Statistics Toolbox

Primary Topic Areas

The Statistics Toolbox has more than 200 M-files, supporting work in these topical areas:

Probability Distributions

The Statistics Toolbox supports 20 probability distributions. For each distribution there are five associated functions. They are

• Probability density function (pdf)
• Cumulative distribution function (cdf)
• Inverse of the cumulative distribution function
• Random number generator
• Mean and variance as a function of the parameters

For data-driven distributions (beta, binomial, exponential, gamma, normal, Poisson, uniform, and Weibull), the Statistics Toolbox has functions for computing parameter estimates and confidence intervals.

Descriptive Statistics

The Statistics Toolbox provides functions for describing the features of a data sample. These descriptive statistics include measures of location and spread, percentile estimates and functions for dealing with data having missing values.

Linear Models

In the area of linear models, the Statistics Toolbox supports 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 supports nonparametric versions of one- and two-way ANOVA. It also supports multiple comparisons of the estimates produced by ANOVA and ANOCOVA functions.

Nonlinear Models

For nonlinear models, the Statistics Toolbox provides functions for parameter estimation, interactive prediction and visualization of multidimensional nonlinear fits, and confidence intervals for parameters and predicted values. It provides functions for using classification and regression trees to approximate regression relationships.

Hypothesis Tests

The Statistics Toolbox also provides functions that do the most common tests of hypothesis -- t-tests, Z-tests, nonparametric tests, and distribution tests.

Multivariate Statistics

The Statistics Toolbox supports methods in multivariate statistics, including principal components analysis, factor analysis, one-way multivariate analysis of variance, cluster analysis, and classical multidimensional scaling.

Statistical Plots

The Statistics Toolbox adds box plots, normal probability plots, Weibull probability plots, control charts, and quantile-quantile plots to the arsenal of graphs in MATLAB. There is also extended support for polynomial curve fitting and prediction. There are functions to create scatter plots or matrices of scatter plots for grouped data, and to identify points interactively on such plots. There is a function to interactively explore a fitted regression model.

Statistical Process Control (SPC)

For SPC, the Statistics Toolbox provides functions for plotting common control charts and performing process capability studies.

Design of Experiments (DOE)

The Statistics Toolbox supports full and fractional factorial designs, response surface designs, and D-optimal designs. There are functions for generating designs, augmenting designs, and optimally assigning units with fixed covariates.

Introduction

Random Numbers in Examples