RESEARCH METHOD COHEN ok

560 MULTIDIMENSIONAL MEASUREMENT
(1957) refers to ‘a category of people or other
objects (personal constructs in our example) such
that the members are internally self-contained in
being like one another’.
Seven constructs were elicited from an infant
school teacher who was invited to discuss the
ways in which she saw the children in her class
(see Chapter 20). She identified favourable and
unfavourable constructs as follows: ‘intelligent’
(+), ‘sociable’ (+), ‘verbally good’ (+), ‘well
behaved’ (+), ‘aggressive’ (−), ‘noisy’ (−) and
‘clumsy’ (−).
Four boys and six girls were then selected at
random from the class register and the teacher
was asked to place each child in rank order under
each of the seven constructs, using rank position
1toindicatethechildmostliketheparticular
construct, and rank position 10, the child least
like the particular construct. The teacher’s rank
ordering is set out in Box 25.1. Notice that on
three constructs, the rankings have been reversed
in order to maintain the consistency of Favourable
1, Unfavourable = 10.
Box 25.2 sets out the intercorrelations between
the seven personal construct ratings shown in
Box 25.1 (Spearman’s rho is the method of
correlation used in this example).
Elementary linkage analysis enables the
researcher to cluster together similar groups of
variables by hand.
Steps in elementary linkage analysis
1 In Box 25.2, underline the strongest, that is
the highest, correlation coefficient in each
column of the matrix. Ignore negative signs.
2 Identify the highest correlation coefficient in
the entire matrix. The two variables having
this correlation constitute the first two of
Cluster 1.
3 Now identify all those variables which are
most like the variables in Cluster 1. To do
this, read along the rows of the variables
which emerged in Step 2, selecting any of
the coefficients which are underlined in the
rows. Box 25.3 illustrates diagrammatically
the ways in which these new cluster members
are related to the original pair which initially
constituted Cluster 1.
4 Now identify any variables which are most
like the variables elicited in Step 3. Repeat
this procedure until no further variables are
identified.
5 Excluding all those variables which belong
within Cluster 1, repeat Steps 2 to 4 until all
the variables have been accounted for.
Factor analysis
Factor analysis is a method of grouping together
variables which have something in common. It
is a process which enables the researcher to take
asetofvariablesandreducethemtoasmaller
number of underlying factors which account for
as many variables as possible. It detects structures
and commonalities in the relationships between
variables. Thus it enables researchers to identify
where different variables in fact are addressing
the same underlying concept. For example, one
variable could measure somebody’s height in
centimetres; another variable could measure the
same person’s height in inches. The underlying
factor that unites both variables is height; it is a
latent factor that is indicated by the two variables.
Factor analysis can take two main forms:
exploratory factor analysis and confirmatory factor
analysis. The former refers to the use of
factor analysis (principal components analysis
in particular) to explore previously unknown
groupings of variables, to seek underlying patterns,
clusterings and groups. By contrast confirmatory
factor analysis is more stringent, testing a found
set of factors against a hypothesized model
of groupings and relationships. This section
introduces the most widely used form of factor
analysis: principal components analysis. We refer
the reader to further books on statistics for a fuller
discussion of factor analysis and its variants.
The analysis here uses SPSS output, as it is the
most commonly used way of undertaking principal
components analysis by educational researchers.
As an example of factor analysis, one could have
the following variables in a piece of educational
research: