Research Methodology - Dr. Krishan K. Pandey

Multivariate Analysis Techniques 315
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Multivariate Analysis Techniques
All statistical techniques which simultaneously analyse more than two variables on a sample of
observations can be categorized as multivariate techniques. We may as well use the term ‘multivariate
analysis’ which is a collection of methods for analyzing data in which a number of observations are
available for each object. In the analysis of many problems, it is helpful to have a number of scores
for each object. For instance, in the field of intelligence testing if we start with the theory that general
intelligence is reflected in a variety of specific performance measures, then to study intelligence in
the context of this theory one must administer many tests of mental skills, such as vocabulary, speed
of recall, mental arithmetic, verbal analogies and so on. The score on each test is one variable, X i , and
there are several, k, of such scores for each object, represented as X 1 , X 2 …X k . Most of the research
studies involve more than two variables in which situation analysis is desired of the association
between one (at times many) criterion variable and several independent variables, or we may be
required to study the association between variables having no dependency relationships. All such
analyses are termed as multivariate analyses or multivariate techniques. In brief, techniques that
take account of the various relationships among variables are termed multivariate analyses or
multivariate techniques.
GROWTH OF MULTIVARIATE TECHNIQUES
Of late, multivariate techniques have emerged as a powerful tool to analyse data represented in
terms of many variables. The main reason being that a series of univariate analysis carried out
separately for each variable may, at times, lead to incorrect interpretation of the result. This is so
because univariate analysis does not consider the correlation or inter-dependence among the variables.
As a result, during the last fifty years, a number of statisticians have contributed to the development
of several multivariate techniques. Today, these techniques are being applied in many fields such as
economics, sociology, psychology, agriculture, anthropology, biology and medicine. These techniques
are used in analyzing social, psychological, medical and economic data, specially when the variables
concerning research studies of these fields are supposed to be correlated with each other and when
rigorous probabilistic models cannot be appropriately used. Applications of multivariate techniques in
practice have been accelerated in modern times because of the advent of high speed electronic
computers.