# 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, these sites will be referred to by the first letters of their name.

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

Each of these chemical constituents will be abbreviated using the chemical symbol in the examples that follow.

One would like to know whether the chemical content of the pottery depend on the site from which the pottery was obtained?

If this is the case then we might be able to use the chemical content of a pottery sample of unknown origin to determine which site the sample came from using *discriminant analysis*.

**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)