Chapter 5 Introduction to Experimentation
This chapter will briefly introduce the following models which will be described in detail in subsequent chapters.
- Observational Studies vs Controlled Experiments
- Completely Randomized Design
- Randomized Block Design
- Factorial Designs
- Chi-Square Tests for Categorical Variables
- Regression Models
Studies can be described as Observational or as Controlled Experiments. Observational studies occur when experimental/sampling units are obtained from existing populations. These could be different brands of a product, animals from different species, or people who do or do not practice a particular habit. In controlled experiments, a sample of units is obtained, and the individual elements of the sample are randomly assigned to the various conditions/treatments. This could involve batches of raw material being assigned to various machines, mice being assigned to various doses of a chemical compound, or humans assigned to various advertising campaigns.
The Completely Randomized Design (CRD) simply randomizes the experimental units to the various treatments in the most basic manner with no restrictions on randomization. The Randomized Block Design (RBD) first creates “blocks” of units that are similar based on some external criteria (e.g. age or skill) and then assigns units to treatments within blocks. In many experiments, each individual unit may receive each treatment, and the units are treated as blocks.
In Factorial Designs, there are multiple treatment factors that are simultaneously controlled. These can be structured as a CRD or a RBD. In some cases, one or more of the factors may be controlled, while others may be observed. In many engineering applications, a set of \(k\) factors, each at two or more levels, may be observed to determine which variables have the largest impacts on the response, or to optimize the response.
When the independent and dependent variables are categorical, Chi-Square Tests can be conducted to determine whether two variables are associated, that is whether the probability distribution of one variable depends on the level of the other variable.
When the independent and dependent variables are both numeric, Regression Models can be applied to measure the associations among variables. These models can be extended in many ways to various types of predictor and response variables.