Probability Calculator

• Computes probability density function, cumulative distribution function, inverse cumulative distribution function, and upper-tail 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

• Mersenne-Twister 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 add-on module.)

Design of Experiments

• Choose between Classic and Advanced DOE with dynamic wizard
• Optimal Designs
• Complete and incomplete factorial designs
• Latin square designs, 3-12 levels per factor
• Box and Hunter 2-level incomplete designs
• Taguchi designs
• Plackett and Burman designs
• Mixture: lattice, centroid, axial, and screening
• Response surface designs: Box-Behnken 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, t-tests, z-tests, ANOVA (one-way and two-way), and generic designs
• Conforms to the Hypothesis tests on means and their various options
• One-sided and two-sided 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
  • Shapiro-Wilk normality test
  • Anderson-Darling normality test
  • Multivariate skewness and kurtosis, testing for significance of these
  • Henze-Zirkler 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
  • Stem-and-Leaf 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
  • Shapiro-Wilk normality test
  • Anderson-Darling normality test
  • Multivariate skewness and kurtosis, testing for significance of these
  • Henze-Zirkler 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
  • Stem-and-Leaf 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
• Chi-squared and Kolmogorov-Smirnov goodness-of-fit tests; Shapiro-Wilk 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 chi-square, 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, Goodman-Kruskal's lambda, and uncertainty coefficients
• r x c ordered levels: Spearman's rho, Goodman-Kruskal's gamma, Kendall's tau-b, Stuart's tau-c, Somers' D
• Multiway tables: Mantel-Haenszel test
• Table of counts and percents
• Row-dependent and symmetric statistics
• Cell statistics
• Association measures for two-way tables along with confidence intervals; specified confidence level
• Standardized tables (two-way 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 chi-square
• Expected values, lambda, SE lambda
• Covariance matrix, correlation matrix
• Deviates, Pearson deviates, Iikelihood deviates, Freeman-Tukey deviates, log-likelihood
• Resampling - Bootstrap, without replacement, Jackknife
• Dialog box with facility to type the desired model directly

Nonparametric Tests

• Independent samples: Kruskal-Wallis, two- sample Kolmogorov-Smirnov, Mann-Whitney
• Related variables; sign test, Wilcoxon signed rank test, Friedman test , Quade test
• One-sample: Wald-Wolfowitz runs test
• One-sample: Kolmogorov-Smirnov test providing 9 discrete and 28 continuous univariate distributions, also Lilliefors test
• One-sample: Anderson-Darling test providing 29 continuous univariate distributions
• Resampling - Bootstrap, without replacement, Jackknife

Multinormal Tests

• Shapiro-Wilk (marginal) normality test
• Multivariate skewness and kurtosis, testing for significance of these
• Henze-Zirkler test for multivariate normality
• Save Mahalanobis distances
• Quick Graph: beta Q-Q plot

Hypothesis Testing

• Mean: One-Sample z-test, Two-sample z-test, One-Sample t-test, Two-Sample t-test, Paired t-test, Poisson test with Bonferroni, Dunn-Sidak 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, city-block, Bray-Curtis, QSK
• Rank order data: Spearman, gamma, mu2, tau-b, tau-c
• Unordered data: phi, Cramer's V, contingency, Goodman-Kruskal'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, Dunn-Sidak
• 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 rank-ordered data

Set and Canonical Correlation

• Whole, semi and bi-partial set correlations
• Rao F, R-square, shrunk R-square, T-square, shrunk T-square, P-square, shrunk P-square, within, between and inter-set correlations
• Row/Column betas, standard errors, T-statistics and probabilities
• Stewart-Love 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

• Least-squares
  • Crossvalidation, saving residuals and diagnostics, Durbin-Watson 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) normal-gamma 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 Least-Squares 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

Two-Stage Least-Squares

• 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 (2-Level): Repeated Measures, Clustered Data
• Unbalanced or balanced data
• Quick Graph: scatterplot, histogram or scatterplot matrix of empirical Bayes estimates

Smooth & Plot

• 126 non-parametric 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

• Gauss-Newton, Quasi Newton, Simplex
• Output: predicted values, residuals, asymptotic standard errors and correlations, confidence curves and regions
• Special features: Cook-Weisberg 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: one-way, 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 - Tukey-Kramer HSD, Bonferroni, Fisher's LSD, Scheffe, Dunnett, Sidak, Tukey's b, Duncan, R-E-G-W-Q, Hochberg GT2, Gabriel Students-Newman_Keuls, Tamhane T2, Games-Howell, 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
• Within-group and between-group 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
• Post-hoc 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, Lawley-Hotelling, 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, R-squared, Minkowski, chi-square, phi-square, 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, k-neighborhood, uniform, weighted
  • Cutting cluster tree based on specified nodes and tree height
  • Five indices for cluster validity: RMSTTD, Dunn, Davies-Bouldin, Pseudo F, Pseudo T2
  • Quick Graphs: dendrogram, matrix and polar
  • Resampling - Bootstrap, without replacement, Jackknife
• K-means and K-medians
  • Distance measures: Euclidean, MWSS, gamma, Pearson, R-squared, Minkowski, chi-square, phi-square, 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
• Box-Jenkins ARIMA model
• Specify autoregressive, difference and moving average parameters
• Forecast and standard errors
• Polynomially distributed lags
• Trend Analysis: Mann-Kendall 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, Box-and-Whisker Plot
• Control Charts: Run Chart, Shewhart Control Chart, Average Run Length, Operating Characteristic Curve, Cumulative Sum Chart, Moving Average, Expected Weighted Moving Average, X-MR Chart, Regression Chart, TSQ
• Process Capability Analysis

Survival Analysis

• Nonparametric: Kaplan-Meier, Nelson-Aalen 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, log-logistic
• 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, Cox-Snell 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 least-squares)
• OLS (ordinary least-squares)
• 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

• Two-way scaling: Kruskal, Guttman, Young
• Three-way scaling: INDSCAL
• Non-metric 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)

• Guttman-Shye algorithm; automatic serialization
• Quick Graph: item plot
• Resampling - Bootstrap, without replacement, Jackknife

Test Item Analysis

• Classical analysis
• One- and two-parameter logistic model
• Quick Graph: item plot

Signal Detection Analysis

• Models: normal, Chi-square, exponential
• Quick Graph: receiver operating characteristic curve

Spatial Statistics

• 2D & 3D variogram, Kriging and simulation
• Variogram types: semi, covariance, correlogram, general relative, pairwise relative, semi-log, 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: least-squares, 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 (Add-on)

• Mersenne-Twister 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): Metropolis-Hastings (M-H) and Gibbs sampling algorithms
• Monte Carlo integration

Quality Analysis (Add-on)

• Gauge R & R studies
• Sigma measurements
• Taguchi's loss function
• Taguchi's online control - beta correction, taguchi's loss/savings

	Added in SYSTAT Version 12
	Enhanced in SYSTAT Version 12