RESEARCH METHOD COHEN ok

584 MULTIDIMENSIONAL MEASUREMENT
and Goldstein 1991). This has been done using
multilevel regression and hierarchical linear
modelling. Multilevel models enable researchers
to ask questions hitherto unanswered, e.g. about
variability between and within schools, teachers
and curricula (Plewis 1997: 34–5), in short
about the processes of teaching and learning. 4
Useful overviews of multilevel modelling can
be found in Goldstein (1987), Fitz-Gibbon (1997)
and Keeves and Sellin (1997).
Multilevel analysis avoids statistical treatments
associated with experimental methods (e.g.
analysis of variance and covariance); rather
it uses regression analysis and, in particular,
multilevel regression. Regression analysis, argues
Plewis (1997: 28), assumes homoscedasticity (where
the residuals demonstrate equal scatter), that the
residuals are independent of each other, and
finally, that the residuals are normally distributed.
The whole field of multilevel modelling has
proliferated rapidly since the early 1990s and
is the basis of much research that is being
undertaken on the ‘value added’ component of
education and the comparison of schools in public
‘league tables’ of results (Fitz-Gibbon 1991; 1997).
However, Fitz-Gibbon (1997: 42–4) provides
important evidence to question the value of some
forms of multilevel modelling. She demonstrates
that residual gain analysis provides answers to
questions about the value-added dimension of
education which differ insubstantially from those
answers that are given by multilevel modelling
(the lowest correlation coefficient being 0.93
and 71.4 per cent of the correlations computed
correlating between 0.98 and 1). The important
point here is that residual gain analysis is
a much more straightforward technique than
multilevel modelling. Her work strikes at the
heart of the need to use complex multilevel
modelling to assess the ‘value-added’ component
of education. In her work (Fitz-Gibbon 1997: 5)
the value-added score – the difference between a
statistically-predicted performance and the actual
performance – can be computed using residual
gain analysis rather than multilevel modelling.
Nonetheless, multilevel modelling now attracts
worldwide interest.
Whereas ordinary regression models do not
make allowances, for example, for different
schools (Paterson and Goldstein 1991), multilevel
regression can include school differences, and, indeed
other variables, for example: socio-economic
status (Willms 1992), single and co-educational
schools (Daly 1996; Daly and Shuttleworth
1997), location (Garner and Raudenbush 1991),
size of school (Paterson 1991) and teaching
styles (Zuzovsky and Aitkin 1991). Indeed Plewis
(1991) indicates how multilevel modelling can be
used in longitudinal studies, linking educational
progress with curriculum coverage.
Cluster analysis
Whereas factor analysis and elementary linkage
analysis enable the researcher to group together
factors and variables, cluster analysis enables
the researcher to group together similar and
homogeneous subsamples of people. Thisisbest
approached through software packages such as
SPSS, and we illustrate this here. SPSS creates
adendrogramofresults,groupingandregrouping
groups until all the variables are embraced.
For example, here is a simple cluster based on
20 cases (people). Imagine that their scores have
been collected on an item concerning the variable
‘the attention given to teaching and learning in
the school’. One can see that, at the most general
level there are two clusters (cluster one = persons
19, 20, 2, 13, 15, 9, 11, 18, 14, 16, 1, 10, 12,
5, 17; cluster two = persons 7, 8, 4, 3, 6). If one
were to wish to have smaller clusters then three
groupings could be found: cluster one: persons 19,
20, 2, 13, 15, 9, 11, 18; cluster two: persons 14, 16,
1, 10, 12, 5, 17; cluster three: persons 7, 8, 4, 3, 6
(Box 25.22).
Using this analysis enables the researcher to
identify important groupings of people in a
post-hoc analysis, i.e. not setting up the groupings
and subgroupings at the stage of sample design,
but after the data have been gathered. In the