SYSTAT Statistics
For the price, there is no other program with the depth of statistical analysis that SYSTAT provides:
Probability Calculator
 Computes probability density function, cumulative distribution function, inverse cumulative distribution function, and uppertail probabilities for 9 univariate discrete and 28 continuous probability distributions
 Quick Graphs: graphs of the probability density function and the cumulative distribution function for continuous distributions
Random Sampling

 MersenneTwister random number generator
 Random Sampling from a list of 9 univariate discrete and 28 univariate continuous distributions with given parameters
 (Also, 5 multivariate distributions as part of the Monte Carlo addon module.)
Design of Experiments
 Choose between Classic and Advanced DOE with dynamic wizard
 Optimal Designs
 Complete and incomplete factorial designs
 Latin square designs, 312 levels per factor
 Box and Hunter 2level incomplete designs
 Taguchi designs
 Plackett and Burman designs
 Mixture: lattice, centroid, axial, and screening
 Response surface designs: BoxBehnken and central composite designs
Power Analysis
 Determine sample size to achieve a specified power
 Determine power for a single sample size or a range of sample sizes
 Proportions, correlations, ttests, ztests, ANOVA (oneway and twoway), and generic designs
 Conforms to the Hypothesis tests on means and their various options
 Onesided and twosided alternatives
 Quick Graph: power curve
Descriptive Statistics
 Column
 Arithmetic mean, median, sum and number of cases
 Min, max, range and variance
 Coefficient of variation, std err of mean
 Adjustable confidence intervals of mean
 Skewness, kurtosis, including standard errors
 ShapiroWilk normality test
 AndersonDarling normality test
 Multivariate skewness and kurtosis, testing for significance of these
 HenzeZirkler test for multivariate normality
 N & P Tiles: Cleveland, Weighted average 1, Weighted average 2, Weighted average 3, Closest, Empirical CDF, Empirical CDF (average)
 Trimmed, Geometric, and Harmonic means
 StemandLeaf display
 Resampling – Bootstrap, without replacement, Jackknife
 Bootstrap estimates, bias, standard error and confidence intervals, histograms of estimates
 Row
 Arithmetic mean, median, sum and number of cases
 Min, max, range and variance
 Coefficient of variation, std err of mean
 Adjustable confidence intervals of mean
 Skewness, kurtosis, including standard errors
 ShapiroWilk normality test
 AndersonDarling normality test
 Multivariate skewness and kurtosis, testing for significance of these
 HenzeZirkler test for multivariate normality
 N & P Tiles: Cleveland, Weighted average 1, Weighted average 2, Weighted average 3, Empirical CDF, Empirical CDF (average), Closest
 Trimmed, Geometric, and Harmonic means
 StemandLeaf display
 Resampling – Bootstrap, without replacement, Jackknife
 Bootstrap estimates, bias, standard error and confidence intervals, histograms of estimates
Fitting Distributions
 9 discrete and 21 continuous univariate distributions with given or estimated parameters
 QuickGraphs: graph of the respective observed and expected frequencies while fitting
 Chisquared and KolmogorovSmirnov goodnessoffit tests; ShapiroWilk normality test for normal, lognormal and logit normal
Crosstabulation and Measures of Association
 One, two, and multiway tables
 Row and column frequencies, percents, expected values and deviates
 List layouts, order categories, define intervals, including missing intervals
 2 x 2 tables: likelihood ratio chisquare, Yates’, Fisher’s exact test, odds ratio, Yule’s Q
 2 x k tables: Cochran test
 r x r tables: McNemar’s test, Cohen’s kappa
 r x c tables, unordered levels: phi, Cramer’s V, contingency, GoodmanKruskal’s lambda, and uncertainty coefficients
 r x c ordered levels: Spearman’s rho, GoodmanKruskal’s gamma, Kendall’s taub, Stuart’s tauc, Somers’ D
 Multiway tables: MantelHaenszel test
 Table of counts and percents
 Rowdependent and symmetric statistics
 Cell statistics
 Association measures for twoway tables along with confidence intervals; specified confidence level
 Standardized tables (twoway tables after controlling the effect of a third variable)
 Resampling – Bootstrap, without replacement, Jackknife
Correspondence Analysis
 Simple and multiple – raw data or data in tabular form
 Quick Graphs: vector and casewise plots
 Resampling – Bootstrap, without replacement, Jackknife
Loglinear Models
 Full maximum likelihood
 Pearson and likelihood ratio chisquare
 Expected values, lambda, SE lambda
 Covariance matrix, correlation matrix
 Deviates, Pearson deviates, Iikelihood deviates, FreemanTukey deviates, loglikelihood
 Resampling – Bootstrap, without replacement, Jackknife
 Dialog box with facility to type the desired model directly
Nonparametric Tests
 Independent samples: KruskalWallis, two sample KolmogorovSmirnov, MannWhitney
 Related variables; sign test, Wilcoxon signed rank test, Friedman test , Quade test
 Onesample: WaldWolfowitz runs test
 Onesample: KolmogorovSmirnov test providing 9 discrete and 28 continuous univariate distributions, also Lilliefors test
 Onesample: AndersonDarling test providing 29 continuous univariate distributions
 Resampling – Bootstrap, without replacement, Jackknife
Multinormal Tests
 ShapiroWilk (marginal) normality test
 Multivariate skewness and kurtosis, testing for significance of these
 HenzeZirkler test for multivariate normality
 Save Mahalanobis distances
 Quick Graph: beta QQ plot
Hypothesis Testing
 Mean: OneSample ztest, Twosample ztest, OneSample ttest, TwoSample ttest, Paired ttest, Poisson test with Bonferroni, DunnSidak adjustments
 Variance: Single Variance, Equality of Two Variances, Equality of Several Variances
 Correlation: Zero Correlation, Specific Correlation, Equality of Two Correlations
 Proportion: Single Proportion, Equality of Two Proportions
 Appropriate Quick Graphs
 Resampling – Bootstrap, without replacement, Jackknife
Correlations, Distances and Similarities
 Continuous data: Pearson correlations, covariance, SSCP
 Distance measures: Euclidean, cityblock, BrayCurtis, QSK
 Rank order data: Spearman, gamma, mu2, taub, tauc
 Unordered data: phi, Cramer’s V, contingency, GoodmanKruskal’s lambda, uncertainty coefficients
 Binomial data: S2, S3, S4, S5, S6, Tetrachoric, Anderberg (S7), Yule’s Q, Hamman, Dice, Sneath, Ochiai, Kulczynski, Gower2
 Missing data: pairwise, listwise deletion, EM
 Hadi outlier detection and estimation
 Probabilities: Bonferroni, DunnSidak
 Quick Graph: scatterplot matrix
 Resampling – Bootstrap, without replacement, Jackknife
 Bootstrap estimates, bias, standard error and confidence intervals, histograms of estimates in the case of Pearson correlations and rankordered data
Set and Canonical Correlation
 Whole, semi and bipartial set correlations
 Rao F, Rsquare, shrunk Rsquare, Tsquare, shrunk Tsquare, Psquare, shrunk Psquare, within, between and interset correlations
 Row/Column betas, standard errors, Tstatistics and probabilities
 StewartLove canonical redundancy index
 Canonical coefficients, loadings and redundancies
 Varimax rotation
 Resampling – Bootstrap, without replacement, Jackknife
Cronbach’s Alpha
 Cronbach’s alpha value for tow or more variables
 Resampling – Bootstrap, without replacement, Jackknife
Linear Regression
 Leastsquares
 Crossvalidation, saving residuals and diagnostics, DurbinWatson statistic
 Multiple linear regression
 Prediction for new observations
 Stepwise regression: automatic, customized and interactive stepping, partial correlations
 AIC, AICc, BIC computation
 Hypothesis testing, mixture models
 Automatic outlier and influential point detection
 Quick Graph: residuals vs. predicted values, fitted model plot in the case of one or two predictors (confidence and prediction intervals in the case of one predictor)
 Resampling – Bootstrap, without replacement, Jackknife
 Bootstrap estimates, bias, standard error and confidence intervals, histograms of estimates
 Bayesian
 Prior distribution: diffuse or (multivariate) normalgamma distribution
 Bayes estimates and credible intervals for regression coefficients computed
 Parameters of the posterior distribution provided
 Quick Graphs: plots of prior and posterior densities of regression coefficients
 Ridge
 Two types of ridge coefficients: standardized and unstandardized
 Quick Graph: plot of the ridge factor against the ridge coefficients
Robust Regression
 Least Absolute Deviation (LAD) regression
 M regression
 Least Median of Squares (LMS) regression
 Least Trimmed Squares (LTS) regression
 Scale (S) regression
 Rank Regression
Logistic Regression
 Binary, multinomial, discrete choice and conditional
 AIC, AICc, BIC computation
 Robust standard errors, prediction success table, derivatives table
 Classification table with specified cutoff point
 Dummy variables and interactions
 Forward, backward, automatic and interactive stepwise regression
 Deciles of risk, quantiles and simulation
 Hypothesis tests
 Quick Graph: ROC curve for binary logistic regression
Probit Regression
 Dummy variables and interactions
 AIC, AICc, BIC computation
Partial LeastSquares Regression
 Useful in situations where the number of variables is large relative to the number of cases or there is likely to be multicollinearity among the predictor variables
 NIPALS and SIMPLS algorithms
 Crossvalidation
TwoStage LeastSquares
 Model with independent and/or instrumental variables, with lags
 Diagnostic tests for heteroskedasticity and nonlinearity
 Polynomially distributed lags
 Hypothesis tests
Mixed Regression
 Hierarchical Linear Models (HLM)
 Specify effects as fixed or random
 Autocorrelated error structures
 Nested Models (2Level): Repeated Measures, Clustered Data
 Unbalanced or balanced data
 Quick Graph: scatterplot, histogram or scatterplot matrix of empirical Bayes estimates
Smooth & Plot
 126 nonparametric smoothers including LOESS
 Windows: fixed width or nearest neighbors
 Kernels: uniform, Epanechnikov, biweight, triweight, tricube, Gaussian, Cauchy
 Method: median, mean, polynomial, robust, trimmed mean
 Save predicted values and residuals
 Resampling – Bootstrap, without replacement, Jackknife
Nonlinear Regression
 GaussNewton, Quasi Newton, Simplex
 Output: predicted values, residuals, asymptotic standard errors and correlations, confidence curves and regions
 Special features: CookWeisberg confidence intervals, Wald intervals, Marquardting
 Robust estimation: absolute, power, trim, Huber, Hampel, t, bisquare, Ramsay, Andrews, Tukey
 Maximum likelihood estimation
 Piecewise regression, kinetic models, logistic model for quantal response data
 Exact derivatives
 Quick Graph: scatterplot with fitted curve
 Resampling – Bootstrap, without replacement, Jackknife
ANOVA
 Designs: unbalanced, randomized block, complete block, fractional factorial, mixed model, nested, split plot, Latin square, crossover and change over, Hotelling’s T2
 ANCOVA
 Means model for missing cells designs
 Repeated measures: oneway, two or more factors, three or more factors
 Options to test normality and homoscedasticity assumptions
 Type I , II and III sums of squares
 Automatic outlier and influential point detection
 AIC, AICc, BIC computation
 Multiple comparison tests – TukeyKramer HSD, Bonferroni, Fisher’s LSD, Scheffe, Dunnett, Sidak, Tukey’s b, Duncan, REGWQ, Hochberg GT2, Gabriel StudentsNewman_Keuls, Tamhane T2, GamesHowell, Dunnett’s T3
 Confidence intervals and hypothesis tests for adjacent difference, polynomial of specified order and metric, sum, custom, Helmert, reverse Helmert, deviation and simple contrasts
 Quick Graph: least squares means
 Resampling – Bootstrap, without replacement, Jackknife
MANOVA
 Handles wide variety of designs
 Performs repeated measures analysis
 Means model for missing cells designs
 Withingroup and betweengroup testing
 MANCOVA
 AIC, AICc, BIC computation
 Resampling – Bootstrap, without replacement, Jackknife
General Linear Model
 Any general linear model Y = XB+e
 Any general linear hypothesis ABC’ = D
 Mixed categorical and continuous variables
 Stepwise model building
 AIC, AICc, BIC computation
 Posthoc tests
 Resampling – Bootstrap, without replacement, Jackknife
 See also linear regression and ANOVA
Mixed Model Analysis
 Variance components and linear mixed model structures
 Estimates of parameters by:
 Maximum likelihood (ML)
 Restricted maximum likelihood (REML)
 MIVQUE(0) in the case of variance components
 ANOVA in the case of variance components
 Confidence intervals and hypothesis tests based on these estimates
 Structures of covariance matrix of random effects
 Variance components
 Diagonal
 Compound symmetry
 Unstructured
 Structures for error matrix:
 Variance components
 Compound symmetry
 AIC, AICc, BIC computation
Discriminant Analysis
 Classical Discriminant Analysis (Linear or quadratic)
 Prior probabilities, contrasts
 Output: F statistics, F matrix, eigenvalues, canonical correlations, canonical scores, classification matrix, Wilks’ lambda, LawleyHotelling, Pillai and Wilks’ trace, classification tables, including jackknifed, canonical variables, covariance and correlation matrix, posterior probabilities and Mahalanobis distances
 Stepwise modeling: automatic, forward, backward and interactive stepping
 Resampling – Bootstrap, without replacement, Jackknife
 Robust Discriminant Analysis
 Useful when the data sets are suspected to contain outliers
 Linear or quadratic analysis
 Save the robust Mahalanobis distance, weights, and predicted group membership
Cluster Analysis
 Hierarchical
 Distance measures: Euclidean, percent, gamma, Pearson, Rsquared, Minkowski, chisquare, phisquare, absolute, Anderberg, Jaccard, Mahalanobis, RT, Russel, SS
 Additional options to specify the covariance matrix for computing the Mahalanobis distance
 Linkage methods: single, complete, centroid, average, median, Ward, flexible beta, kneighborhood, uniform, weighted
 Cutting cluster tree based on specified nodes and tree height
 Five indices for cluster validity: RMSTTD, Dunn, DaviesBouldin, Pseudo F, Pseudo T2
 Quick Graphs: dendrogram, matrix and polar
 Resampling – Bootstrap, without replacement, Jackknife
 Kmeans and Kmedians
 Distance measures: Euclidean, MWSS, gamma, Pearson, Rsquared, Minkowski, chisquare, phisquare, absolute, Mahalanobis
 Additional options to specify the covariance matrix for computing the Mahalanobis distance
 Initial seeds can be specified from: None, first, last or random k, random or hierarchical segmentation, principal component, partition variable, from file
 Quick Graphs: parallel coordinate and mean/std deviation profile plots
 Additive trees
 Input: similarity, dissimilarity matrices
 Quick Graph: dendrogram
Factor Analysis
 Principal components, iterated principal axis, maximum likelihood
 Rotation: varimax, quartimax, equimax, orthomax, oblimin
 Resampling – Bootstrap, without replacement, Jackknife
Time Series
 Smoothing: LOWESS, moving average, running median, and exponential
 Seasonal adjustment
 Fourier and inverse Fourier transforms
 BoxJenkins ARIMA model
 Specify autoregressive, difference and moving average parameters
 Forecast and standard errors
 Polynomially distributed lags
 Trend Analysis: MannKendall test for nonseasonal data, and seasonal Kendall and Homogeneity tests with Sen slope estimator
 Quick Graphs: series plot, autocorrelation, partial autocorrelation, cross correlation, periodogram
Missing Value Analysis
 EM Algorithm
 Regression imputation
 Save estimates, correlation, covariance, SSCP matrices
 Resampling – Bootstrap, without replacement, Jackknife
Quality Analysis
 Histogram, Pareto Chart, BoxandWhisker Plot
 Control Charts: Run Chart, Shewhart Control Chart, Average Run Length, Operating Characteristic Curve, Cumulative Sum Chart, Moving Average, Expected Weighted Moving Average, XMR Chart, Regression Chart, TSQ
 Process Capability Analysis
Survival Analysis
 Nonparametric: KaplanMeier, NelsonAalen and actuarial life tables with confidence intervals
 Turnbull KM estimation (EM)
 Cumulative hazards and log cumulative hazards
 Cox regression, parametric models: exponential, accelerated exponential, Weibull, accelerated Weibull, lognormal, loglogistic
 Type I, II and III censoring
 Stratification, time dependent covariates
 Forward, backward, automatic and interactive stepwise regression
 AIC, AICc, BIC computation
 Quick Graphs: survival function, quantile, reliability and hazard plots, CoxSnell residual plot
Response Surface Methods
 Fits a second degree polynomial to one or more responses on several factors
 Output: regression coefficients, analysis of variance, tests of significance
 Optimum factor settings using canonical (for each response) or desirability (for all responses jointly) analysis,
 Quick Graphs: Desirability plots
 Contour and surface plots with fixed settings for one or more factors
Path Analysis (RAMONA)
 Analyze covariance or correlation matrices
 MWL (maximum Wishart likelihood)
 GLS (generalized leastsquares)
 OLS (ordinary leastsquares)
 ADFG (asymptotically distribution free estimate biased, Gramian)
 ADFU (unbiased)
Conjoint Analysis
 Monotonic, linear, log and power
 Stress and tau loss functions
 Quick Graph: utility function plot
 Resampling – Bootstrap, without replacement, Jackknife
Multidimensional Scaling
 Twoway scaling: Kruskal, Guttman, Young
 Threeway scaling: INDSCAL
 Nonmetric unfolding
 EM estimation
 Power scaling for ratio data
 Quick Graphs: MDS plot, Shepard diagram
Perceptual Mapping
 MDPREF
 Preference mapping (vector, circle, ellipse)
 Procrustes and canonical rotations
 Quick Graph: biplots
Partially Ordered Scalogram Analysis with Coordinates (POSAC)
 GuttmanShye algorithm; automatic serialization
 Quick Graph: item plot
 Resampling – Bootstrap, without replacement, Jackknife
Test Item Analysis
 Classical analysis
 One and twoparameter logistic model
 Quick Graph: item plot
Signal Detection Analysis
 Models: normal, Chisquare, exponential
 Quick Graph: receiver operating characteristic curve
Spatial Statistics
 2D & 3D variogram, Kriging and simulation
 Variogram types: semi, covariance, correlogram, general relative, pairwise relative, semilog, semimadogram
 Semivariogram models: spherical, exponential, gaussian, power and hole effect
 Kriging types: simple, ordinary, nonstationary and drift
 Quick Graphs: variogram and contour plot
 Resampling – Bootstrap, without replacement, Jackknife
Classification and Regression Trees
 Loss functions: leastsquares, trimmed mean, LAD, phi coefficient, Gini index, twoing
 Quick Graph: unique tree mobile including split statistics and color coded subgroup densities (box, dot, dit, jitter, stripe)
 Resampling – Bootstrap, without replacement, Jackknife
Monte Carlo (Addon)
 MersenneTwister random number generator
 Multivariate random sampling: multinomial, bivariate exponential, Dirichlet, multivariate normal, and Wishart distributions
 IID Monte Carlo: Two generic algorithms – rejection sampling and adaptive rejection sampling (ARS)
 Markov Chain Monte Carlo (MCMC): MetropolisHastings (MH) and Gibbs sampling algorithms
 Monte Carlo integration
Quality Analysis (Addon)
 Gauge R & R studies
 Sigma measurements
 Taguchi’s loss function
 Taguchi’s online control – beta correction, taguchi’s loss/savings