RESEARCH METHOD COHEN ok

FACTOR ANALYSIS 563
Box 25.3
The structuring of relationships among the seven
personal constructs
CLUSTER 1
CLUSTER 2
badly behaved
noisy
verbally good
clumsy
aggressive
unsociable
intelligent
denotes a reciprocal relationship between two variables
Source: Cohen 1977
the consultation abilities or activities of the
leader
the example set by the leader
the commitment of the leader to the school
the versatility of the leader’s styles
the ability of the leader to communicate clear,
individualized expectations
the respect in which the leader is held by staff
the staff’s confidence in the senior management
team
the effectiveness of the teamwork of the SMT
the extent to which the vision for the school
impacts on practice
educators given opportunities to take on
leadership roles
the creativity of the SMT
problem-posing, problem-identifying and
problem-solving capacity of the SMT
the use of data to inform planning and school
development
valuing of professional development in the
school
staff consulted about key decisions
the encouragement and support for innovativeness
and creativity
everybody is free to make suggestions to inform
decision-making
the school works in partnership with parents
people take positive risks for the good of the
school and its development
staff voluntarily taking on coordination roles
teamwork among school staff.
Here we have 24 different variables. The question
here is, ‘Are there any underlying groups of factors
(latent variables) that can embrace several of
these variables, or of which the several variables
are elements or indicators’ Factor analysis will
indicate whether there are. We offer a threestage
model for undertaking factor analysis. In
what follows we distinguish factors from variables:
afactorisanunderlyingorlatentfeatureunder
which groups of variables are included; a variable
is one of the elements that can be a member of an
underlying factor. In our example here we have 24
variables and, as we shall see, 5 factors.
Stage 1
Let us imagine that we have gathered data from
1,000 teachers in several different schools, and
we wish to see how the 24 variables above can
be grouped, based on their voting (using ratio
data by awarding marks out of ten for each of
the variables). (This follows the rule that there
should be more subjects in the sample than there
are variables.) Bryman and Cramer (1990: 255)
suggest that there should be at least 5 subjects per
variable and a total of no fewer than 100 subjects
in the total sample. This analysis will be based on
SPSS processing and output, as Box 25.4.
Although Box 25.4 seems to contain a lot
of complicated data, in fact most of this need
not trouble us at all. SPSS has automatically
found and reported 5 factors for us through
sophisticated correlational analysis, and it presents
data on these 5 factors (the first 5 rows of the
chart, marked ‘Component’). Box 25.4 takes the
24 variables (listed in order on the left-hand
column (Component)) and then it provides three
sets of readings: Eigenvalues, Extracted Sums of
Squared Loadings, and Rotated Sums of Squared
Loadings. Eigenvalues are measures of the variance
between factors. We are interested only in those
Eigenvalues that are greater than 1, since those
that are smaller than 1 generally are not of
interest to researchers as they account for less
than the variation explained by a single variable.
Indeed SPSS automatically filters out for us the
Eigenvalues that are greater than 1, using the
Kaiser criterion (in SPSS this is termed the Kaiser
Normalization).
Chapter 25