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# Statistics Toolbox

## Hypothesis Testing, Design of Experiments, and Statistical Process Control

### Hypothesis Testing

Random variation can make it difficult to determine whether samples taken under different conditions are actually different. Hypothesis testing is an effective tool for analyzing whether sample-to-sample differences are significant and require further evaluation or are consistent with random and expected data variation.

Statistics Toolbox supports widely used parametric and nonparametric hypothesis testing procedures, including:

• One-sample and two-sample t-tests
• Nonparametric tests for one sample, paired samples, and two independent samples
• Distribution tests (chi-square, Jarque-Bera, Lillifors, and Kolmogorov-Smirnov)
• Comparison of distributions (two-sample Kolmogorov-Smirnov)
• Tests for autocorrelation and randomness
• Linear hypothesis tests on regression coefficients

Selecting a Sample Size (Example)
Calculate the sample size necessary for a hypothesis test.

### Design of Experiments

Functions for design of experiments (DOE) enable you to create and test practical plans to gather data for statistical modeling. These plans show how to manipulate data inputs in tandem to generate information about their effect on data outputs. Supported design types include:

• Full factorial
• Fractional factorial
• Response surface (central composite and Box-Behnken)
• D-optimal
• Latin hypercube

You can use Statistics Toolbox to define, analyze, and visualize a customized DOE. For example, you can estimate input effects and input interactions using ANOVA, linear regression, and response surface modeling, then visualize results through main effect plots, interaction plots, and multivari charts.

Fitting a decision tree to data. The fitting capabilities in Statistics Toolbox enable you to visualize a decision tree by drawing a diagram of the decision rule and group assignments.
Model of a chemical reaction for an experiment using the design-of-experiments (DOE) and surface-fitting capabilities of Statistics Toolbox.

### Statistical Process Control

Statistics Toolbox provides a set of functions that support statistical process control (SPC). These functions enable you to monitor and improve products or processes by evaluating process variability. With SPC functions, you can:

• Perform gage repeatability and reproducibility studies
• Estimate process capability
• Create control charts
• Apply Western Electric and Nelson control rules to control chart data
Control charts showing process data and violations of Western Electric control rules. Statistics Toolbox provides a variety of control charts and control rules for monitoring and evaluating products or processes.