RESEARCH METHOD COHEN ok

FACTOR ANALYSIS 569
The school works in partnership with parents
(factor loading 0.804).
People take positive risks for the good of the
school and its development (factor loading
0.778).
Teamwork among school staff (factor loading
0.642).
The effectiveness of the teamwork of the SMT
(factor loading 0.445).
Factor 3: Promoting staff development by creativity
and consultation
Cut-off point: 0.55
Variables included:
Staff consulted about key decisions (factor
loading 0.854).
The creativity of the SMT (factor loading
0.822).
Valuing of professional development in the
school (0.551).
Factor 4: Respect for, and confidence in, the senior
management team
Cut-off point: 0.44
Variables included:
The respect in which the leader is held by staff
(factor loading 0.810).
The staff’s confidence in the SMT (factor
loading 0.809).
The effectiveness of the teamwork of the SMT
(factor loading 0.443).
Factor 5: Encouraging staff development through
participation in decision-making
Cut-off point 0.64
Variables included:
Staff voluntarily taking on coordination roles
(factor loading 0.779).
The encouragement and support for innovativeness
and creativity (factor loading 0.661).
Everybody is free to make suggestions to inform
decision-making (factor loading 0.642).
Each factor should usually contain a minimum of
three variables, though this is a rule of thumb
rather than a statistical necessity. Further, in
the example here, though some of the variables
included have considerably lower factor loadings
than others in that factor (e.g. in factor 2:
the effectiveness of the teamwork of the SMT
(0.445)), nevertheless the conceptual similarity
to the other variables in that factor, coupled
with the fact that, with 1,000 teachers in the
study, 0.445 is still highly statistically significant,
combine to suggest that this still merits inclusion.
As we mentioned earlier, factor analysis is an art
as well as a science.
If one wished to suggest a more stringent level
of exactitude then a higher cut-off point could
be taken. In the example above, factor 1 could
have a cut-off point of 0.74, thereby including
only 2 variables in the factor; factor 2 could have
acut-offpointof0.77,therebyincludingonly2
variables in the factor; factor 3 could have a cut-off
point of 0.82, thereby including only 2 variables
in the factor; factor 4 could have a cut-off point
of 0.80, thereby including only 2 variables in the
factor; and factor 5 could have a cut-off point
of 0.77, thereby including only 1 variable in the
factor. The decision on where to place the cut-off
point is a matter of professional judgement when
reviewing the data.
In reporting factor analysis the above data would
all be included, together with a short commentary,
for example:
In order to obtain conceptually similar and
significant clusters of issues of the variables, principal
components analysis with varimax rotation and
Kaiser Normalization were conducted. Eigenvalues
equal to or greater than 1.00 were extracted. With
regard to the 24 variables used, orthogonal rotation
of the variables yielded 5 factors, accounting for
16.820, 11.706, 11.578, 11.386 and 8.556 per cent
of the total variance respectively, a total of 60.047
per cent of the total variance explained. The factor
loadings are presented in table such-and-such. To
enhance the interpretability of the factors, only
Chapter 25