RESEARCH METHOD COHEN ok

PROCEDURES IN GRID ANALYSIS 441
Box 20.5
Difference score for constructs
Construct
1
2
−2
1
−2
Construct
2 15
Chapter 20
15
ΣD
Constructs Match Difference score
1–2 6 6 − 8 =−2
By matching Construct 1 against all remaining
constructs (3 ...15), we get a score for each
comparison. Beginning then with Construct 2,
and comparing this with every other construct
(3 ...15), and so on, every construct on the grid
is matched with every other one and a difference
score for each obtained. This is recorded in matrix
form, with the reflected half of the table also
filled in (see difference score for Constructs 1–2
in Box 20.5). The sign of the difference score is
retained. It indicates the direction of the linkage.
A positive sign shows that the constructs are
positively associated, a negative sign that they are
negatively associated.
Now add up (without noting sign) the sum of
the difference scores for each column (construct)
in the matrix. The construct with the largest
difference score is the one which, statistically,
accounts for the greatest amount of variance
in the grid. Note this down. Now look in the
body of the matrix for that construct which has
the largest non-significant association with the
one which you have just noted (in the case of
a 16-element grid as in Box 20.4, this will be
a difference score of ±3 or less). This second
construct can be regarded as a dimension which is
orthogonal to the first, and together they may form
the axes for mapping the person’s psychological
space.
If we imagine the construct with the highest
difference score to be ‘kind–cruel’ and the
highest non-significant associated construct to be
‘confident–unsure’, then every other construct
in the grid may be plotted with reference to
these two axes. The coordinates for the map
are provided by the difference scores relating
to the matching of each construct with the
two used to form the axes of the graph.
In this way a pictorial representation of the
individual’s ‘personal construct space’ can be
obtained, and inferences made from the spatial
relationships between plotted constructs (see
Box 20.6).
By rotating the original grid 90 degrees
and carrying out the same matching procedure
on the columns (figures), a similar map may
be obtained for the people (figures) included
in the grid. Grid matrices can be subjected
to analyses of varying degrees of complexity.
We have illustrated one of the simplest ways
Box 20.6
Grid matrix
Confindent
+8 Kind
Unsure
-8 0 +8
-8 Cruel