Jonkheere-Terpstra.

IRRISTAT -- for data management and basic statistical analysis of experimental data (Windows). Primarily for analysis of agricultural field trials, but many features can be used for analysis of data from other sources. Includes: Data management with a spreadsheet , Text editor, Analysis of variance, Regression, Genotype x environment interaction analysis, Quantitative trait analysis, Single site analysis, Pattern analysis, Graphics, Utilities for randomization and layout, general factorial EMS, and orthogonal polynomial.

Hypercard stack that performs basic statistical analyses. Runs on the Mac (a free HyperCard Player program can be downloaded from the Apple web site). Thank you, Mike! (mmessieh@aol.com)

Subset Packages: Each of these programs deals with a specific area of statistics (such as power analysis or mulitvariate analysis), or carries out a specific test or computation.
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
PS -- a very well-implemented Windows 95/NT program for power and sample size calculations from Vanderbilt Univ Med Ctr. Handles dichotomous, continuous, or survival response measures. Alternative hypothesis specified either in terms of differing response rates, means, or survival times, or in terms of relative risks or odds ratios. Studies with dichotomous or continuous outcomes may involve either a matched or independent study design. Can determine sample size for a specified power, power for a specified sample size, or the specific alternative hypotheses that can be detected with a given power and sample size. Produces graphs of relationships between power, sample size and detectable alternative hypotheses (with any two of these variables on x & y, and the third variable generating a family of curves on a single graph). Linear or logarithmic axes may be specified. Can print professional-quality power charts.

PEPI -- a collection of 43 small DOS / Windows programs that perform a large assortment of statistical tests. They can be downloaded individually, or as a single ZIP file. (A new Windows version is being developed; the test version can be downloaded here.) They were written to accompany the book Computer Programs for Epidemiologic Analyses: PEPI v. 4.0, by Abramson and Gahlinger, which is available for purchase. The programs include: p-value adjustments for multiple significance tests; Attributable and Prevented Fractions: Case-Control Studies; Analysis of 2 x 2 Tables; Chi-square Tests of Association; Combining Measures of Association or Probabilities; Confidence Intervals; Aids to Use of Pearson's Correlation Coefficients; ifference Between Rates, Proportions or Means; Direct Standardization; Exact Test for a 2 x K Table; Tests for Goodness of Fit ; Fitting of Poisson and Binomial Distributions; Appraisal of Frequency Distribution ; Indirect Standardization; Agreement Between Categorical Ratings; Life Table Analysis;  Logistic Regression Analysis (Unconditional and Conditional); Wilcoxon-Mann-Whitney Test and Related Procedures ; Extended Mantel-Haenszel Procedure: Trend Analysis; Multiple Matched Controls; Correcting for Misclassification in 2 x 2 Tables; Analysis of Paired Samples ; Poisson Probability: Observed vs Expected Events; Poisson Regression Analysis; Power of a Test Comparing Two Proportions or Means; Probability and Inverse Probability Values: Z, t, Chi Square, F; Procedures using Random Numbers; Association Between Ordinal-Scale Variables; Comparison of Two Rates or Proportions; Comparison of Person-Time Incidence Rates; ower and Sample Size for Regression and Correlation Analyses; Comparison of Several Related Samples; Sample Size for Estimation of Proportion, Rate, or Mean; Sample Sizes for Comparison of Two Samples ; Internal Consistency of a Scale; Screening and Diagnostic Tests ; Seasonal Variation ; Smoothing of Curves and Median Polish Procedure; Kaplan-Meier Life Table Analysis, Log-rank and Logit-rank Tests; Calculation of Elapsed Time; Trend Analysis and Multiple Comparisons, and two special calculators: WHATIS and WHATS.

EpiData -- a comprehensive yet simple tool for documented data entry. Overall frequency tables (codebook) and listing of data included, but no statistical analysis tools.

Biomapper  -- a kit of GIS and statistical tools designed to build habitat suitability (HS) models and maps for any kind of animal or plant. Deals with: preparing ecogeographical maps for use as input for ENFA (e.g. computing frequency of occurrence map, standardisation, masking, etc.); Exploring and comparing them by mean of descriptive statistics (distribution analysis, etc.); Computing the Ecological Niche Factor Analysis and exploring its output; and Computing and evaluating a Habitat Suitability map

StatCalc -- a PC calculator that computes table values and other statistics for 34 probability distributions. Also includes some nonparametric table values, tolerance factors, and bivariate normal distribution. A help file is provided for each distribution.

BKD: Bayesian Knowledge Discoverer  -- a computer program able to learn Bayesian Belief Networks from (possibly incomplete) databases. Based on a new estimation method called Bound and Collapse. Developed within the Bayesian Knowledge Discovery project. See also the commercial product, called Bayesware Discoverer, available free for non-commercial use.

RoC: The Robust Bayesian Classifier -- a computer program able to perform supervised Bayesian classification from incomplete databases, with no assumption about the pattern of missing data. Based on a new estimation method called Robust Bayesian Estimator. Developed within the Bayesian Knowledge Discovery project.

DQO-PRO -- a sample-size calculator for MS Windows that performs three types of calculations:

  • determining the rate at which an event occurs (confidence levels versus numbers of false positive or negative conclusions),
  • determining an estimate of an averge within a tolerable error (given the standard deviation of individual measurements), and
  • determining the sampling grid necessary to detect “hot spots” of various assumed shapes.

Probability Calculator -- Regular (p-value) and inverse calculation for most popular central and non-central probability distributions: Beta, Binomial, Bivariate Normal, Chi Square, Correlation, Fisher F, Gamma, Hypergeometric, Negative Binomial, Normal (Gaussian), Poisson, Student t, Studentized Range, Weibull.

Binomial Probability Program (BPP) is a menu driven program which performs a variety of functions related to the success/ failure situation. Given the probability of occurrence for a specific event, this program calculates the probability that EXACTLY, NO MORE THAN, or AT LEAST a certain number of events occur in a given number of trials for all possible outcomes, and will generate plots for each of these.

The program allows the user to repeatedly combine probabilities in series or in parallel, and at any time will show a trail of the calculations which led to the current probability value. Other program capabilities are the calculation of probabilities from input data, Gaussian approximation, and the generation of a mean time between failure (MTBF) table for various levels of confidence. Up to 2200 trials may be run, limited by IBM PC BASIC memory utilization. It is assumed that the user is familiar with the theory behind binomial probability distribution.

ADE-4 -- multivariate analysis and graphical display software package for Mac andWin 95/NT. Includes component analysis and correspondence analysis, spatial data analysis methods (analogous to Moran and Geary indices), discriminant analysis and within/between groups analyses, many linear regression methods including lowess and polynomial regression, multiple and PLS (partial least squares) regression and orthogonal (principal component) regression, projection methods like principal component analysis on instrumental variables, canonical correspondence analysis and many other variants, coinertia analysis and the RLQ method, and several three-way table (k-table) analysis methods. Graphical displays include an automatic collection of elementary graphics corresponding to groups of rows or to columns in the data table, automatic k-table graphics and geographical mapping options, searching, zooming, selection of points, and display of data values on factor maps. Simple and homogeneous user interface.

R (Not to be confused with the "R" statistical programming language!)  -- A group of programs (Macintosh and VAX/VMS), originally developed for ecologists, various complex multidimensional and spatial analysis procedures. Contains AutoCorrelation, BioGeo, Chrono, Cluster, Cocopan, COnvert, GeoDistances, Import-Export, K-Means, Links, Look, Mantel, PCoord, Periodograph, PnComp, Simil, and VerNorm. Full documentation is provided.

G*Power -- a general Power Analysis program for DOS and Macintosh. Performs high-precision analysis for t-tests, F-tests, Chi-square tests. Computes power, sample sizes, alpha, beta, and alpha/beta ratios. Has a comprehensive web-based tutorial and reference manual.

Tests of Proportions- applies tests of significance for proportions (between observed vs expected and between two independent proportions). (Mac, 335K)

CAcalculator -- calculates chronological age when given date of birth and date of test. (Mac, 700K)

MacKappa -- calculates general and partial kappa coefficients for nominal data. (Mac, 220k)

Weibull Trend Toolkit -- Fits a Weibull distribution function (like a normal distribution, but more flexible) to a set of data points by matching the skewness of the data. (Windows)

CASSATT -- A pure Java graphical program to create linked scatterplots and parallel-coordinate plots. Runs on any platform that can run Java (Win/95/98/NT/2000, Mac, Unix, etc.)

TURNER -- Macintosh software for interactivly analysing multidimensional discrete data. Uses interactive paradigms from exploratory graphical data analysis to the concise treatment of categorical data, typically arranged in two- or multi-way contingency tables. Including standard features for categorical data like Pearson's chi-squared test and log-linear models it offers the whole goodness-of-fit family of power divergence statistics and the N-value. Interactive contingency tables provide the user with the facility of easily switching between all two-dimensional views of multivariate data. All displays dealing with the same data set are fully linked and may be interacted with directly.

BUGS -- Bayesian inference Using Gibbs Sampling. Software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. Command-line interface versions available for major computer platform; a Windows version, WinBUGS, supports a graphical user interface, on-line monitoring and convergence diagnostics.

QUEST (Quick, Unbiased and Efficient Statistical Tree), and CRUISE (Classification Rule with Unbiased Interaction Selection and Estimation. Two statistical decision tree algorithms for classification and data mining, by Wei-Yin Loh and Yu-Shan Shih.

AMELIA -- A program for substituting reasonable values for missing data (called "imputation")

Curve-fitting & Modeling:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
EasyReg (Easy Regression Analysis), by Herman J. Bierens. Incredibly powerful and multi-featured program for data manipulation and analysis. Designed for econometrics, but useful in many other disciplines as well. For Win 98/98/NT4.

WinSAAM -- Windows implementation of SAAM (System Analysis and Modeling Software). Lets you create mathematical models, design and simulate experiments, and analyze data. Models can contain differential equations, which will be numerically integrated and fit to data. Graphic and tabular output is provided.

Boomer -- Non-linear Regression Program for Analysis of Pharmacokinetic and Pharmacodynamic Data. Includes normal fitting, Bayesian estimation, or simulation-only, with integrated or differential equation models. Allows selection of weighting schemes and methods for numerical integration. Free downloads for Macintosh and PC; online manual, tutorial, sample data sets.

PLS-PC 1.8 -- A DOS program to do Partial Least Squares regression (PLS). Developed by J. Lohm÷ller, and distributed for free by J. McArdle. An introductory overview of PLS by Wynne CHin can be found here.

DEMETRA -- user-friendly interface to TRAMO/SEATS and X-12-ARIMA .

Biostatistics and Epidemiology:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
Anderson Statistical Archives -- A large collection of statistical programs for PC(DOS) and Mac, plus Fortran and C source, from the Biomathematics department of the M.D. Anderson Cancer Center. Software is distributed in the form of program source files (Fortran-77 or ANSI C) and/or self-extracting archives of executable programs for PC-compatible (under DOS) or Macintosh (68xxx-based or PowerMac) computers.

STPLAN -- Performs power, sample size, and related calculations needed to plan studies. Covers a wide variety of situations, including studies whose outcomes involve the Binomial, Poisson, Normal, and log-normal distributions, or are survival times or correlation coefficients. Available for MS-DOS and Mac; also as Fortran and C source code.

EpiInfo -- a set of programs for word processing, data management and epidemiologic analysis, designed for public health professionals. Consists of Epi Info (forms design, data entry, data management), Epi Map (generated geographical, map-based output), SSS1 (Box-Jenkins time series analysis, MMWR graphs, trend analysis, and 2-source comparisons). Also, check out the excellent online companion textbook: Data Analysis with Epi Info, by Bud Gerstman.

See the entry in the Subset Programs section  of this page for PEPI -- a collection of 43 small DOS / Windows programs that perform a large assortment of statistical tests. They can be downloaded individually, or as a single ZIP file.

Free Public Health & Epidemiology Software -- written by Mark Myatt)and others:

PAMCOMP (Person-years And Mortality COMputation Program) -- a free Windows 95/98/NT application for calculating person-years and standardised mortality ratios (SMRs). The calculation of person-years allows flexible stratification by sex, and self-defined and unrestricted calendar periods and age groups, and can lag person-years to account for latency periods.The SMR computation includes calculation of 90%, 95%, and 99% confidence intervals. Has filters for ASCII, dBase, Excel, Access, Paradox to import cohort and reference data and to export distributions of person-years and deaths.

ARIMA -- a seasonal adjustment program for PC and Unix, developed by the Census Bureau. Click here for a review of version X-12.

DEMETRA -- (Win 9x/NT) a user-friendly interface to the seasonal adjustment methods TRAMO/SEATS and X-12-ARIMA . Developed by Eurostat to facilitate the application of these modern time series techniques to large-scale sets of time series and in the explicit consideration of the needs of production units in statistical institutes. Client/server architecture can access various kinds of databases and files. Contains two main modules: seasonal adjustment and trend estimation with an automated procedure (e.g. for unexperienced users or for large-scale sets of time series), and with a user-friendly procedure for detailed analysis of single time series.

EasyMA -- a free user-friendly MS-DOS program for the meta-analysis of clinical trials results. Developed to help physicians and medical researchers to synthesize evidence in clinical or therapeutic research.

EPIMETA (from CDC) -- a DOS-based meta-analysis program that features a Windows-like interface which makes data entry, file manipulation, and subgroup analysis easy.

Life Table -- available in Lotus and Excel formats.

Diagnostic Statistics -- calculates diagnostic efficiency statistics (i. e., sensitivity, specificity, positive and negative predictive power, Kappa, etc.). (Mac, 335K)

ABSRISK -- a program (MS-DOS) for estimating absolute risks from relative risks. Uses age-specific mortality and morbidity data to convert relative risk estimates into absolute risk estimates. That is, it estimates the probability that a patient will suffer a specific morbid or mortal outcome in a given time interval. The user first specifies a data file that contains the needed mortality and morbidity data for the disease of interest. She then gives her patient's age and relative risk, and the time interval over which the risk estimate is to be derived. The program derives this risk, which is given both interactively and in a log file.

Biodiversity Research Software -- Five software packages, with documentation:

  1. LUMP, LINK, and JOIN: Utility Programs for Biodiversity Research
  2. COLLECT1 and COLLECT2: Programs for Calculating Statistics of Collectors' Curves
  3. BOUNDARY: A Program for Detecting Boundaries in Ecological Landscapes
  4. EXTSPP1 and EXTSPP2: Programs for Comparing and Performance-Testing Eight Extrapolation-Based Estimators of Total Taxonomic Richness
  5. RARE, SPPDISS, and SPPRANK: Programs for Detecting Between- Sample Differences in Community Structure

Surveys, Testing, and Measurement:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
Q-Method -- a statistical program for analyzing data from the Q-Sort Technique. Enter data (Q-Sorts) the way they are collected, i.e. as 'piles' of statement numbers. It computes intercorrelations among Q-Sorts, which are then factor-analysed with the Centroid (or, alternatively, PCA) method. Resulting factors can be rotated either analytically (Varimax), or judgmentally with the help of two-dimensional plots. Finally, after selecting the relevant factors and 'flagging' the entries that define the factors, the analysis step produces an extensive report with a variety of tables on factor loadings, statement factor scores, discriminating statements for each of the factors as well as consensus statements across factors, etc.

AnSWR -- Analysis Software for Word-based Records -- a free software system from the C.D.C. for coordinating and conducting large-scale, team-based analysis projects that integrate qualitative and quantitative techniques (for Windows).

ez-text -- a software program from the C.D.C. developed to assist researchers create, manage, and analyze semi-structured qualitative databases.

CSPro (Census and Survey Processing System) -- a public-domain software package for entering, tabulating and mapping census and survey data.

IMPS (Integrated Microcomputer Processing System) -- performs the major tasks in survey and census data processing: data entry, data editing, tabulation, data dissemination, statistical analysis and data capture control. (from CDC)

WebQ -- a set of HTML files for performing Q-Sorts online and collecting the data for subsequent analysis.

Stats -- Windows program for several commonly-needed statistical functions for marketing researchers: random numbers;sample sizes needed for surveys; mean, standard deviation, standard error and range for keyboard-entered data; standard error of a proportion; significance testing between two percentages from independent samples; significance between two percentages from dependent samples; significance testing between two averages from independent samples; contingency table analysis (i.e., Chi-Square)

SABRE -- a Fortran program for statistical analysis of binary, ordinal and count recurrent events. Such data are common in many surveys either with recurrent information collected over time or with a clustered sampling scheme. It is particularly appropriate for the analysis of work and life histories, and has been used intensively on many longitudinal datasets.

POSDEM -- Uses simulation techniques to analyze and compare alternate sampling strategies for surveys. Performs power / sample size / precision analyses for different sampling methods: systematic, stratified, random, etc. Windows versions available in Spanish and English.

SSCalculator -- calculates standard scores (z, t, NCE) as well as percentiles and Wechsler test scores. (Mac, 315K)

ASCAcalculator for Macintosh and Windows -- performs syndromic profile analysis with both generalized distance and r(p) calculation methods for Adjustment Scales for Children and Adolescents (ASCA) scores. (Mac:200K, Win:500K)

MacPotthoff -- performs Potthoff regression bias analysis. (Mac, 200K)

WISC-III Profile Calculator for Macintosh and Windows -- uses generalized distance method to determine if the subtest profile of a single case is multivariately unusual or common in comparison to subtest clusters found in the WISC-III standardization sample. (Mac, 360K; Win anticipated in September)

DEMETRA -- user-friendly interface to TRAMO/SEATS and X-12-ARIMA .

Excel Spreadsheets and Add-Ins:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
PopTools -- Windows DLL for Excel 97 and 2000 (PC's only). Facilitates analysis of matrix population models & simulation of stochastic processes. Adds a new menu item and installs many powerful functions: matrix decompositions (Cholesky, QR, singular values, LU), eigenanalysis (eigenvalues and eigenvectors of square matrices) and formulas for generation of random variables (Normal, binomial, gamma, exponential, Poisson, logNormal). Also has routines for iterating spreadsheets to run Monte Carlo simulations, conduct randomisation tests (including the Mantel test) and calculate bootstrap statistics. Some facilities for maximum-likelihood parameter estimation, and some other generally useful functions. Free download from website, which also has documentation, examples, and related links.

DE Histograms -- an Excel add-in that provides comprehensive descriptives stats, histograms, outlier detection, normality testing, and much more.

Exact confidence intervals for samples from the Binomial and Poisson distributions -- an Excel spreadsheet with several built-in functions for calculating probabilities and confidence intervals. (42k long).

Confidence interval around a difference between two proportions (and around the "number needed to treat", using the Newcombe Wilson hybrid score, by Dan Tandberg. More accurate than the usual normal-approximation formulas.

Essential Regression and Experimental Design -- an Excel 95/97 add-in and electronic book package for linear multiple and polynomial regression. Includes significance tests of model and parameters, model adequacy checking, tests for multicollinearity and variance inflation factors, autocorrelation, model optimization, stepwise regression, and experimental design (screening designs, orthogonality and rotatability, and response surface modeling).

Life Table -- available in Lotus and Excel formats

Weighted Least Squares Linear Fits -- an Excel add-in from Philip Kromer (Univ. of Texas)

ASCA Profile Analysis -- EXCEL spreadsheet template for performing syndromic profile analysis of Adjustment Scale for Children and Adolescents scores. (Mac, 25K)

Correlation Tests -- EXCEL spreadsheet template which tests the significance of difference between correlations (both independent and dependent). (Mac, 25K)

Receiver Operating Characteristic (ROC) -- EXCEL template, graphs the ROC curve and calculates Area Under the ROC Curve (AUC) using a nonparametric method. Mac, 20K)

Programming Languages and Routines:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
MuPAD -- a very powerful and general computerized algebra system, developed at the University of Paderborn, now distributed by SciFace Software. In the same category as Mathematica and Maple, it does numerical calculations, symbolic manipulation (algebra, differentiation & integration), graphing, and programming. A free "lite" (but still very powerful) version for PC and Mac can be downloaded.

R -- a programming language and environment for statistical computing and graphics. Similar to S or S-plus (will run most S code unchanged). Available for Windows, various Unix flavors (including Linux), NextStep and Mac. 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. Well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed. The R environment includes:

  • an effective data handling and storage facility,
  • a suite of operators for calculations on arrays, in particular matrices,
  • a large, coherent, integrated collection of intermediate tools for data analysis,
  • graphical facilities for data analysis and display either on-screen or on hardcopy, and
  • a well-developed, simple and effective programming language which includes conditionals, loops, user-defined recursive functions and input and output facilities.

Octave -- a high-level mathematical programming language, similar to MATLAB, for numerical computations -- solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages. Runs under Linux and Windows.

Ox -- an object-oriented matrix programming language with a comprehensive mathematical and statistical function library. Matrices can be used directly in expressions, for example to multiply two matrices, or to invert a matrix. The major features of Ox are its speed, extensive library, and well-designed syntax, which leads to programs which are easier to maintain. Versions of Ox are available for many platforms. The "Console" version can be freely downloaded for academic and research use; the "Professional" version must be purchased.

Mx  -- a matrix algebra interpreter and numerical optimizer for exploration of matrix algebra. Many built-in fit fuctions for structural equation modeling and other statistical modeling. Has fitting fuctions like those in LISREL, LISCOMP, EQS and CALIS, along with facilities for maximum likelihood estimation of parameters from missing data structures, under normal theory. Users can easily specify complex 'nonstandard' models, define their own fit functions, and perform optimization subject to linear and nonlinear equality or boundary constraints.

Visual Basic Subroutines for Statistical Computations -- Eigensystems, conjugate gradient, finite differencing, maximum likelihood regression, iteratively reweighted least squares, non-linear regression by finite differencing or partial derivatives, linear categorical regression, Poisson regression by log-likelihood & iteratively-reweighted least squares, unconditional (non-matched) and conditional (1:M matching) logistic regression by log-likelihood. Also subroutines for simulating probability distributions: uniform U(0,1) (linear congruential), normal (quantiles), N(0,1) and N(mu,sigma^2), log-normal (quantiles), LN(GM,GSD^2), asymmetric triangle (quantiles), TRI(a,c,b), binomial (quantiles), B(n,p), Poisson (quantiles), P(lambda), Chi-square (quantiles), CHI(df). Also Factor Analysisof cDNA microarray data with varimax rotation. Also Histogram Frequencies and Plotting, X-Y scatter, line, or 2D vertical bar(histogram), X-Y Scatter, Line, Horizontal bar. Also VB Code Optimization for Large Sample Analysis (using arrays with millions of elements). New: kernel density estimation.

JDB -- Relational Database and Elementary Statistics for a Unix environment. Useful for manipulating experimental data (joining files, cleaning data, reformatting for input into other programs). Computes basic statistics (mean, std. dev., confidence intervals, quartiles, n-tiles, percentiles, histograms, correlations, z-scores, t-scores.

B/D -- an interactive programming language for a priori and diagnostic analyses of Bayes linear statistical problems (subjective statistical analyses based on expectation and covariance structures, rather than on distributional assumptions). Quickly and easily specify beliefs about quantities of interest, attach data to some or all of those quantities, and carry out the general process of Bayes linear adjustment. Produces interactive Bayes linear influence diagrams for the adjustments, providing simple graphical summaries of the adjustments and accompanying diagnostics.

MacANOVA -- comprehensive statistical package for the Mac and PC/Windows. MacAnova has macros which are used just like functions. Several macros are built in, and three files of additional macros (general, time series, design of experiments) are distributed with MacAnova. Like S, MacAnova is a programming language with for and while loops, if, else, elseif, break, and a full range of operations including bit manipulation.

Lisp-Stat  -- an extensible statistical computing environment for data analysis, statistical instruction and research, and  for exploring the use of dynamic graphical methods. Based on an extended subset of Common Lisp, performs element-wise operations on lists and vectors, and adds a variety of basic statistical and linear algebra functions. Graphics system is object-oriented, and can be customized and adapted. Supports linear and nonlinear regression models and generalized linear models. Runs on Mac, X-window (UNIX), and MS Windows. Be sure to download the documentation, or you won't get anywhere with it.

Miscellaneous:
Completely Free... can be freely downloaded and used in their fully-functional mode (no strings attached)
Meta-analysis 5.3 -- Free DOS statistics software for meta-analysis. Probably still the most frequently used meta-analysis software in the world. Can select the analysis of exact p values or effect sizes (d or r, with a cluster size option). Can plot a stem-and-leaf display of correlation coefficients. A utility menu is provided that allows various transformations and preliminary computations that are typically required before the final meta-analysis can be performed.

First Bayes -- a free, easy-to-use Windows application for elementary Bayesian Statistics. Performs most standard, elementary Bayesian analyses, including: plotting and summarizing distributions, defining and examining arbitrary mixtures of distributions, analysis of two kinds of linear model (one or more normal samples with common but unknown variance, and simple linear regression), examination of marginal distributions for arbitrary linear combinations of the location parameters, and the generation of predictive distributions.

IND -- Creation and manipulation of decision trees from data.  For supervised classification and prediction in artificial intelligence and statistical pattern recognition. A tree is "grown" from data using a recursive partitioning algorithm to create a tree which (hopefully) has good prediction of classes on new data. IND improves on standard algorithms and introduces Bayesian and MML methods, producing more accurate class probability estimates that are important in applications like diagnosis. For UNIX systems. Currently available only in beta-test mode, and only to US citizens.

MANET -- ("Missings Are Now Equally Treated") Macintosh software for interactive graphics tools for data sets with missing values. Generates missing values chart, histograms & barcharts, boxplots & dotplots, scatterplots, mosaic plots, polygon plots, highlighted boxplots, interactive trellis displays, traces, context-sensitive interrogation, cues, redframing, selection sequences.

GrafProg -- a Windows graphing program design, copy and save graphs generated by functions or by spreadsheet; also includes some statistical graphing processes.

Scott Warner's collection of MS-DOS and Windows programs useful in a clinical laboratory setting. Also includes LOOEE (Laboratory One-Operator Expression Evaluator), a simple programming language for laboratories.

WAFO -- Wave Analysis for Fatigue and Oceanography. A toolbox of Matlab (ver. 5.x / 6.x, for Windows & Unix) routines for statistical analysis and simulation of random waves and random loads. Tools are provided for analysis of measured data with routines for estimation of parameters in statistical distributions, estimation of spectra, plotting in probability papers, etc. Has routines for theoretical distributions of characteristic wave parameters from observed or theoretical power spectra of the sea. Another part is related to statistical analysis of fatigue. The theoretical density of rainflow cycles can be computed from parameters of random loads. Has routines is included for modelling of switching loads (hidden Markov models). Also contains general statistical tools.