RESEARCH METHOD COHEN ok

566 MULTIDIMENSIONAL MEASUREMENT
be plotted quite close to each other, such that
discrimination between the factors would not
be very clear. However, if we were to plot the
factors and variables on a three-dimensional chart
that includes not only horizontal and vertical
axes but also depth by rotating the plotted points
through 90 degrees, then the effect of this would
be to bring closer together those variables that
are similar to each other and to separate them
more fully – in distance – from those variables that
have no similarity to them, i.e. to render each
group of variables (factors) more homogeneous
and to separate more clearly one group of variables
(factor) from another group of variables (factor).
The process of rotation keeps together those
variables that are closely interrelated and keeps
them apart from those variables that are not closely
related. This is represented in Box 25.6.
This distinguishes more clearly one factor from
another than that undertaken in the Extraction
Sums of Squared Loadings. Rotation is undertaken
by varimax rotation. Thismaximizesthevariance
between factors and hence helps to distinguish
them from each other. In SPSS the rotation is
called orthogonal because the factors are unrelated
to, and independent of, each other.
In the column ‘Rotation Sums of Squared
Loadings’ the fuller power of factor analysis is
Box 25.6
Three-dimensional rotation
tapped, in that the rotation of the variables from
atwo-dimensionaltoathree-dimensionalchart
has been undertaken, thereby identifying more
clearly the groupings of variables into factors,
and separating each factor from the other much
more clearly. We advise researchers to use the
Rotation Sums of Squared Loadings rather than
the Extraction Sums of Squared Loadings. With
the Rotation Sums of Squared Loadings the
percentage of variance explained by each factor is
altered, even though the total cumulative per cent
(60.047 per cent) remains the same. For example,
one can see that the first factor in the rotated
solution no longer accounts for 38.930 per cent
as in the Extraction Sums of Squared Loadings,
but only 16.820 per cent of the variance, and
that factors 2, 3 and 4, which each accounted for
only just over 5 per cent of the variance in the
Extraction Sums of Squared Loadings now each
account for over 11 per cent of the variance, and
that factor 5, which accounted for 4.520 per cent
of the variance in the Extraction Sums of Squared
Loadings now accounts for 8.556 per cent of the
variance in the Rotated Sums of Squared Loadings.
By this stage we hope that the reader has been
able to see that:
Factor analysis brings variables together into
homogeneous and distinct groups, each of
which is a factor and each of which has an
Eigenvalue of greater than 1.
Factor analysis in SPSS indicates the amount
of variance in the total scenario explained
by each individual factor and all the factors
together (the cumulative per cent).
The Rotation Sums of Squared Loadings is
preferable to the Extraction Sums of Squared
Loadings.
We are ready to proceed to the second stage.
Stage 2
Stage 2 consists of presenting a matrix of all of
the relevant data for the researcher to be able to
identify which variables belong to which factor
(Box 25.7). SPSS presents what at first sight is a
bewildering set of data, but the reader is advised