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Statistics
(Letters in orange color are new features in Version 11 of Systat)
Descriptive Statistics
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Column
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Mean, median, sum and number of cases |
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Min, max, range and variance |
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Coefficient of variation, std err of mean |
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Adjustable confidence intervals of mean |
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Skewness, kurtosis, including standard errors |
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Shapiro-Wilk normality test |
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N- & P- Tiles: Cleveland, Weighted average 1, Weighted average 2, Weighted average 3, Empirical CDF, Empirical CDF (average), Closest |
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Stem-and-Leaf display |
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Resampling Bootstrap, without replacement, Jackknife |
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Row
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Mean, median, sum and number of cases |
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Min, max, range and variance |
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Coefficient of variation, std err of mean |
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Adjustable confidence intervals of mean |
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Skewness, kurtosis, including standard errors |
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Shapiro-Wilk normality test |
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N- & P- Tiles: Cleveland, Weighted average 1, Weighted average 2, Weighted average 3, Empirical CDF, Empirical CDF (average), Closest |
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Stem-and-Leaf display |
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Resampling Bootstrap, without replacement, Jackknife |
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Fitting Distribution
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Discrete Uniform, Zipf, Geometric, Hypergeometric, Negative Binomial, Poisson, Binomial |
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Continuous Triangular, Double exponential (Laplace), Cauchy, Gumbel, Gompertz, Lognormal, Pareto, Rayleigh, Inverse Gaussian, Lognormal, Uniform, Beta, Normal, Chi-square, Weibull, Exponential, Logistic, Gamma |
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QuickGraphs: graph of the respective observed and expected observations |
Crosstabulation and measures of association
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One-, two-way and multiway tables |
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Row and column frequencies, percents, expected values and deviates |
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List layouts, order categories, define intervals, including missing intervals |
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2 x 2 tables: likelihood ratio chi square, Yates, Fishers, odds ratio, Yules Q |
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R x R tables: McNemars test, Cohens kappa |
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R x C tables: unordered levels, phi, Cramers V, contingency coefficient, uncertainty coefficient, Goodman - Kruskals lambda |
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R x C ordered levels: rho, Goodman-Kruskals gamma, Kendalls tau-b, Stuart s tau-c, Somers D |
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Others: Mantel-Haenszel test, Cochran test |
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Resampling Bootstrap, without replacement, Jackknife |
Correlations, distances and similarities
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Continuous data: Pearson correlations, Euclidean, city, Bray-Curtis, QSK |
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Rank order data: Spearman, gamma, mu2, tau |
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Binomial data: S2, S3, S4, S5, S6 |
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Missing data: pairwise, listwise deletion, EM |
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Hadi outlier detection and estimation |
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Probabilities: Bonferroni, Dunn-Sidak |
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Tetrachoric correlations |
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QuickGraph: scatterplot matrix |
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Resampling Bootstrap, without replacement, Jackknife |
Set and canonical correlations
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Whole, semi and bipartial set correlations |
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Rao F, R-Square, Shrunk R-Square, T-Square, Shrunk T-Square, P-Square, Shrunk P-Square Within, between and inter set correlations |
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Row/Column betas, standard errors, T-statistics and probabilities |
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Stewart-Love canonical redundancy index |
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Canonical coefficients, loadings and redundancies |
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Varimax rotation |
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Resampling Bootstrap, without replacement, Jackknife |
Missing Value Analysis
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EM Algorithm |
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Regression imputation |
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Save estimates, correlation, covariance, SSCP matrices |
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Resampling Bootstrap, without replacement, Jackknife |
Loglinear models
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Full maximum likelihood |
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Pearson and likelihood ratio chi-square |
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Expected values, lambda, SE lambda |
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Covariance matrix, correlation matrix |
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Deviates, Pearson deviates, Iikelihood deviates, Freeman Tukey deviates, log likelihood |
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Resampling Bootstrap, without replacement, Jackknife |
Linear regression
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Least squares
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Cross validation, saving residuals and diagnostics, Durbin-Watson statistic |
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Multiple linear regression |
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Stepwise regression: automatic, customized and interactive stepping, partial correlations |
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Hypothesis testing, mixture models |
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Automatic outlier and influential point detection |
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QuickGraph: residuals vs. predicted values |
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Resampling Bootstrap, without replacement, Jackknife |
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Bayesian
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Prior distribution - (multivariate) normal-gamma distribution |
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Bayes estimates and credible intervals for regression coefficients computed |
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Parameters of the posterior distribution provided |
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Plots of prior and posterior densities of regression coefficients |
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Ridge |
Robust regression
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Least Median of Squares (LMS) regression |
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Rank Regression |
Logistic regression
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Binary, multinomial, discrete choice and conditional |
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Quasi maximum likelihood |
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Dummy variables and interactions |
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Deciles of risk, quantiles and simulation |
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Forward, backward, automatic and interactive stepwise regression |
Probit
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Dummy variables and interactions |
Nonlinear regression
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Gauss Newton, Quasi Newton, simplex |
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Output: predicted values, residuals, asymtotic standard errors and correlations, confidence curves and regions |
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Special features: Cook-Weisberg confidence intervals, Wald intervals, Marquardting |
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Robust estimation: absolute, power, trim, Huber, Hampel, t, bisquare, Ramsay, Andrews, Tukey |
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Maximum likelihood estimation |
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Piecewise regression, kinetic models, logistic model for quantal response data |
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Exact derivatives |
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QuickGraph: scatterplot with fitted curve |
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Resampling Bootstrap, without replacement, Jackknife |
Two stage least squares
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Heteroscedasticity-consistent standard errors |
Smooth & Plot
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126 non-parametric smoothers including LOESS |
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Windows: fixed width or nearest neighbors |
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Kernels: uniform, Epanechnikov, biweight, triweight, tricube, Gaussian, Cauchy |
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Method: median, mean, polynomial, robust, trimmed mean |
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Save predicted values and residuals |
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Resampling Bootstrap, without replacement, Jackknife |
Mixed Regression
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Hierarchical Linear Models (HLM) |
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Specify effects as fixed or random |
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Autocorrelated error structures |
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Nested Models (2-Level): Repeated Measures, Clustered Data |
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Unbalanced or balanced data |
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QuickGraph: Scatterplot matrix of empirical Bayes estimates |
Hypothesis Testing
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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 |
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Variance: Single Variance, Equality of Two Variances, Equality of Several Variances |
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Correlation: Zero Correlation, Specific Correlation, Equality of Two Correlations |
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Proportion: Single Proportion, Equality of Two Proportions |
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Appropriate QuickGraphs |
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Resampling Bootstrap, without replacement, Jackknife |
ANOVA
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One-way ANOVA: multiple tests, Bonferroni, Tukey-Kramer HSD, Scheffe, Fishers LSD |
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Two-way ANOVA: post hoc tests on least squares means (Bonferroni, Tukey, LSD, Scheffe) |
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Repeated measures: one-way, two or more factors, three or more factors |
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Designs: unbalanced, randomized block, complete block, fractional factorial, mixed model, nested, split plot, Latin square, crossover and change over, Hotellings T2 |
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ANCOVA |
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Means model for missing cells designs |
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Automatic outlier and influential point detection |
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QuickGraph: least squares means |
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Resampling Bootstrap, without replacement, Jackknife |
General linear model
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Any general linear model Y = XB+e |
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Any general linear hypothesis ABC = D |
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Mixed categorical and continuous variables |
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Stepwise model building |
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Post-hoc tests |
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See also linear regression and ANOVA |
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Resampling Bootstrap, without replacement, Jackknife |
Quality Analysis
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Histogram, Pareto Chart, Box-and-Whisker Plot |
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Gauge R&R Studies |
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Process Capability Analysis |
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Sigma Measurements |
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Taguchis On-Line SPC |
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Signal-to-Noise Ratio Analysis of Taguchi designs |
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Control Charts: Run Chart, Shewart Control Chart, Average Run Length, Operating Characteristic Curve, Cumulative Sum Chart, Moving Average, Expected Weighted Moving Average, X-MR Chart, Regression Chart, TSQ, Run Tests |
Nonparametric tests
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Independent samples: Kruskal-Wallis, two- sample Kolmogorov-Smirnov, Mann-Whitney |
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Related variables; sign test, Wilcoxon signed rank test, Friedman test |
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One-sample: Kolmogorov-Smirnov, Wald-Wolfowitz runs test, Shapiro-Wilk normality test |
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Resampling Bootstrap, without replacement, Jackknife |
MANOVA
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Handles wide variety of designs |
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Performs repeated measures analysis |
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Means model for missing cells designs is available |
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Within-group and between-group testing is now part of menus |
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MANCOVA |
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Resampling Bootstrap, without replacement, Jackknife |
Factor analysis
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Principal components, iterated principal axis, maximum likelihood |
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Rotation: varimax, quartimax, equimax, orthomax, oblimin |
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Resampling Bootstrap, without replacement, Jackknife |
Discriminant analysis
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Classical Discriminant Analysis (Linear or quadratic)
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Prior probabilities, contrasts |
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Output: F statistics, F matrix, eigenvalues, canonical correlations, canonical scores, classification matrix, Wilk s lambda, Lawley-Hotelling, Pillai and Wilks trace, classification tables, including jackknifed, canonical variables, covariance and correlation matrix, posterior probabilities and Mahalanobis distances |
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Stepwise modeling: automatic, forward, backward and interactive stepping |
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Resampling Bootstrap, without replacement, Jackknife |
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Robust Discriminant Analysis (Linear or quadratic) |
Cluster analysis
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Hierarchical
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Euclidean, percent, gamma, Pearson, R-squared, Minkowski, chi-square, phi-square |
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Linkage methods: single, complete, centroid, average, median and Ward |
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QuickGraphs: dendrogram, matrix and polar |
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Resampling Bootstrap, without replacement, Jackknife |
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K-means
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Euclidean, MWSS, gamma, Pearson, R-squared, Minkowski, chi-square, phi-square |
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QuickGraphs: parallel coordinate and mean/std deviation profile plots |
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Additive trees
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Input: similarity, dissimilarity matrices |
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QuickGraphs: dendrogram |
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Correspondence analysis
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Simple and multiple |
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QuickGraphs: vector and casewise plots |
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Resampling Bootstrap, without replacement, Jackknife |
Classification and regression trees
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Loss functions: least squares, trimmed mean, LAD, phi coefficient, Gini index, twoing |
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QuickGraph: unique tree mobile including split statistics and color coded subgroup densities (box, dot, dit, jitter, stripe) |
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Resampling Bootstrap, without replacement, Jackknife |
Cronbachs alpha
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Resampling Bootstrap, without replacement, Jackknife |
Test item analysis
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Classical analysis |
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One and two parameter logistic model |
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QuickGraph: item plot |
Multidimensional scaling
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Two-way scaling: Kruskal, Guttman, Young |
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Three-way scaling: INDSCAL |
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Nonmetric, nonmetric unfolding |
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EM estimation |
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Power scaling for ratio data |
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QuickGraphs: MDS plot, Shepard diagram |
Partially Ordered Scalogram Analysis with Coordinates (POSAC)
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Guttman-Shye algorithm; automatic seriation |
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QuickGraph: item plot |
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Resampling Bootstrap, without replacement, Jackknife |
Perceptual mapping
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MDPREF |
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Preference mapping (vector, circle, ellipse) |
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Procrustes and canoncial rotations |
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QuickGraph: biplots |
Conjoint analysis
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Monotonic, linear, log and power |
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Stress and Tau loss functions |
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QuickGraph: utility function plot |
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Resampling Bootstrap, without replacement, Jackknife |
Time series
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Smoothing: LOWESS, moving average, running median, and exponential |
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Seasonal adjustment |
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Fourier and inverse Fourier transforms |
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Box-Jenkins ARIMA model |
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Specify autoregressive, difference and moving average parameters |
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Forecast and standard errors |
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Polynomially distributed lags |
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QuickGraphs: series plot, autocorrelation, partial autocorrelation, cross correlation, periodogram |
Spatial Statistics
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2D & 3D variogram, Kriging and simulation |
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Variogram types: semi, covariance, correlogram, general relative, pairwise relative, semi-log, semimadogram |
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Semivariogram models: spherical, exponential, gaussian, power and hole effect |
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Kriging types: simple, ordinary, nonstationary and drift |
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QuickGraphs: variogram and contour plot |
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Resampling Bootstrap, without replacement, Jackknife |
Signal detection analysis
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Models: normal, Chi-square, exponential |
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QuickGraph: receiver operating characteristic curve |
Survival Analysis
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Kaplan-Meier and actuarial life tables |
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Turnbull KM estimation (EM) |
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Cumulative hazards and log cum hazard s |
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Cox regression, parametric models: exponential, accelerated exponential, Weibull, accelerated Weibull, lognormal, logistic |
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Type I, II and III censoring |
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Stratification, time dependent covariates |
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Forward, backward, automatic and interactive stepwise regression |
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QuickGraphs: survival, quantile, reliability and hazard |
Path analysis (RAMONA)
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Analyze covariance or correlation matrices |
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MWL (maximum Wishart likelihood) |
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GLS (generalized least squares) |
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OLS (ordinary least squares) |
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ADFG (asymptotically distribution free estimate biased, Gramian) |
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ADFU (unbiased) |
Monte Carlo
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Random Sampling from a list of 33 distributions (univariate discrete, univariate continuous and multivariate) with given parameters |
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IID Monte Carlo consists of two generic algorithms, viz., Rejection Sampling and Adaptive Rejection Sampling (ARS) |
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Markov Chain Monte Carlo (MCMC) algorithms: Metropolis-Hastings (M-H) algorithm and the Gibbs sampling algorithm |
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Monte Carlo Integration |
Probability Calculator
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Computes probability density function, cumulative distribution function, inverse cumulative distribution function, and upper-tail probabilities for a wide variety of univariate discrete and continuous probability distributions |
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QuickGraphs: graph of the probability density function and the cumulative distribution function for continuous distributions |
Design of experiments
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Choose between Classic and Advanced DOE with dynamic wizard |
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Central composite designs |
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Optimal Designs |
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Complete and incomplete factorial designs |
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Latin square designs, 3-12 levels per factor |
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Box and Hunter 2-level incomplete designs |
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Taguchi designs |
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Plackett and Burman designs |
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Box and Behnken designs |
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Mixture: lattice, centroid, axial, screening |
Power Analysis
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Determine sample size to achieve a specified power |
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Determine power for a single sample size or a range of sample sizes |
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Proportions, correlations, t-tests, z-tests, ANOVA (one-way, two-way), generic designs |
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Conforms to the Hypothesis tests on means and their various options |
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Previously only for two-sided alternatives, now for one-sided alternatives also |
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QuickGraph: power curve |
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Graphs
(Letters in orange color are new features in Version 11 of Systat)
General
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Systat 11 now makes use of Microsofts 16M color palette |
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New interactive Graph Editor |
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Displaying Each Individual Element Name (e.g. Line Plot, Histogram, X-axis Legend etc.) on moving the Mouse over the Editor |
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Interactive Aesthetic change (Line style, Fill Style Font & Color) of each element while editing by clicking Right Button of mouse |
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Editing Text by double clicking on the text elements |
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Interactive changing of coordinate system |
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Interactive Axis settings and showing or hiding of Grid Lines |
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Different formats for legends and changing the formats from graph editor |
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Changing Axis variable to produce another graph from the graph editor |
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Automatic and Mouse Interactive animation for three dimensional graphs |
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New added saving formats for graph Image GIF, TIFF, PS, PNG |
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A whole new Zoom In & Out feature with selection Zoom and Zooming individual axis and moving in the graph by holding and dragging the graph using mouse |
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Newly added Annotation Objects: Ploy Line and Arrow |
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Setting Error Bar Parameters from Graph editor and also Anchor Bars |
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Changing gradient in surface plots |
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Overlay an unlimited number of graphs |
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Automatically plot and color subgroups side-by-side or overlaid |
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Page view, drawing objects and annotations |
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Point-and-click editing for graph location, scale, axis labels, titles, colors, symbols, and more |
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Save charts to BMP, EPS, EMF, JPG, PICT, WMF and CGM |
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Graph Gallery for automatic graph creation |
Interactive EDA
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QuickGraphs automatically graph results |
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Dynamic Explorer: 3-D rotation, power and log transformations, confidence intervals, smoothing parameter, bars on bar chart |
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Select cases with lasso across all charts and in data editor |
Bar, dot, line, pie, profile and pyramid charts
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Plot Medians instead of mean for Bar, Dot, Line, Profile and Pyramid graphs |
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Bar: 2-D, 3-D, stacked, error bars, repeated measures, percent, polar, mirror, mosaic |
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Dot: 2-D, 3-D, line connected, error bars, repeated measures, percent, polar, mirror |
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Line: 2-D, 3-D, errors, rep measures, %, mirror |
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Pie: 2-D, 3-D, concentric rings, offset slice |
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Profile: 2-D, 3-D, stacked, rep measures, %, mirror |
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Pyramid: 2-D, 3-D, rep measures, %, mirror |
Histograms, box and density plots
| 2-D displays |
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Box Plot: box and whisker, notched, dot/box |
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Dot/Densities: dit, symmetric dit (dot), jitter, fuzzy and stripe |
| 2-D/3-D displays |
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Histogram: counts, cumulative counts, control bars/widths |
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Normal and Kernel densities |
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Contour and mosaic plots |
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Data driven or specified intervals |
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Pseudo 3-D displays, mirror plots |
Scatterplots and scatterplot matrices
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Repeated measures |
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Smoothers (2-D/3-D): linear, quadratic, DWLS, step, nexpo, inverse, Andrews, bisquare, Huber, Kriging |
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Smoother residuals and tension parameter |
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Line connected, mini spanning tree, traveling salesman path, Voronoi tessellation, Delaunay triangles, vectors, spikes |
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Size points by influence, sunflower symbols |
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Spherical/Polar and triangular coordinates |
Other 2-D plot and SPLOM options
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Smoothers: log, power, LOWESS, spline, mean, median, mode, midrange, trimmed mean |
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Confidence interval contours: Bivariate ellipsoid, bivariate centroid CI, regression line CI, kernel density |
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Display univariate densities on borders: histogram, box, box/dot, dot, dit, frequency polygon, normal, kernel, fuzzy, stripe, jitter |
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High-low-close plots (2-D) |
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Mirror plots (2-D) |
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Geographic projections (2-D): Gnomonic, stereo, Mercator, ortho, Lambert, Robinson, sinusoidal, Miller, Peters, fish-eye |
Quantile and probability plots
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See 2-D scatterplot options above |
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28 theoretical densities |
Maps
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Present statistical data on maps |
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US: states, counties, metro areas, census tracts, and related demographics |
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World: continents, nations, West European provinces |
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Nine geographic projections |
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Import Arc View map and data files |
Additional graphs
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Multiplots: based on Trellis plots, multiple displays based on grouping variables for bar, dot, line, pplot, plot, profile pyramid and qplot graphs |
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Icon plots: Chernoff faces, Fourier blobs, histograms, profiles, thermometers, weather vanes, stars, arrows |
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Parallel coordinate and Andrews Fourier |
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Function plots: specify any function and new functions relating to distributions |
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