Statistics Toolbox

Introduction

There is a world of difference between data and information. To extract information from data you have to make assumptions about the system that generated the data. Using these assumptions and physical theory you may be able to develop a mathematical model of the system.

Generally, even rigorously formulated models have some unknown constants. The goal of experimentation is to acquire data that enable you to estimate these constants.

But why do you need to experiment at all? You could instrument the system you want to study and just let it run. Sooner or later you would have all the data you could use.

In fact, this is a fairly common approach. There are three characteristics of historical data that pose problems for statistical modeling:

• Suppose you observe a change in the operating variables of a system followed by a change in the outputs of the system. That does not necessarily mean that the change in the system caused the change in the outputs.
• A common assumption in statistical modeling is that the observations are independent of each other. This is not the way a system in normal operation works.
• Controlling a system in operation often means changing system variables in tandem. But if two variables change together, it is impossible to separate their effects mathematically.

Designed experiments directly address these problems. The overwhelming advantage of a designed experiment is that you actively manipulate the system you are studying. With Design of Experiments (DOE) you may generate fewer data points than by using passive instrumentation, but the quality of the information you get will be higher.

The Statistics Toolbox provides several functions for generating experimental designs appropriate to various situations. These are discussed in the following sections:

• Full Factorial Designs
• Fractional Factorial Designs
• Response Surface Designs
• D-Optimal Designs

Design of Experiments

Full Factorial Designs