# Lesson 8: Multivariate Analysis of Variance (MANOVA)

### Introduction

The Multivariate Analysis of Variance (MANOVA) is the multivariate analog of the Analysis of Variance (ANOVA) procedure used for univariate data. We will introduce the Multivariate Analysis of Variance with the Romano-British Pottery data example.

Pottery shards are collected from four sites in the British Isles:

*L*: Llanedyrn*C*: Caldicot-
*I*: Isle Thorns -
*A*: Ashley Rails

Subsequently, we will use the first letter of the name to distinguish between the sites.

Each pottery sample was returned to the laboratory for chemical assay. In these assays the concentrations of five different chemicals were determined:

*Al*: Aluminum-
*Fe*: Iron *Mg*: Magnesium-
*Ca*: Calcium *Na*: Sodium

We will abbreviate the chemical constituents with the chemical symbol in the examples that follow.

MANOVA will allow us to determine whether the chemical content of the pottery depends on the site where the pottery was obtained. If this is the case, then in Lesson 10, we will learn how to use the chemical content of a pottery sample of unknown origin to hopefully determine which site the sample came from.

**Learning objectives & outcomes**

Upon completion of this lesson, you should be able to do the following:

- Use SAS/Minitab to perform a multivariate analysis of variance;
- Draw appropriate conclusions from the results of a multivariate analysis of variance;
- Understand the Bonferroni method for assessing the significance of individual variables;
- Understand how to construct and interpret orthogonal contrasts among groups (treatments)