RESEARCH METHOD COHEN ok

568 MULTIDIMENSIONAL MEASUREMENT
as these contain figures that are so small as to be
able to be discarded. Look at the column labelled
‘1’ (factor 1). Here we have a range of numbers
that range from 0.114 for the variable ‘Teamwork
among school staff’ to 0.758 for the variable ‘The
drive and confidence of the leader’. The researcher
now has to use his or her professional judgement
to decide what the ‘cut-off’ points should be for
inclusion in the factor. Not all 24 variables will
appear in factor 1, only those with high values
(factor loadings – the amount that each variable
contributes to the factor in question). The decision
on which variables to include in factor 1 is not
astatisticalmatterbutamatterofprofessional
judgement. Factor analysis is an art as well as a
science. The researcher has to find those variables
with the highest values (factor loadings) and
include those in the factor. The variables chosen
should not only have high values but also have
values that are close to each other (homogeneous)
and be some numerical distance away from the
other variables. In the column labelled ‘1’ we can
see that there are 7 such variables, and we set these
out in the example below. Other variables from
the list are some numerical distance away from
the variables selected (see below) and also seem to
be conceptually unrelated to the seven variables
identified for inclusion in the factor. The variables
selected are high, close to each other and distant
from the other variables. The lowest of these 7
values is 0.513; hence the researcher would report
that 7 variables had been selected for inclusion in
factor 1, and that the cut-off point was 0.51 (i.e.
the lowest point, above which the variables have
been selected). Having such a high cut-off point
gives considerable power to the factor. Hence we
have factor 1, which contains 7 variables.
Let us look at a second example, that of
factor 2 (the column labelled ‘2’). Here we
can identify 4 variables that have high values
that are close to each other and yet some
numerical distance away from the other variables
(see example below). These 4 variables would
constitute factor 2, with a reported cut-off point
of 0.445. At first glance it may seem that 0.445
is low; however, recalling that the data in the
example were derived from 1,000 teachers, 0.445
is still highly statistically significant, statistical
significance being a combination of the coefficient
and the sample size.
We repeat this analysis for all 5 factors, deciding
the cut-off point, looking for homogeneous high
values and numerical distance from other variables
in the list.
Stage 3
By this time we have identified 5 factors. However,
neither SPSS nor any other software package tells
us what to name each factor. The researcher has to
devise a name that describes the factor in question.
This can be tricky, as it has to catch the issue that
is addressed by all the variables that are included
in the factor. We have undertaken this for all 5
factors, and we report this below, with the factor
loadings for each variable reported in brackets.
Factor 1: Leadership skills in school management
Cut-off point: 0.51
Variables included:
The drive and confidence of the leader (factor
loading 0.758).
The ability of the leader to motivate and inspire
the educators (factor loading 0.743).
The use of data to inform planning and school
development (factor loading 0.690).
The example set by the leader (factor loading
0.572).
The clarity of the direction set by the school
leadership (factor loading 0.559).
The consultation abilities/activities of the
leader (factor loading 0.548).
The commitment of the leader to the school
(factor loading 0.513).
Factor 2: Parent and teacher partnerships in school
development
Cut-off point: 0.44
Variables included: