Statistics Toolbox Getting Started Introduction What Is the Statistics Toolbox? Primary Topic Areas Random Number Generators in the Statistics Toolbox Mathematical Notation Examples Probability Distributions Introduction Displaying Probability Distributions and Random Samples Probability Distributions Demo Random Sample Generation Demo Overview of the Functions Probability Density Function (pdf) Cumulative Distribution Function (cdf) Inverse Cumulative Distribution Function Random Number Generator Mean and Variance as a Function of Parameters Distribution Fitting Tool Main Window of the Distribution Fitting Tool Example: Fitting a Distribution Creating and Managing Data Sets Creating a New Fit Displaying Results Managing Fits Evaluating Fits Excluding Data Saving and Loading Sessions Generating an M-File to Fit and Plot Distributions Using Custom Distributions Additional Distributions Available in the Distribution Fitting Tool Overview of the Distributions Reproducing the Output of Random Number Functions Beta Distribution Binomial Distribution Chi-Square Distribution Noncentral Chi-Square Distribution Discrete Uniform Distribution Exponential Distribution Extreme Value Distribution F Distribution Noncentral F Distribution Gamma Distribution Geometric Distribution Hypergeometric Distribution Lognormal Distribution Negative Binomial Distribution Normal Distribution Poisson Distribution Rayleigh Distribution Student's t Distribution Noncentral t Distribution Uniform (Continuous) Distribution Weibull Distribution Descriptive Statistics Measures of Central Tendency (Location) Measures of Dispersion Functions for Data with Missing Values (NaNs) Function for Grouped Data Percentiles and Graphical Descriptions Percentiles Probability Density Estimation Empirical Cumulative Distribution Function The Bootstrap Linear Models Introduction One-Way Analysis of Variance (ANOVA) Example: One-Way ANOVA Multiple Comparisons Example: Multiple Comparisons Two-Way Analysis of Variance (ANOVA) Example: Two-Way ANOVA N-Way Analysis of Variance Example: N-Way ANOVA with Small Data Set Example: N-Way ANOVA with Large Data Set ANOVA with Random Effects Setting Up the Model Fitting a Random Effects Model F Statistics for Models with Random Effects Variance Components Analysis of Covariance The aoctool Demo Multiple Linear Regression Mathematical Foundations of Multiple Linear Regression Example: Multiple Linear Regression Polynomial Curve Fitting Demo Quadratic Response Surface Models Exploring Graphs of Multidimensional Polynomials Stepwise Regression Stepwise Regression Demo Generalized Linear Models Example: Generalized Linear Models Generalized Linear Model Demo Robust and Nonparametric Methods Robust Regression Kruskal-Wallis Test Friedman's Test Nonlinear Regression Models Nonlinear Least Squares Example: Nonlinear Modeling An Interactive GUI for Nonlinear Fitting and Prediction Regression and Classification Trees Multivariate Statistics Principal Components Analysis Example: Principal Components Analysis The Principal Component Coefficients (First Output) The Component Scores (Second Output) The Component Variances (Third Output) Hotelling's T2 (Fourth Output) Visualizing the Results of a Principal Components Analysis -- The Biplot Factor Analysis Example: Finding Common Factors Affecting Stock Prices Factor Rotation Predicting Factor Scores Visualizing the Results of a Factor Analysis -- The Biplot Comparison of Factor Analysis and Principal Components Analysis Multivariate Analysis of Variance (MANOVA) Example: Multivariate Analysis of Variance Cluster Analysis Hierarchical Clustering K-Means Clustering Multidimensional Scaling Overview Classical Multidimensional Scaling Nonclassical Metric Multidimensional Scaling Nonmetric Multidimensional Scaling Example -- Reconstructing a Map from Intercity Distances Hypothesis Tests Introduction Hypothesis Test Terminology Hypothesis Test Assumptions Example: Hypothesis Testing Available Hypothesis Tests Statistical Plots Introduction Box Plots Distribution Plots Normal Probability Plots Quantile-Quantile Plots Weibull Probability Plots Empirical Cumulative Distribution Function (CDF) Scatter Plots Statistical Process Control Control Charts Xbar Charts S Charts EWMA Charts Capability Studies Design of Experiments Introduction Full Factorial Designs Fractional Factorial Designs Response Surface Designs Central Composite Designs Box-Behnken Designs Design of Experiments Demo D-Optimal Designs Generating D-Optimal Designs Augmenting D-Optimal Designs Designing Experiments with Uncontrolled Inputs Controlling Candidate Points Including Categorical Factors Hidden Markov Models Introduction Example of a Hidden Markov Model Markov Chains How the Toolbox Generates Random Sequences Analyzing a Hidden Markov Model Setting Up the Model and Generating Data Computing the Most Likely Sequence of States Estimating the Transition and Emission Matrices Calculating Posterior State Probabilities Changing the Probabilities of the Initial States Example: Changing the Initial Probabilities References Functions -- Categorical List Probability Distributions Descriptive Statistics Statistical Plotting Statistical Process Control Linear Models Nonlinear Regression Design of Experiments Multivariate Statistics Decision Tree Techniques Hypothesis Tests Distribution Testing Nonparametric Testing Hidden Markov Models File I/O Demonstrations Data Utility Functions -- Alphabetical List Selected Bibliography Recommended Reading Other References Cited Release Notes Statistics Toolbox 5.0.2 Release Notes New Features Cophenetic Correlation Major Bug Fixes Statistics Toolbox 5.0.1 Release Notes New Features New nancov Function regstats Function Returns Two New Statistics Major Bug Fixes Statistics Toolbox 5.0 Release Notes New Features Distribution Fitting Tool New Functions N-Dimensional Support for Functions Enhancements to Function mle Enhancement to Other Functions Major Bug Fixes Statistics Toolbox 4.1 Release Notes New Features Improved N-way Analysis of Variance Hidden Markov Model Functions New Functions for Weibull Distributions New Functions for Extreme Value Distributions Distribution Functions that Now Accept Censored Data New Stepwise Regression Tools and Improved GUIs New Utility Functions for Statistics Options Major Bug Fixes Upgrading from an Earlier Release New Format of Terms Output for anovan Might Cause Errors in Existing Code Statistics Toolbox 4.0 Release Notes New Features Multivariate Analysis Nonlinear Regression Models Probability Distributions Descriptive Statistics Design of Experiments Function Summary Major Bug Fixes Upgrading from an Earlier Release Linear and Quadratic Discriminant Analysis Added to classify Use playshow Command to Run glmdemo Statistics Toolbox 3.0 Release Notes New Features Summary of Enhancements New Functions New Demos New Sample Data Files Updated Functions for ANOVA-Type Tables Other Updated Functions Printable Documentation (PDF) Product Page (Web)