Grafiti LLC

SYSTAT 13.2 Statistics

Statistics

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
  • Bootstrap estimates, bias, standard error and confidence intervals, histograms of estimates
  • Resampling – Bootstrap, without replacement, Jackknife

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

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

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

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

Random Sampling

  • Mersenne-Twister random number generator
  • Random Sampling from a list of 9 univariate discrete and 28 univariate continuous distributions with given parameters

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

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

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

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

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

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

Correspondence Analysis

  • Simple and multiple – raw data or data in tabular form
  • Quick Graphs: vector and casewise plots
  • 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

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

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

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

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

Cronbach’s Alpha

  • Cronbach’s alpha value for tow or more variables
  • Resampling – Bootstrap, without replacement, Jackknife

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

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

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
  • Cross validation

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

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

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
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