Statistics Toolbox

Preface

How to Use This Guide

This guide introduces the MATLAB statistics environment through the toolbox functions. It describes the functions with regard to particular areas of interest, such as probability distributions, linear and nonlinear models, principal components analysis, design of experiments, statistical process control, and descriptive statistics. It also describes use of the graphical tools.

Introduction
Introduces the toolbox, and explains the mathematical notation it uses.

Probability Distributions
Describes the distributions and the distribution-related functions supported by the toolbox.

Descriptive Statistics
Explores toolbox features for working with descriptive statistics such as measures of location and spread, percentile estimates, and data with missing values.

Linear Models
Describes toolbox support for one-way, two-way, and higher-way analysis of variance (ANOVA), analysis of covariance (ANOCOVA), multiple linear regression, stepwise regression, response surface prediction, ridge regression, and one-way multivariate analysis of variance (MANOVA). It also describes support for nonparametric versions of one- and two-way ANOVA, and multiple comparisons of the estimates produced by ANOVA and ANOCOVA functions.

Nonlinear Regression Models
Discusses parameter estimation, interactive prediction and visualization of multidimensional nonlinear fits, and confidence intervals for parameters and predicted values. It also introduces classification and regression trees as a way to approximate a regression relationship.

Hypothesis Tests
Describes support for common tests of hypothesis - t-tests, Z-tests, nonparametric tests, and distribution tests.

Multivariate Statistics
Explores toolbox features that support methods in multivariate statistics, including principal components analysis, factor analysis, one-way multivariate analysis of variance, cluster analysis, and classical multidimensional scaling.

Statistical Plots
Describes box plots, normal probability plots, Weibull probability plots, control charts, and quantile-quantile plots which the toolbox adds to the arsenal of graphs in MATLAB. It also discusses extended support for polynomial curve fitting and prediction, creation of scatter plots or matrices of scatter plots for grouped data, interactive identification of points on such plots, and interactive exploration of a fitted regression model.

Statistical Process Control
Discusses the plotting of common control charts and the performing of process capability studies.

Design of Experiments
Discusses toolbox support for full and fractional factorial designs, response surface designs, and D-optimal designs. It also describes functions for generating designs, augmenting designs, and optimally assigning units with fixed covariates.

Demos
Describes GUIs that enable you to explore the probability distributions, random number generation, curve fitting, and design of experiments functions.

Functions -- By Category
Lists the functions for each area supported by the toolbox.

Functions -- Alphabetical List
Lists the functions in alphabetical order.

Selected Bibliography
Lists published materials that support concepts described in this guide.

Introduction	Introduces the toolbox, and explains the mathematical notation it uses.
Probability Distributions	Describes the distributions and the distribution-related functions supported by the toolbox.
Descriptive Statistics	Explores toolbox features for working with descriptive statistics such as measures of location and spread, percentile estimates, and data with missing values.
Linear Models	Describes toolbox support for one-way, two-way, and higher-way analysis of variance (ANOVA), analysis of covariance (ANOCOVA), multiple linear regression, stepwise regression, response surface prediction, ridge regression, and one-way multivariate analysis of variance (MANOVA). It also describes support for nonparametric versions of one- and two-way ANOVA, and multiple comparisons of the estimates produced by ANOVA and ANOCOVA functions.
Nonlinear Regression Models	Discusses parameter estimation, interactive prediction and visualization of multidimensional nonlinear fits, and confidence intervals for parameters and predicted values. It also introduces classification and regression trees as a way to approximate a regression relationship.
Hypothesis Tests	Describes support for common tests of hypothesis - t-tests, Z-tests, nonparametric tests, and distribution tests.
Multivariate Statistics	Explores toolbox features that support methods in multivariate statistics, including principal components analysis, factor analysis, one-way multivariate analysis of variance, cluster analysis, and classical multidimensional scaling.
Statistical Plots	Describes box plots, normal probability plots, Weibull probability plots, control charts, and quantile-quantile plots which the toolbox adds to the arsenal of graphs in MATLAB. It also discusses extended support for polynomial curve fitting and prediction, creation of scatter plots or matrices of scatter plots for grouped data, interactive identification of points on such plots, and interactive exploration of a fitted regression model.
Statistical Process Control	Discusses the plotting of common control charts and the performing of process capability studies.
Design of Experiments	Discusses toolbox support for full and fractional factorial designs, response surface designs, and D-optimal designs. It also describes functions for generating designs, augmenting designs, and optimally assigning units with fixed covariates.
Demos	Describes GUIs that enable you to explore the probability distributions, random number generation, curve fitting, and design of experiments functions.
Functions -- By Category	Lists the functions for each area supported by the toolbox.
Functions -- Alphabetical List	Lists the functions in alphabetical order.
Selected Bibliography	Lists published materials that support concepts described in this guide.

Information about specific functions and tools is available online and in the PDF version of this document. For functions and graphical tools, reference descriptions include a synopsis of the syntax, as well as a complete explanation of options and operation. Many reference descriptions also include examples, a description of the function's algorithm, and references to additional reading material. Demos further describes the use of the graphical tools.