RESEARCH METHOD COHEN ok

FACTOR ANALYSIS 565
Box 25.5
Ascreeplot
10
Chapter 25
8
Eigenvalue
6
4
2
0
1
3
5
7
9 11 13 15
17
19
21
23
Component number
Next we turn to the columns labelled
‘Extraction Sums of Squared Loadings’. The
Extraction Sums of Squared Loadings contain
two important pieces of information. First, in the
column marked ‘% of variance’ SPSS tells us how
much variance is explained by each of the factors
identified, in order from the greatest amount of
variance to the least amount of variance. So,
here the first factor accounts for 38.930 per cent
of the variance in the total scenario – a very
large amount – while the second factor identified
accounts for only 5.931 per cent of the total
variance, a much lower amount of explanatory
power. Each factor is unrelated to the other, and so
the amount of variance in each factor is unrelated
to, or explained by, the other factors; they are
independent of each other. By giving us how
much variance in the total picture is explained by
each factor we can see which factors possess the
most and least explanatory power – the power to
explain the total scenario of 24 variables. Second,
SPSS keeps a score of the cumulative amount of
explanatory power of the 5 factors identified. In
the column ‘Cumulative’ it tells us that in total
60.047 per cent of the total picture (of the 24
variables) is accounted for – explained – by the
5factorsidentified.Thisisamoderateamount
of explanatory power, and researchers would be
happy with this.
However, the three columns under ‘Extraction
Sums of Squared Loadings’ give us the initial,
rather crude, unadjusted percentage of variance
of the total picture explained by the 5 factors
found. These are crude in the sense that the full
potential of factor analysis has not been caught.
What SPSS has done here is to plot the factors
on a two-dimensional chart (which it does not
present in the data output) to identify groupings
of variables, the two dimensions being vertical
and horizontal axes as in a conventional graph
like a scattergraph. On such a two-dimensional
chart some of the factors and variables could