RESEARCH METHOD COHEN ok

25
Multidimensional measurement
and factor analysis
Introduction
However limited our knowledge of astronomy,
many of us have learned to pick out certain
clusterings of stars from the infinity of those that
crowd the Northern skies and to name them as the
familiar Plough, Orion and the Great Bear. Few of
us would identify constellations in the Southern
Hemisphere that are instantly recognizable by
those in Australia.
Our predilection for reducing the complexity of
elements that constitute our lives to a more simple
order doesn’t stop at star gazing. In numerous
ways, each and every one of us attempts to discern
patterns or shapes in seemingly unconnected
events in order to better grasp their significance
for us in the conduct of our daily lives. The
educational researcher is no exception.
As research into a particular aspect of
human activity progresses, the variables being
explored frequently turn out to be more complex
than was first realized. Investigation into the
relationship between teaching styles and pupil
achievement is a case in point. Global distinctions
between behaviour identified as progressive or
traditional, informal or formal, are vague and
woolly and have led inevitably to research
findings that are at worse inconsistent, at best,
inconclusive. In reality, epithets such as informal
or formal in the context of teaching and learning
relate to ‘multidimensional concepts’, that is,
concepts made up of a number of variables.
‘Multidimensional scaling’, on the other hand, is a
way of analysing judgements of similarity between
such variables in order that the dimensionality
of those judgements can be assessed (Bennett and
Bowers 1977). As regards research into teaching
styles and pupil achievement, it has been suggested
that multidimensional typologies of teacher
behaviour should be developed. Such typologies,
it is believed, would enable the researcher to group
together similarities in teachers’ judgements about
specific aspects of their classroom organization
and management, and their ways of motivating,
assessing and instructing pupils.
Techniques for grouping such judgements are
many and various. What they all have in common
is that they are methods for ‘determining the
number and nature of the underlying variables
among a large number of measures’, a definition
which Kerlinger (1970) uses to describe one of the
best known grouping techniques, ‘factor analysis’.
We begin the chapter by illustrating elementary
linkage analysis which can be undertaken by hand,
and move to factor analysis, which is best left to
the computer. Finally, we append a brief note on
multilevel modelling and another about cluster
analysis, the latter as a way of organizing people or
groups rather than variables.
Elementary linkage analysis: an example
Elementary linkage analysis (McQuitty 1957) is
one way of exploring the relationship between the
teacher’s personal constructs, that is, of assessing
the dimensionality of the judgements that the
teacher makes about his or her pupils. It seeks
to identify and define the clusterings of certain
variables within a set of variables. Like factor
analysis, which we shortly illustrate, elementary
linkage analysis searches for interrelated groups
of correlation coefficients. The objective of the
search is to identify ‘types’. By type, McQuitty