Preface
How to Use This Guide
Related Products List
Typographical Conventions
Introduction
What Is the Statistics Toolbox?
Primary Topic Areas
Random Number Generators in the Statistic Toolbox
Mathematical Notation
Examples
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
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
Probability Distributions Demo
Random Sample Generation Demo
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 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 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 -- 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
Hidden Markov Models
File I/O
Demonstrations
Data
Utility
Functions -- Alphabetical List
Selected Bibliography
Printable Documentation (PDF)
Product Page