Multivariate Analysis – The Simplest Guide in the Universe: Bite-Size Stats, #6

Introduction

Multivariate analysis has the reputation of being difficult and confusing.

I’m not going to tell you that it’s easy, but I will say that it’s a lot easier than people think it is.

What is true is that when you move from univariate to multivariate analysis, there is quite a leap in terms of level of difficulty, and it puts most people off.

Basic statistics books stop short of multivariate analysis and books specialising in multivariate analysis are typically extremely mathematical and give little or no practical help in how to answer what appear to be fairly simple questions, such as:

Why should I do multivariate analysis?

How do I choose which type of multivariate test to use?

How do I interpret the results of multivariate tests?

What should I do when my univariate and multivariate results do not agree?

You will find the answers to all these questions – and many more – in this book.

So let’s jump right in and answer the first of these questions – Why should I do multivariate analysis?

Events happen in the real world, and they rarely happen in isolation. An outcome that you see, measure or detect will often have a number of causes, and these causes are related to one another.

Univariate analysis is a statistical tool to analyse the contribution of an individual factor to a single outcome. While the answers you get are useful, they do not take into account the effect of any other potential influences on the outcome. In other words, you are checking this variable against that without taking into account the effect of the others.

Multivariate analysis, on the other hand, takes into account the contributions of all the possible factors of an outcome at the same time. In multivariate analysis you are assessing many variables (predictor variables) against a single variable (target, outcome or hypothesis variable) simultaneously; in other words, testing this, that and all the others against a single outcome.

It is this fact that makes multivariate analysis so much more powerful – and so much more complex – than univariate analysis.

The big advantage to doing multivariate analysis is that when you test multiple variables simultaneously, interactions between the variables can be controlled for.

OK, enough of the jargon, what does ‘controlled for’ really mean?

A univariate analysis of this against that tells you whether there is a relationship between a pair of variables, but it doesn’t tell you whether that relationship is independent of other factors.

For example, if you find a significant relationship between this and that in univariate analysis, you’re unlikely to be seeing the full story, because the influence of the others have not been tested for.

For this, you need to run a multivariate analysis, which distinguishes between those variables that are:

not related

dependently related

i.e.