Multivariate Analysis: A Taxonomy of Quantitative Analysis Techniques
Part I
The collective term used for most of the common analysis tools used in research today is ‘multivariate analysis.’ So, what does the term include and what is left that is not multivariate?
To answer this question, we work through a taxonomy of quantitative analysis techniques. The process of doing this provides a very practical and useful decision pathway for determining the statistical technique that is most appropriate in a given situation. If the so determined technique is not multivariate, then it must be univariate (whilst bi-variate exists, it is commonly included in multivariate).
The distinction between these two approaches is that univariate techniques are appropriate when there is a single measurement of each element in the sample or when there are several measurements of each element but each variable is analysed in isolation. Alternatively, multivariate techniques are suitable for analysing data when there are two or more measurements of each element and the variables are analysed simultaneously. That is, the focus of multivariate techniques is on analysing the simultaneous relationships among two or more phenomena.
Having made the distinction between multivariate and univariate analysis, let us take the next step in our taxonomy trip. Where univariate analysis is relevant, in order to determine the appropriate technique, we must know whether the data are metric or non-metric and if it has come from a single sample or two or more samples. Where there are two or more samples involved, we need to know whether they are independent or related samples. The answers to these questions lead to the identification of the univariate technique that is most appropriate to use in the given situation. Below is a list of the numerous univariate techniques available with an example of their application in practice.
Where the conditions are such that multivariate analysis is warranted, again there are many different techniques to choose from, so it is important to know how the techniques are classified and which questions to ask so that the right technique can be selected.
Part II
Multivariate analysis is a term that is commonly used to generically describe most of the analysis tools used in research today. But what techniques does this term include and what is left that is not multivariate?
So far, we have explained that if the technique is not multivariate then it must be univariate (whilst bi-variate exists, it is commonly included in multivariate). We then explored our way through a trip of taxonomy with the numerous univariate techniques, where our aim was to identify the most appropriate univariate technique for a given situation. That complete, we can now set out on the next trip of classification involving multivariate techniques.
Having decided that multivariate analysis is relevant, we must then choose the multivariate technique that is most appropriate for the given situation. Multivariate techniques are classified into two types: dependence and interdependence techniques. Dependence techniques are relevant when one or more variables are dependent with the remaining variables being independent. Whilst with interdependence techniques, there is no classification of dependent or independent variables, rather the whole set of interdependent relationships is examined. Using this classification criteria, the choice of multivariate technique can then be drawn from the table provided.
With such a broad set of tools available to the researcher, there is little value in claiming that the analyst undertakes the collective term, multivariate analysis. Instead, it would be both more informative and accurate to identify the specific tool/s the researcher is actually skilled in using.
