Statistics Toolbox

Preface

How to Use This Guide

Related Products List

Typographical Conventions

Introduction

What Is the Statistics Toolbox?

Primary Topic Areas

Random Numbers in Examples

Mathematical Notation

Probability Distributions

Introduction

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

Overview of the Distributions

Beta Distribution

Binomial Distribution

Chi-Square Distribution

Noncentral Chi-Square Distribution

Discrete Uniform Distribution

Exponential 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

Weibull Distribution

Descriptive Statistics

Introduction

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

Multiple Linear Regression

Mathematical Foundations of Multiple Linear Regression

Example: Multiple Linear Regression

Quadratic Response Surface Models

Exploring Graphs of Multidimensional Polynomials

Stepwise Regression

Example: Stepwise Regression

Stepwise Regression Plot

Stepwise Regression Diagnostics Table

Generalized Linear Models

Example: Generalized Linear Models

Robust and Nonparametric Methods

Robust Regression

Kruskal-Wallis Test

Friedman's Test

Nonlinear Regression Models

Introduction

Nonlinear Least Squares

Example: Nonlinear Modeling

An Interactive GUI for Nonlinear Fitting and Prediction

Regression and Classification Trees

Hypothesis Tests

Introduction

Hypothesis Test Terminology

Hypothesis Test Assumptions

Example: Hypothesis Testing

Available Hypothesis Tests

Multivariate Statistics

Introduction

Principal Components Analysis

Example: Principal Components Analysis

The Principal Components (First Output)

The Component Scores (Second Output)

The Component Variances (Third Output)

Hotelling's T2 (Fourth Output)

Factor Analysis

Example: Finding Common Factors Affecting Stock Prices

Factor Rotation

Predicting Factor Scores

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

Classical Multidimensional Scaling

Overview

Reconstructing a Map from Inter-City Distances

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

Introduction

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

D-Optimal Designs

Generating D-Optimal Designs

Augmenting D-Optimal Designs

Designing Experiments with Uncontrolled Inputs

Controlling Candidate Points

Including Categorical Factors

Demos

Introduction

The disttool Demo

The polytool Demo

Confidence Bounds

Overfitting

The aoctool Demo

Example: aoctool with Sample Data

The randtool Demo

The rsmdemo Demo

Part 1

Part 2

The glmdemo Demo

The robustdemo Demo

Reference

Functions -- By Category

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

File I/O

Demonstrations

Data

Functions -- Alphabetical List

Selected Bibliography

Index


 Preface