# Multivariate Analysis of Variance in Marketing Research

## Article excerpt

Introduction

The Multivariate analysis of variance (MANOVA) model is a powerful tool for marketing research.4,10 As a straightforward generalization of the analysis of variance (ANOVA), MANOVA allows the marketing researcher to test hypotheses involving differences in means for a set of dependent variables. Mean differences in these dependent variables can be tested across the levels of one or more categorical independent variable(s). Thus MANOVA is appropriate whenever group differences of a set of criterion variables, rather than single criterion variable, must be considered.

Because of advantages in MANOVA technique, it has been used in experimental design along with ANOVA technique. There have not been many studies which have added to the original methodology in marketing research except some specific applications of MANOVA.17 However, the usage of MANOVA is still very viable in the marketing literature and therefore this paper presents MANOVA as a research methodology technique and then presents some concerns regarding its use and then shows the evidence of usage in marketing literature during the past.

What is MANOVA?

MANOVA is the multivariate extension of the univariate techniques for assessing the differences between group means. MANOVA is different from univariate analyses such as t-test and ANOVA in a sense that the univariate methods' null hypothesis tested is the equality of vectors of means on multiple dependent variables across groups. Secondly in the univariate case, a single dependent measure is tested for equality across the groups. However, in the multivariate case, a variate is tested for equality.

In MANOVA, there are two variates, one made up of the dependent variables and another from the independent variables. Especially, the unique aspect of MANOVA is that the variate optimally combines the multiple dependent measures into a single value that maximizes the differences across groups

The history of MANOVA

The development of MANOVA was brought about as a result of two major factors. One major influence was the invention of the computer and the other one was the inadequacy of univariate approaches. Although the necessary mathematics has been known for some time, the electronic computer with its magnificent speed made the multivariate technique possible for practical applications. Furthermore, the influence of the computer has been supplemented by a growing recognition of the inadequacy of the strictly univariate approach to research.

Kerlinger and Pedharzur12 predicted that "We can more multivariate method within the decade." Furthermore, in their behavioral statistics book, they marked that "... the very nature of behavioral research is multivariate. While some of the complexity can be handled with analysis of variance, it is the only in the multivariate methods that the complexity of many behavioral science problems can be attacked."

The most convincing indicator of MANOVA's recognition is the appearance of a chapter on multivariate analysis in an elementary statistics textbook.5,6,9,11 Since MANOVA is the extend form of ANOVA, Fisher7 developed a statistical hypothesis testing procedure known as ANOVA and the one who deserves credit as the developer of the MANOVA.

Fisher8 also developed discriminant analysis as a measure of classifying individuals into groups based on two or more independent measures taken on each individual. McNemar16 observed that if the group classification is a dichotomy, the discriminant function applied to group classification and the multiple regression techniques applied to the prediction of the same dichotomous variable produce equivalent results. Fisher's discriminant function also implies other way. The creation of a synthetic variable and the test of statistical significant are mathematically equivalent for the discriminant function and the simplest case of MANOVA.

The two-group case- Hotelling's T2: Hotelling's T test is a specialized form of MANOVA that is direct extension of the univariate t test. …

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