# Lesson 3: Experiments with a Single Factor - the Oneway ANOVA - in the Completely Randomized Design (CRD)

### Lesson 3: Introduction

By the end of this chapter we will understand how to proceed when the ANOVA tells us that the mean responses differ, (i.e., the levels are significantly different), among our treatment levels. We will also briefly discuss the situation that the levels are a random sample from a larger set of possible levels, such as a sample of brands for a product. (Note that this material is in Chapter 3.9 of the 8th edition and Chapter 13.1 of the 7th edition.) We will briefly discuss multiple comparison procedures for qualitative factors, and regression approaches for quantitative factors. These are covered in more detail in the STAT 502 course, and discussed only briefly here.

### Learning objectives & outcomes

We focus more on the design and planning aspects of these situations:

- How many observations do we need?

- to achieve a desired precision when the goal is estimating a parameter, and
- to achieve a desired level of power when hypothesis testing.

- Which multiple comparison procedure is appropriate for your situation?
- How should we allocate our observations among the k treatment groups? Usually equally, but the Dunnett Test situation has a different optimum allocation.
- The last section describes the
*F*-test as an example of the General Linear Test.