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A NEW APPROACH TO MEASURING
CONFLICT OR INCONSISTENCY
IN GRIDS
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Richard C. Bell
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Department of Psychology, University of
Melbourne, Australia |
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Personal
construct oriented researchers and
clinicians have long been interested in the notion of conflict or
inconsistency
of construing in repertory grid data. One approach which seemed
theoretically
promising but difficult to operationalise was built on Heider’s balance
notion,
where relationships among three constructs were assessed for
consistency. Here,
the same underlying notion is employed but the inconsistency is
evaluated
between one element and two constructs. This has the advantage of a
common
approach to inconsistency for both elements and constructs. The
approach also
permits an evaluation of the variation in conflict within grids and may
provide
a way of examining movement between tightness (where there is no
inconsistency)
and looseness (where there may be substantial inconsistency) in
construing. The
approach is illustrated with a previously published grid and some data
for
groups of grids.
Keywords: repertory grid, conflict,
inconsistency, balance, triangular inequality, variation in conflict.
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CONFLICT IN GRIDS
The notion that people have
inconsistencies
in their thinking is neither new nor confined to personal construct
theory.
Daniel Kahneman was awarded the Nobel Prize for Economics in 2002 for
his psychological
research showing that people were not rational decision makers.
Interestingly
Kahneman’s PhD (see Kahneman, 1963) was based on the semantic
differential, a
technique producing data not wholly dissimilar to that of the repertory
grid
technique. The personal construct theory of George Kelly (1955/91)
allowed for
such inconsistencies in construing through the Fragmentation Corollary.
Subsequently constructivists have been
interested
in construct systems where there are inconsistencies (Honess, 1982),
contradictions (Krauthauser, Bassler, and Potratz, 1994), or conflict
(Slade
and Sheehan, 1979) among the components of the construct system. While
these
terms have been used interchangeably [we could also consider it as
ambiguity in
construing], ‘conflict’ has been the most widely used term, and will be
used
here. There have been two distinct approaches to the measurement of
conflict in
repertory grid data.
In the first and better known approach
Slade and Sheehan (1979) adapted Lauterbach’s use of Heider’s (1946)
balance
theory where three concepts are assigned positive or negative valances,
and
balanced triads of concepts have either a pattern of all positive
valences or a
pattern of one positive and two negative valences (Lauterbach, 1975).
Slade and
Sheehan proposed using triads of the signs of correlations among three
constructs
in a similar fashion. Winter (1983) however found the percentage of
imbalance
triads of constructs to be highly correlated with measures of cognitive
complexity.
One issue arising from this measure is
the
level of correlation at which a triad is designated as ‘balanced’ or
‘imbalanced’.
If all correlations are used, whatever their size, then correlations of
0.01
and -0.02 and -0.03 will be said to be balanced. But those correlations
most
would agree are very likely to be not significantly different from
zero, and
should therefore not be taken into account as suggesting any
relationship.
Bassler, Krauthauser, and Hoffman (1992) have suggested a modification
to the
procedure which would take account of the size of the correlations. In
a subsequent
empirical evaluation of 140 grids from psychiatric patients,
Krauthauser, Bassler,
and Potratz (1994) found that large numbers of imbalanced triads were
rare, and
that the presence of imbalanced triads was affected by the number of
constructs
(more constructs led to more imbalanced triads) and the number of
elements
(fewer elements led to more imbalanced triads). Monolithic construing
was also
associated with more imbalanced triads.
Another measure of conflict or
ambivalence
that could be used with specific kinds of grids in which figures were
seen as
both elements and constructs was suggested by Fransella and Crisp
(1971)
A NEW APPROACH TO CONFLICT
/ INCONSISTENCY
The present approach combines aspects of
both these approaches; assessing triads for balance, but forming triads
from
both elements and constructs. The genesis of this idea lies in
Lauterbach’s
original example. (I like parties, I don’t like depression, but alas I
associate parties with depression).These concepts can be interpreted as
one
element (‘I’) and two constructs, going
to parties or not and depressing or
not.
Here we adopt the position that
Conflict/Inconsistency/Contradictions
will exist in a grid where either of the following two conditions hold:
1. An element is at the same time
similar or
close to two constructs which are themselves different or distant.
2. An element is similar or close to one
construct’s
pole and at the same time is different to or distant from another
construct’s
pole, where the two construct poles are similar or close.
This can be operationalised in the
following way.
1. Define relationships between
constructs and
elements, and among constructs, as distances.
2. Let the rating of an element on a
construct
be the distance between that element and the construct. The rating will
designate one pole as the basis of the distance, it is immaterial which
pole it
is, since reversing the construct ratings will change all three
distances and
the relationship among them is preserved.
3. Let the distance between constructs
be determined
by the average distance determined from all other elements.
4. We then define the presence of
conflict as
the presence of a ‘triangular inequality’. That is, in any three
distances
defined on three points (one element and two constructs) the longest
distance
must not exceed the sum of the two smaller distances (in such a case
the distances
cannot form a triangle). Consider the eight elements rated on three
constructs
in Table 1 below.
Table 1. Illustrative Grid Data
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A
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B
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C
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D
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E
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F
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G
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X
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warm
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3
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4
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4
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7
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6
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7
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4
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1
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cold
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kind
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3
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5
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4
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7
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7
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6
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2
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6
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cruel
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harsh
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5
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3
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1
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1
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1
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2
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7
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1
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gentle
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7
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< Ratings >
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1
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Element X is both cold
and kind and cold and gentle.
The distances between the constructs are shown in Table 2.
Table 2.
Construct Euclidean Distances (There is an error in this table; see ERRATA, added 22 August 2014)
kind
vs cruel |
5.7
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harsh
vs gentle |
10.4
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12.4
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warm vs cold
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kind vs cruel
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The sum of the distances from X to warm vs cold and kind vs cruel is 1 + 6
= 7, but the distance from warm vs cold to kind
vs cruel is only 5.7. The triangular inequality is not
satisfied and there is conflict. Also the sum of the distances from X
to warm
vs cold and harsh vs gentle is 1 + 1 = 2, but the distance from warm vs cold to harsh vs gentle is 10.4.
Again the triangular inequality is not
satisfied and there is conflict.
1. This simple example is a relatively
easy
one in which to detect such conflict. However the number of possible
conflict
situations in a grid is NE * NC * (NC – 1) / 2, where NE is the number
of
elements and NC is the number of constructs. Thus in this tiny example
there
are 8 by 3 by 2 divided by 2 equals 24 possible conflict situations. In
an
ordinary grid, say 10 by 10 there would be 450.
2. We then define overall conflict as
the
ratio of observed conflict situations to possible conflict situations.
The
overall conflict may be partitioned to identify proportions of conflict
attributable to each element and each construct.
3. Variation in conflict within a grid
may
also be important. Since it seems likely that there will be a certain
degree of
error or random conflict in any grid, we could assume that such
conflict will
be distributed randomly across elements and randomly across constructs.
A null
hypothesis for these distributions of conflict across elements and
constructs
is that it they are uniform distributions. If we make such as
assumption we can
use departures from such a distribution to indicate the presence of
systematic
rather than error conflict. We could find the average conflict per
element by
dividing the total conflict by the number of elements and compare this
to the
actual conflict attributable to each element. These could be combined
by
summing the ratio of squared discrepancies over the square expected
(average)
conflict to give a pseudo-chi-square measure. While this could not be
tested
for significance [1], it could be
transformed into a standardized measure, Cramer’s V [2], whose values range from zero - no departure
from the expected values, to a maximum of 1.0 which would enable
conflict variation
to be compared across grids.
There are a number of advantages to this
approach.
The procedure involves both elements and constructs and can be applied
to any
repertory grid data, and involves minimal departure from the actual
grid data.
Element – Construct distances are taken directly from the grid, while
the
estimation of the between construct grid retains the grid data
properties.
Unlike correlation approaches there is no data standardization, and as
with
distances, conflict is invariant over construct pole reversal. The
outcome can
be interpreted at grid, element, construct, and element by construct
level.
AN EXAMPLE
As an example we consider a grid
published
by Leach, Freshwater, Aldridge, and Sunderland (2001).
This was a grid completed prior to therapy with a victim of
child sexual abuse. It had fourteen constructs and nine elements,
giving a
total of 819 potential element-construct conflict situations. In 340 of
these
situations (42%) conflict was observed. The distribution of conflict by
construct and element is shown in Table 3.
Table 3. Percentage of 340 Conflict
Instances by Construct and Element
Construct
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%
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Element
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%
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assertive
vs not assertive
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8.1
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Child Self
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10.9
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confident
vs unconfident
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7.6
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Self Now
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7.9
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does
not feel guilty vs feels guilty
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9.1
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Women in General
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1.8
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abusive
vs not abusive
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7.4
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Men in General
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8.2
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frightening
vs not frightening
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6.5
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Father
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16.5
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untrustworthy
vs trustworthy
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6.8
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Partner
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10.3
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powerful
vs powerless
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6.2
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Ideal Self
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14.7
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big
headed vs not big headed
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6.0
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Mother
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10.6
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independent
vs dependent
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6.0
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Abuser in Childhood
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19.1
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confusing
vs not confusing
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6.9
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guilty
vs not guilty
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6.2
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cold
vs shows feelings
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6.0
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masculine
vs feminine
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7.5
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interested
in sex vs
not interested in sex
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9.6
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100.0
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100.0
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Index of
Conflict Variation
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.109
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.309
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The index here termed an index of
conflict
variation is the Cramer’s V coefficient referred to earlier. In can be
seen in
this grid the variation in conflict across elements is nearly three
times as
great as across elements. The abuser in childhood figure has the
highest level
of conflict. Conflict involving any element can be further examined to
see
which constructs most often are involved in conflict situations with
the
element and the other constructs. Table 4 shows how the conflict for
this
figure was distributed across constructs.
Table 4. Distribution of conflict across
constructs for Abuser figure
Percentage Conflict
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Construct |
6.9
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assertive vs not assertive
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7.7
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confident vs unconfident
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7.7
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does not feel
guilty vs feels
guilty
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6.9
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abusive vs not abusive
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6.9
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frightening vs not frightening
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6.9
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untrustworthy vs trustworthy
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5.4
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powerful vs powerless
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5.4
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big headed vs not big headed
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6.2
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independent vs dependent
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5.4
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confusing vs not confusing
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6.2
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guilty vs not guilty
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10.0
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cold vs shows feelings
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8.5
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masculine vs feminine
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10.0
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interested in
sex vs not
interested |
It can be seen that the conflict for
this
figure occurs primarily with respect to the constructs cold
vs shows feelings and interested
in sex vs not interested. Although it was shown earlier that the
number of
potential conflict situations in a grid is large, when we have
identified a
particular element involved in more conflict than others, we can
examine
directly the discrepancies between this element and all pairs of
constructs.
Table 5 shows these data. There are 91 possible conflict situations and
there
is no conflict (discrepancy of zero) in 28 (31%) of these situations.
In some
situations the conflict is minimal (for example the conflict between big headed vs not and independent vs
dependent is only 0.1).
We can see the conflict is most evident for this figure between
constructs cold vs shows feelings and both big
headed vs not
(3.6) and masculine vs feminine (4.1).
Table
5. Discrepancies between paired
constructs for Childhood Abuser figure.
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Construct
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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1
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assertive
vs
not assertive
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2
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confident
vs unconfident
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0.0
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3
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does
not feel
guilty vs
feels guilty
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0.0
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0.0
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4
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abusive vs
not abusive |
1.1
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1.7
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2.4
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5
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frightening
vs
not frightenin |
0.0
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0.7
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1.4
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0.5
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6
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untrustworthy
vs trustworthy
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1.1
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1.8
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2.5
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0.0
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0.3
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7
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powerful
vs
powerless |
0.0
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0.3
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0.7
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0.9
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0.0
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0.9
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8
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big
headed vs
not big headed |
0.3
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0.9
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1.5
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0.0
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0.0
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0.0
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0.0
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9
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independent
vs dependent
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0.0
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0.0
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0.0
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1.3
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0.3
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1.4
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0.0
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0.1
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10
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confusing
vs not
confusing
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0.3
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0.9
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1.4
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0.0
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0.0
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0.0
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0.0
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0.0
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0.4
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11
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guilty vs
not guilty
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1.3
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1.9
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2.4
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0.0
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0.0
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0.0
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0.7
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0.0
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1.2
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0.0
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12
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cold vs shows feelings
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1.9
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1.3
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0.7
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3.3
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2.4
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3.4
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2.6
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3.6
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1.8
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3.2
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4.1
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13
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masculine
vs feminine |
0.4
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0.6
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0.7
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1.2
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0.2
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1.2
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0.0
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0.4
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0.0
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0.4
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1.3
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1.7
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14
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interested in
sex
vs not interested |
1.3
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1.3
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1.1
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2.1
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1.1
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2.2
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0.7
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1.2
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0.0
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1.2
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1.7
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1.0
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0.3
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These
discrepancies can be standardized,
and those with z-scores greater than some critical level can be
identified. In
the above table, the following pairs of constructs (shown in Table 6)
reached
the 5% level (1.96).
Table 6. Construct Pairs
involved in extreme levels of conflict for Childhood
abuser figure.
Z |
Construct
Pair |
2.41 |
abusive vs not abusive <> cold vs shows feelings
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2.57 |
untrustworthy vs trustworthy <> cold
vs shows feelings
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2.79 |
big headed vs not big headed <> cold vs shows feelings
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2.35 |
confusing vs not confusing <> cold vs shows feelings |
3.24 |
guilty vs not guilty <> cold vs shows feelings |
We can similarly examine the conflict by
construct,
looking at the pair formed by other constructs and element. Table 7
shows the
constructs and elements associated at a more extreme level of
inconsistency
with the construct masculine vs feminine.
Table 7. Element-Construct
Pairs involved in extreme levels of conflict for the
construct masculine vs feminine.
Z
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Element-Construct
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2.53
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Child
Self <> assertive vs not assertive
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3.44
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Child
Self <> confident vs unconfident
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3.40 |
Child
Self <> does not feel guilty vs feels guilty
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2.67 |
Father
<> abusive vs not abusive |
2.65 |
Father
<> frightening vs not frightening
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2.67 |
Father
<> untrustworthy vs trustworthy |
2.43 |
Father
<> big headed vs not big headed
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2.45 |
Father
<> confusing vs not confusing |
2.60
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Father
<> guilty vs not guilty
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2.07 |
Father
<> cold vs shows feelings |
2.60 |
Mother
<> interested in sex vs not interested in sex
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Analyses of this kind then may inform
individual decision-making (or rather question-asking) in the
diagnostic-therapeutic
setting.
VARIATIONS
In a more normative research oriented
setting, we may wish to inquire about expected levels of conflict and
distribution of conflict. To exemplify this situation (and not use it
as the
basis for drawing conclusions beyond slightly idle speculation) we
consider two
data sets previously analysed in different settings. One data set was
first
reported in Bell and McGorry (1994) consisting of 111 grids of patients
recovering
from a psychotic episode. The other data set is the responses of 170
insurance
salespeople to grids featuring employment advertisements used by Bell
(2000) to demonstrate
a way of testing the commonality of constructs. More details about both
these
grids are also given in Bell, Vince and Costigan (2002). Naively we might expect to
see more
extreme patterns of conflict in the clinical sample and more consistent
patterns in the community sample (although Kahneman might caution us
otherwise).
Statistics for the percentage conflict
and
variation in conflict are shown in Table 8.
Table 8. Differences in level of conflict and conflict variation for
two samples
(A: 111 Recovering Psychotic Grids, B: 170 Insurance Job Adv Grids)
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Sample Statistics
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Levene's Test
for Equality of Variances |
t-test for
Equality of
Means (separate variance estimates) |
Index
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Group
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Mean
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Std. Deviation
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F
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prob
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t
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df
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Percent Conflict
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A
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34.6
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8.06
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7.0
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.009
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-5.1*
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174.3
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B
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39.0
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5.41
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Element Conflict
Variation Index |
A
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.36
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.15
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41.5
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.000
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6.5
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148.8
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B
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.26
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.08
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Construct Conflict
Variation Index |
A
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.11
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.04
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7.7
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.006
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1.0
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187.8
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B
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.10
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.03
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Variation across constructs is almost
the
same for both groups. The community sample grids contain more conflict
on
average, but have lower levels of variation across elements. However
the
community sample is more consistent with respect all measures with
significantly lower standard deviations. This suggests that the
clinical grids
were more likely to be either ‘tighter’ with less conflict or ‘looser’
with
more conflict. Such a finding might reconcile the contradictory
findings by Bell and McGorry (1994)
and Lorenzini, Sassaroli, and Rocchi (1989). The former found that
grids from
recovering psychotic patients were extremely tight or cognitively
simple while
the latter argued that schizophrenia is characterized by loose things.
DISCUSSION
Both excessive tightness and excessive
looseness are associated with less than optimal construing. The indices
discussed here, based on inconsistencies in construing, and variations
in this
inconsistency, might provide an alternative approach to the evaluation
of tightness
and looseness in construing through the repertory grid. Current
measures of
conflict based on correlations discard the information from individual
elements
when evaluating constructs and thus preclude the use of detailed
feedback in
therapeutic situations about inconsistency in terms of actual grid
data. The
present approach provides such information.
Kelly (1955, p.514) also
suggests that the
‘tightness-looseness dimension is
useful in plotting the shifts in the construction process of a single
person’.
The measurement of ‘conflict’ or inconsistency of construing as
proposed here
may prove to be a useful device for monitoring such changes where grids
are
used serially to monitor the stages of therapy.
----------------------------------
[1] Because of the lack of independence of the cell
frequencies (based on
the same constructs for elements or the same elements and constructs
for
constructs) the chi-square calculated cannot be tested for significance.
[2] Cramer’s V is
the square root of the ratio of the value of
chi-square to (in this case) the number of conflicts found. This
coefficient
has a minimum of zero and a maximum of 1.0. It is also equal (in this
case) to
the phi coefficient.
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ERRATA (added 22 August 2014)
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There is an
error in Table 2 in that the table shows total distances not average distances as
indicated by the preceding text. As a consequence the paragraph following is also
in error. Table 2 and the following paragraph should read as follows:
Table 2. Average Construct
Euclidean Distances.
Kind/Cruel
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1.0
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Harsh/Gentle
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4.0
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4.3
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Warm/Cold
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Kind/Cruel
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The largest
distance is from X to Kind/Cruel (6) , but the sum of the average distance from
Warm/Cold to Kind/Cruel (1) and X to Warm/Cold (1) is only 2. The triangular
inequality is not satisfied and there is conflict. Also the sum of the
distances from X to Warm/Cold and Harsh/Gentle is 1 + 1 = 2, but the distance
from Warm/Cold to Harsh Gentle is 4, and again the triangular inequality is not
satisfied and there is conflict.
|
I should also like to take this opportunity
to point out (as I subsequently discovered) the conceptual notion of linking
elements and constructs as a balance situation was first put forward by Carroll
& Carroll (1981).
Finally I would like to thank Bojan
Korenini and Willfred Greyling for drawing the
discrepancy in the paper to my attention.
Carroll, W. K.
& Carroll, R. C. (1981). Cognitive balance in personal construct systems. In H. Bonarius, R.
Holland, & S. Rosenberg (eds.), Personal construct psychology: Recent
advances in theory and practice (pp. 83-94). London: Macmillan.
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REFERENCES
Bassler, M., Krauthauser, H., &
Hoffman S.O. (1992) A new approach to the identification of cognitive
conflicts
in the repertory grid: An illustrative case study. International
Journal of
Personal Construct Psychology, 5,
95-111.
Bell, R. C. (2000) On
testing the Commonality of Constructs in Supplied Grids. Journal of
Constructivist
Psychology, 13, 303-311.
Bell, R. C. (2004)
GRIDSTAT Version 4: A program for analysing the data of a repertory
grid. [Computer
software] Melbourne: Author.
Bell, R., McGorry P. (1994) Monitoring the recovery of psychotics using
repertory grids. In A. Thomson & P. Cummins (Eds.) European
Perspectives
in Personal Construct Psychology. Lincoln, England: European Personal Construct
Association. pp. 137-150.
Bell, R. C., Vince, J., &
Costigan, J. (2002) Which vary more in repertory grid data: Constructs
or
elements? Journal of Constructivist
Psychology, 15, 305-314.
Fransella, F.,
Crisp, A.H.
(1970) Conceptual organization and weight change. Psychotherapy and
Psychosomatics, 18, 176-185.
Heider, F.
(1946) Attitude and
cognitive organization. Journal of Psychology, 2,
107-112.
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ABOUT THE
AUTHOR
Richard
Bell, Ph.D., is an Associate Professor of Psychology at the
University of Melbourne, Australia. He is interested in practical
problems of measurement in clinical, organizational and educational
settings. He has written extensively on the analysis of repertory grid
data and has authored widely used software for the analysis of such
data. E-mail: rcb@unimelb.edu.au.
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REFERENCE
Bell, R. C.
(2004). A new approach to measuring conflict or inconsistency in grids. Personal
Construct Theory & Practice,
1, 53-59
(Retrieved from http://www.pcp-net.org/journal/pctp04/bell042.html)
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Received: 23 Feb 2004 - Accepted:
22 April 2004 -
Published: 31 May 2004 |
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