THE ANALYSIS OF WRONG ANSWERS
GIVEN BY UNIVERSITY STUDENTS
TO RAVEN PM47, REV. 1962,
FORM I
Renato
COCCHI, a neurologist and a medical psychologist
Summary.
The analysis
of wrong answers given by 39 college students to Raven's Progressive Matrices,
Form I, revision 1962, carried out according to criteria used by Pola, Cocchi
& Zerbi, 1988, brought to light 170 non random significantly grouped
answers (.04 - .0001).
A
proposed classification into 7 categories showed the distribution of all 170
answers into the category of i. Partial identity or metaphore (25.29%); ii.
Identity by contiguity or metonimy (32.94%); iii. Opposition (14.71%); iv. Confabulation (14.12%); v. Choice
of the first figure the drawing of which was not present in the correspondent
matrix ("first not present" = 12.94%).
The
results are very interesting and confirm that the analysis of wrong answers
given to Raven’s Progressive Matrices can be used to elicit the
neuro-physio-psychological levels the cognitive processes in problem solving
stop.
Key
words: Raven's
Progressive Matrices; wrong answers; analysis; partial identity; identity by
contiguity; opposition; confabulation; first not present;
neuro-physio-psychological mechanisms.
The
results obtained by University students at Raven's PM47, Series I, Revision
1962 were at the basis of two previous investigations. The former presented
only the results (Pediconi, Russo and Cocchi, 1992) while the latter did an
analysis of wrong answers according to a traditional way (Russo and Pediconi,
1992).
On the
same materials this third research aims to develop the analysis of wrong
answers according to a different method. This one seems more useful to elicit
basic neuro-psychological mechanisms such as partial identity, contiguity, post
hoc ergo propter hoc, opposition etc. One previous attempt like this did the
analysis of the wrong answers of demented people to Raven's Coloured Matrices
(Pola, Zerbi and Cocchi, 1988).
Materials and method.
I grouped
wrong answers to the 12 tables of Raven's PM47, Form I, Revision 1962 as given
by a sample of 39 University students, following the number of the answer
chosen, matrix by matrix. Each group of at least three same wrong answers had
its statistical probability computed as random association. I analysed then
groups of wrong answers with p <= .05.
Results.
Table 1
shows wrong answers grouped by numerosity starting from three same answers, as
given matrix by matrix. Each group had its p computed, being maximum p = .00001
because formatting page problems although many probabilities have higher
denominators.
Table
1:Mistakes
grouped by answers, and their p at the matrices 2 - 12 ( * is pointing out the
right answer).
|
Matrix |
Answers |
Grouped mistakes, out of possible 7, with
related p |
||||||||
|
|
Wrong |
Omitted |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
1 |
1 |
1 |
|
|
|
|
|
|
|
* |
|
2 |
6 |
0 |
|
|
4$ |
* |
|
|
|
|
|
3 |
13 |
0 |
8^ |
|
|
3# |
* |
|
|
|
|
4 |
6 |
0 |
* |
|
|
|
4$ |
|
|
|
|
5 |
18 |
1 |
4$ |
* |
|
3# |
3# |
|
|
6^ |
|
6 |
16 |
1 |
|
3# |
|
6^ |
* |
|
|
5& |
|
7 |
24 |
0 |
|
|
|
8^ |
8^ |
* |
|
6^ |
|
8 |
25 |
2 |
|
3# |
* |
|
6^ |
|
3# |
4$ |
|
9 |
36 |
0 |
4$ |
|
|
17^ |
|
9^ |
* |
|
|
10 |
16 |
0 |
5& |
|
3# |
|
|
3# |
|
* |
|
11 |
32 |
0 |
11^ |
|
|
7^ |
3# |
|
* |
7^ |
|
12 |
23 |
0 |
7^ |
|
5& |
|
5& |
* |
|
|
# <.03 // $ <. 001 // & < .0001
// ^ < .00001
The
wrong answers analysis.
I then
inspected wrong answers groups statistically significant from the matrix 2 to
the matrix 12 and I tried an analysist of the cognitive strategy used to reach
that precipual wrong answer. In front of each table, in brackets, I summarized
the constituting mechanism of the matrices.
Mat.
2.
(Triple subtraction)
Answer #
3: Double opposition of both vertical lines and little squares.
Mat.
3.
(Triple aplification)
Answer #
1: Choice of the first answer not already present into the matrix.
Answer #
4: Complete opposition, as triple reduction.
Mat.
4.
(Triple aplification)
Answer #
5: Horizontal spatial opposition, with double narrowing of both the vertical
figure and horizontal guidelines.
Mat.
5.
(Triple addiction)
Answer #
1: Metaphoric answer of identity by using two attributes out of three.
Answer #
4: Vertical contiguity. Answer # 5: Confabulated answer. Answer # 8: Horizontal
contiguity.
Mat.
6.
(Vertical addiction and horizontal subtraction).
Answer #
2: Double contiguity: As for the lines in the vertical sense, and as for
squares in the horizontal sense.
Answer #
4: Vertical contiguity.
Answer #
8: Horizontal contiguity.
Mat.
7.
(Horizontal identity of the background, vertical identity of permuted
background, both horizontal and vertical permutation of the figure).
Answer #
4: Vertical contiguity of the background.
Answer #
5: Background opposition.
Answer #
8: Background opposition and both horizontal and vertical addition of the
figure.
Mat.
8.
(Both horizontal and vertical permutation of the figure and both horizontal and
vertical permutation of internal squarings).
Answer #
2: First not present (wrong permutation of an internal squaring)
Answer #
5: Metaphorical mistake of identity (one wrong attribute).
Answer #
7: Confabulation with double metaphor.
Answer #
8: Confabulation with simple metaphor.
Mat.
9.
(Vertical inclination identity, numerical vertical progression, with horizontal
numerical identity and horizontal permutation of the shape).
Answer #
1: First not present.
Answer #
4: Metaphorical mistake of identity (one wrong attribute).
Answer #
6: Metaphorical mistake of identity (one wrong attribute).
Mat.
10.
(Both vertical and horizontal addiction of the black parts).
Answer #
1: Mistake of vertical contiguity, in opposition.
Answer #
3: Mistake of vertical and horizontal contiguity, in opposition by subtraction.
Answer #
6: Confabulation (diagonal addiction).
Mat.
11.
(Both horizontal addition of the figures and changing of the background;
Vertical addition of the backgrounds and changing of the figures).
Answer #
1: Confabulation as for the background.
Answer #
4: Wrong answer of contiguity as for the background.
Answer #
8: Wrong answer of identity as for the background.
Mat.
12.
(Subtraction and both horizontal and vertical retrieval of what deducted from).
Answer #
1: First not present.
Answer #
3: Wider double contiguity (addition of the two vertical figures to the two
horizontal figures).
Answer #
5: Double contiguity (addition of the vertical figure to the horizontal
figure).
Tab.
2:
Summary of the 170 wrong answers according to 7 common lines.
|
Matrix / Answer |
Number of
wrong answers split into common lines |
|||||||
|
Identity |
Contiguity |
Post hoc |
Opposition |
First not present |
Confabulation |
Others |
||
|
Matrix 2 |
|
|||||||
|
Answ. 3 |
|
|
|
4 |
|
|
|
|
|
Matrix 3 |
|
|||||||
|
Answ. 1 |
|
|
|
|
8 |
|
|
|
|
Answ. 4 |
|
|
|
3 |
|
|
|
|
|
Matrix 4 |
|
|||||||
|
Answ. 5 |
|
|
|
4 |
|
|
|
|
|
Matrix 5 |
|
|||||||
|
Answ. 1 |
4 |
|
|
|
|
|
|
|
|
Answ.4 |
|
3 |
|
|
|
|
|
|
|
Answ. 5 |
|
|
|
|
|
3 |
|
|
|
Answ. 8 |
|
6 |
|
|
|
|
|
|
|
Matrix 6 |
|
|||||||
|
Answ. 2 |
|
3 |
|
|
|
|
|
|
|
Answ. 4 |
|
6 |
|
|
|
|
|
|
|
Answ. 8 |
|
5 |
|
|
|
|
|
|
|
Matrix 7 |
|
|||||||
|
Answ. 4 |
|
8 |
|
|
|
|
|
|
|
Answ. 5 |
|
|
|
8 |
|
|
|
|
|
Answ. 8 |
|
|
|
6 |
|
|
|
|
|
Matrix 8 |
|
|||||||
|
Rispos. 2 |
|
|
|
|
3 |
|
|
|
|
Answ. 5 |
6 |
|
|
|
|
|
|
|
|
Answ. 7 |
|
|
|
|
|
3 |
|
|
|
Answ.8 |
|
|
|
|
|
4 |
|
|
|
Matrix 9 |
|
|||||||
|
Answ.1 |
|
|
|
|
4 |
|
|
|
|
Answ.4 |
17 |
|
|
|
|
|
|
|
|
Answ. 6 |
9 |
|
|
|
|
|
|
|
|
Matrix 10 |
|
|||||||
|
Answ. 1 |
|
5 |
|
|
|
|
|
|
|
Answ. 3 |
|
3 |
|
|
|
|
|
|
|
Answ. 6 |
|
|
|
|
|
3 |
|
|
|
Matrix 11 |
|
|||||||
|
Answ. 1 |
|
|
|
|
|
11 |
|
|
|
Answ. 4 |
|
7 |
|
|
|
|
|
|
|
Answ. 8 |
7 |
|
|
|
|
|
|
|
|
Matrix 12 |
|
|||||||
|
Answ. 1 |
|
|
|
|
7 |
|
|
|
|
Answ. 3 |
|
5 |
|
|
|
|
|
|
|
Answ. 5 |
|
5 |
|
|
|
|
|
|
|
Totals |
43 |
56 |
0 |
25 |
22 |
24 |
0 |
|
|
% |
25.29 |
32.94 |
0.00 |
14.71 |
12.94 |
14.12 |
0.00 |
|
Discussion.
Some
categories I used on possible classification of wrong answers deserve an
explication. With "Others" I prepared some non specific room to those
answers without any place within the preceeding categories. "Confabulation"
is the category of answers where out context and plain elements join on, not to
be eplained with the "logics" of identity nor the "logics"
of contiguity
But this
type of wrong answer is not always at ease to find and some answers work as an
extension of identity answers, the metaphoric ones.
"First
not present" classifies answers that result from a half-clever strategy
that leads to choose, among the eight possible answers, the first one that
shows a drawing "not present" into the matrix.
As we
pointed out (Pola, Zerbi & Cocchi, 1988), this strategy can drive to the
right answer. This could have come also in these matrices because in table 4
and in table 6 the "first not present" is exactly the right answer. Only
when we note other "first not present" answers ( 12.94% of wrong
answers in this research), we can suspect that the subject could have done the
right answers to the above tables by using a half-correct way of reasoning.
These
results showed a very surprising datum. I could classify 170 wrong answers by
using only five categories. What needs to be pointed out is that those wrong
answers are due to errors of contiguity, identity, confabulation, opposition
and "first not present" in that same order.
We
exclude the "first not present" category, being grounded on an elementary
computation of probability. A drawing "not present" in the matrix has
a larger probability of being the right one, and this is a perfectly legitimate
strategy for these series of matrices.
As for
the first two categories, namely contiguity and identity, I need to recall and
to expand on an explanation suggested with best argumentation by Jacobson and
Halle, 1956, and by Jacobson, 1963. Cocchi, 1982 recalled it and found its
neuro-physiological bases in Pribram, 1976.
The human
brain, but nearly sure the animal one too, inclines to do partial identities
(metaphors) or identities by contiguity (metonimies) even off the verbal
language. On our research we had metaphors and metonimies in an exclusively
visual field.
This is
surely not a novelty because advertising exploits these mechanisms since many
decades.
It is
worthy to note that, in this sample of university students, contiguity was the
most used mechanism.
As for
opposition, already Cocchi et al., 1986 discussed this brain mechanism when
they presented the first case of "mirror speaking" after brain
surgery (Cocchi et al., 1986).
It seems
to me it has a great probability of being constantly present both in human
physiology and pathology. A recent investigation on alcoholics leads to further
confirmation (Cocchi, 1993).
Moreover,
what I termed the confabulation - by extension of this denotative word from
verbal to visual language - is the building of an assertion with disparate
elements. It cannot be framed into "the paleologic" (according to Von
Domarus, 1944) of partial identity. Contiguity or opposition. The inclusion
criterion of this category was the choice of immediately close elements to
build the wrong answer.
Eventually
it is curious to observe that these students did not give any answer I could
include into "post hoc, ergo propter hoc" category.
I can
think that they originate from the proposed task based only on static visual
stimuli, which could not, being so, put into motion a mechanism like this.
Conclusion.
The
analysis of wrong answers given by 39 college students to Raven's Progressive
Matrices, Form I, revision 1962, carried out according to criteria used by
Pola, Cocchi & Zerbi, 1988, brought to light 170 non random significantly
grouped answers (.04 - .0001).
A
proposed classification into seven categories showed the distribution of all
170 answers into the category of partial identity, identity by contiguity,
opposition, confabulation, choice of the first figure the drawing of which was
not present in the correspondent matrix ("first not present").
The
results are very interesting and confirm that the analysis of wrong answers
given to Raven's Progressive Matrices can be used to elicit the
neuro-physio-psychological levels the cognitive processes in problem solving
stop.
References.
Anastasi
A.: Psychological testing. MacMillan, New York,1960.
Campbell
D.T.: A tipology of test, projective and otherwise. J.Consult. Psychol. 1957, 21: 206-212.
Cocchi R.: Meccanismi "logici" nella
acquisizione del linguaggio verbale: Una ipotesi esplicativa neurofisiologica
degli ipercorrettismi. Riv. Neurobiol. 1982, 28: 162-190.
Cocchi R., Alcolisti con punteggio < 20
alle Matrici Colorate di Raven. Analisi degli errori. Riv. It. Disturbo Intell.
1993, 6: 269-275.
Cocchi R., Pola A., Sellerini M., Tosca P.,
Zerbi F.: Mirror speaking after neurosurgery. Case history. Acta Neurol. Belg.
1986, 86: 224-232.
Jacobson R.: Essais de linguistique
generale. Editions de Minuit, Paris 1963.
Jacobson R., Halle M.: Fundamentals of
Language. Mouton, Den Haag, 1956.
Pediconi M.G., Russo E., Cocchi R.:
Somministrazione delle Matrici Progressive di Raven ad un campione di studenti
universitari. Riv. Ital. Disturbo Intellet. 1993, 5: 83-88.
Russo E., Pediconi M.G.: Una analisi degli
errori comuni prodotti al test di Raven da studenti universitari. Riv. Ital.
Disturbo Intellet. 1993, 5: 245-249.
Pola A., Cocchi R., Zerbi F.: Raven's
Progressive Matrices PM
qualitative analysis of mistakes and problem
solving strategies. Ital. J. Intellect. Ipair. 1988, 1: 111-118.
Von Domarus E.: The specific laws of logic
in schizophrenia. In: Kasanin J.S. (ed): Language and thought in schizophrenia.
collected papers. Univ. California Press, Berkeley, 1944.
First printed in Italian on Riv. It. Disturbo Intellet. 1993, 6: 83-90.
First published in Internet on 15 October 2001.
Author's address: dr Renato COCCHi, via
Rabbeno, 3
42100 Reggio Emilia
renatococchi@libero.it
Theoretical and research basses