# Lesson 14: Nested and Split Plot Designs

### Introduction

Nested and Split Plot experiments are *multifactor* experiments that have some important industrial applications although historically these come out of agricultural contexts. "Split plot" designs -- here we are originally talking about fields which are divided into whole and split plots, and then individual plots get assigned different treatments. For instance, one whole plot might have different irrigation techniques or fertilization strategies applied, or the soil might be prepared in a different way. The whole plot serves as the experimental unit for this particular treatment. Then we could divide each whole plot into sub plots, and each subplot is the experimental unit for another treatment factor.

Whenever we talk about split plot designs we focus on the experimental unit for a particular treatment factor.

Nested and split-plot designs frequently involve one or more *random* factors, so the methodology of Chapter 13 of our text (expected mean squares, variance components) is important.

There are *many* variations of these designs – here we will only consider some of the more basic situations.

**Learning Objectives & Outcomes**

- Understanding the concept of nesting factors inside another factor.
- Getting familiar with the two-stage nested designs where either or both of the factors could be fixed or random.
- Getting familiar with split-plot designs and their applications where changing the level of some of the factors is hard, relative to other factors.
- Understanding the two main approaches to analyze the split- plot designs and their derivatives and the basis for each approach.
- Getting familiar with split-split-plot designs as an extension of split-plot designs.
- Getting familiar with strip- plot designs (or split-block designs) and their difference from the split-plot designs.