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brain
sciences
Article
The Raven’s Coloured Progressive Matrices in
Healthy Children: A Qualitative Approach
Daniela Smirni
Department of Psychology, Educational Science and Human Movement, University of Palermo,
90128 Palermo, Italy; [email protected]
Received: 29 September 2020; Accepted: 18 November 2020; Published: 20 November 2020


Abstract:
Studies on the structure of intelligence refer to two main theoretical models: the first
one considers intelligence as a unitary construct, the second one assumes the involvement of a plurality
of factors. Studies using Raven’s Coloured Progressive Matrices (RCPM) tasks have often highlighted
the involvement of different cognitive abilities and brain structures, but in the clinical setting,
RCPM measurement continues to be used as a single score. The current study aimed to analyse the
RCPM performance following qualitative clustering, in order to provide an interpretation of the
intelligence assessment through a factorial criterion. The RCPM have been administered to a large
group of typically developing children between 6 and 11 years of age. The sample was divided into
twelve age groups, and the performance of each age group was shown. Three qualitative item clusters
were identified through a factorial criterion. Data showed that performance on RCPM may arise from
different cognitive abilities, starting from basic attentional skills up to the more complex ones that
require perceptual or analogical reasoning. The qualitative parameters could provide more effective
diagnostic and treatment suggestions than a single total score in the clinical setting, and may be
crucial for focusing on strength and weakness in the intellectual functionality evaluation of children.
Keywords:
intelligence; RCPM qualitative parameters; attentional abilities; analogical reasoning;
concrete and abstract reasoning
1. Introduction
Most theories on the nature and the structure of intelligence can be summarised by two broad
theoretical models: the first one considers intellectual activities as the expression of a unitary construct,
and the second hypothesises a plurality of factors with different primary mental abilities that are
functionally independent [1].
In the early decades of the last century, on the basis of statistical–mathematical methods, Spearman
proved that intelligence tests scores, although different, correlate positively with each other. However,
he noted that the strength of these correlations often was not strong. Therefore, he decomposed the
variance in test scores to the part that is common with all other tests, as well as to the part that is unique
to the given test [
2
]. With this background, Spearman hypothesised that each test measures a general
ability, which he labeled as the gfactor”, and a specific factor tapping abilities or processes unique
to the given test, which he labeled as the sfactor” [
3
,
4
]. In this context, intelligence, as a gfactor”,
could be mediated by a specialised region of the brain or by the whole brain being globally activated [
5
].
Subsequently, the further development of factorial analysis methods has encouraged other
structural theories of intelligence, mainly on a statistical basis. Burt [
6
], for example, hypothesised
a hierarchy of intellectual abilities, and distinguished in each individual test three orders of factors:
general, group, and specific factors. Thurstone [
7
], using factorial analysis, concluded that there is
no general factor, but many lower-order, uncorrelated modules or neural processes (so-called bonds),
while Thomson [
8
] rejected Spearman’s gbecause the positive manifold should emerge without
Brain Sci. 2020,10, 877; doi:10.3390/brainsci10110877 www.mdpi.com/journal/brainsci
pf3
pf4
pf5
pf8
pf9
pfa

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brain

sciences

Article

The Raven’s Coloured Progressive Matrices in

Healthy Children: A Qualitative Approach

Daniela Smirni

Department of Psychology, Educational Science and Human Movement, University of Palermo, 90128 Palermo, Italy; [email protected]

Received: 29 September 2020; Accepted: 18 November 2020; Published: 20 November 2020   

Abstract: Studies on the structure of intelligence refer to two main theoretical models: the first

one considers intelligence as a unitary construct, the second one assumes the involvement of a plurality

of factors. Studies using Raven’s Coloured Progressive Matrices (RCPM) tasks have often highlighted

the involvement of different cognitive abilities and brain structures, but in the clinical setting,

RCPM measurement continues to be used as a single score. The current study aimed to analyse the

RCPM performance following qualitative clustering, in order to provide an interpretation of the

intelligence assessment through a factorial criterion. The RCPM have been administered to a large

group of typically developing children between 6 and 11 years of age. The sample was divided into

twelve age groups, and the performance of each age group was shown. Three qualitative item clusters

were identified through a factorial criterion. Data showed that performance on RCPM may arise from

different cognitive abilities, starting from basic attentional skills up to the more complex ones that

require perceptual or analogical reasoning. The qualitative parameters could provide more effective

diagnostic and treatment suggestions than a single total score in the clinical setting, and may be

crucial for focusing on strength and weakness in the intellectual functionality evaluation of children.

Keywords: intelligence; RCPM qualitative parameters; attentional abilities; analogical reasoning;

concrete and abstract reasoning

1. Introduction

Most theories on the nature and the structure of intelligence can be summarised by two broad

theoretical models: the first one considers intellectual activities as the expression of a unitary construct,

and the second hypothesises a plurality of factors with different primary mental abilities that are

functionally independent [1].

In the early decades of the last century, on the basis of statistical–mathematical methods, Spearman

proved that intelligence tests scores, although different, correlate positively with each other. However,

he noted that the strength of these correlations often was not strong. Therefore, he decomposed the

variance in test scores to the part that is common with all other tests, as well as to the part that is unique

to the given test [ 2 ]. With this background, Spearman hypothesised that each test measures a general

ability, which he labeled as the “g factor”, and a specific factor tapping abilities or processes unique

to the given test, which he labeled as the “s factor” [ 3 , 4 ]. In this context, intelligence, as a “g factor”,

could be mediated by a specialised region of the brain or by the whole brain being globally activated [ 5 ].

Subsequently, the further development of factorial analysis methods has encouraged other

structural theories of intelligence, mainly on a statistical basis. Burt [ 6 ], for example, hypothesised

a hierarchy of intellectual abilities, and distinguished in each individual test three orders of factors:

general, group, and specific factors. Thurstone [ 7 ], using factorial analysis, concluded that there is

no general factor, but many lower-order, uncorrelated modules or neural processes (so-called bonds),

while Thomson [ 8 ] rejected Spearman’s g because the positive manifold should emerge without

Brain Sci. 2020 , 10 , 877; doi:10.3390/brainsci10110877 www.mdpi.com/journal/brainsci

a single general ability, through co-sampling. Guilford [ 9 ] expanded Thurstone’s multifactorial theory,

using parameters to classify the high number of isolated intellectual abilities (about 120). On this basis,

it could be hypothesised that different brain regions mediate distinct and relatively independent

intellectual functions [5].

From then to now, new theoretical accounts have been proposed to explain the positive correlation

between tests, and the debate remains an outstanding issue [ 10 ], although its articulation exceeds the

limits of this study.

Some models proposed a theoretical framework in which the singularity and plurality of factors

seem to be connected. For example, the Cattel–Horn–Carrol theory combines the multifactor theory,

including fluid and crystallised intelligence, and a hierarchical theory [11–14].

Recently, a “mutualistic” dynamic model has been developed to explain the positive

manifold pattern. This model assumes that the cognitive system consists of many basic processes,

such as perception, memory, decision, and reasoning. These processes, initially unrelated, interact with

each other during development, becoming a correlated mutualistic network structure in which each

process favours the development of the others. Therefore, there is no single underlying g factor,

but rather a positive interaction between cognitive processes during development that gives rise to the

positive manifold [15,16].

The recent process–overlap theory [ 17 ] highlights that intelligence is determined by multiple

components, both domain-general and domain-specific, and that certain domain-general processes

overlap with domain-specific processes during mental test performance. The domain-general processes

are tapped by a large number of tests, while specific processes are mostly tapped by tests with

corresponding specific (verbal, spatial, etc.) content only. For example, domain-general attention

modulation allows for stimulus focus and interference inhibition. This mechanism seems to be

a common component of all valid tests of working memory capacity (regardless of the domain) [ 18 ].

In this context, Intelligence Quotient (IQ) seems to be redefined as an index of specific cognitive

abilities, rather than as an expression of a latent general cognitive ability [17].

Even today, then, there is a contentious debate about the right level of test score interpretation,

both in clinical assessments and in research settings. In tests like the Wechsler scales, for example,

some authors argue for a profile-based interpretation of subscale or even subtest scores, especially

when the verbal and performance IQ or Verbal Comprehension Index and Perceptual Organization

Index scores are extremely or significantly different [19–22].

Clinicians take the single full-scale IQ (FSIQ) less into account in favour of a complex

cognitive profile that highlights specific abilities to look for the patient’s cognitive strengths and

weaknesses [23,24]. Fiorello and colleagues, in a direct comparison of typical and atypical populations,

found that FSIQ does not adequately represent global intellectual functioning for either typical

children with significant profile variability or children with disabilities, suggesting that FSIQ should

be de-emphasied as a measure of ability and greater emphasis should be placed on index scores,

especially when significant index score differences are evident [23].

Conversely, many researchers argue against the validity and utility of profile interpretation and

claim that global scores, such as FSIQ, are the most appropriate for diagnostic interpretation [25–29].

FSIQ would be the simplest and most efficient method of Wechsler Intelligence Scale for Children

(WISC) analysis, and a more useful measure than index scores in the prediction of academic

achievement [26,28–30].

Taken together, therefore, the studies presented compelling evidence against both the uniform

interpretation of global FSIQ and cognitive profiles, suggesting that the conception of intelligence test

results should be linked to an intelligence model.

The Raven Progressive Matrices test, both in its usual form [ 31 ] and in the simplest coloured

form, the Raven’s Coloured Progressive Matrices (RCPM) test [ 32 ], are widely considered as the most

specifically designed test to measure the g factor and as the purest measure of fluid intelligence [ 33 ].

They were developed in the 1930s as a “culture-free” and nonverbal test to study the genetic

The hypothesis was that a clustering of items according to three factors, extracted in literature,

could provide a more clinically significant profile of the different cognitive abilities involved in RCPM

in each age group.

2. Materials and Methods

2.1. Participants

As part of a neurodevelopmental assessment, a survey for healthy primary school students was

performed. The survey was aimed at investigating the neurodevelopment of cognitive functions

in healthy children, and it was approved by the local ethical committee and school board. It was

conducted according to the ethical principles of the Helsinki Declaration. Only children whose parents

had given informed consent were examined. Students or parents who did not agree to take the exam

were excluded from the study.

A sample of 947 healthy children participated in the study, 476 boys and 471 girls, subdivided in

12 age groups ranging from 6 to 11 years. The number of subjects in each group and the male/female

distribution were counterbalanced across the groups. Participants were recruited from the population

in 13 Sicilian municipalities; they were volunteers for participating in the survey; of medium

social status; and they had no history of neurological or psychiatric diagnosis, learning disability,

or developmental delay.

2.2. Procedures

The RCPM was administered individually, without time limit, in the book format, according

to Raven’s procedure [ 63 ]. Children were asked to choose the missing element from six options in

a drawing. One point was given for each correct answer, and the total score was the sum of the correct

answers, with a maximum score of 36.

2.3. Statistical Analysis

A qualitative analysis of the items, based on the cognitive abilities required on each item,

was performed.

Following the analysis of the existing literature, the factorial structure of the RCPM was presented

on the basis of criteria that grouped the items through the cognitive processes involved.

The sample was divided into twelve age groups, spaced 6 months from each other, and the

performance on each age group was calculated according to the factor clustering, on which mean

scores and standard deviations of correct answers were calculated. The independent t-test was used to

compare mean scores between age groups.

In addition, mean and standard deviation values were also calculated according to a breakdown

of the sample by age and sex.

3. Results

A qualitative analysis of the cognitive abilities involved in each item of the RCPM is summarised

in Table 1. Some items require only the completion of a pattern on the basis of similarity and identity

(light grey background in Table 1). Other items require additional skills that are more complex than

simple identity, such as the pattern completion based on the closure principle of a configuration,

the directionality of the elements (medium grey background in Table 1), or high abstract reasoning

(dark grey background in Table 1).

Table 2 shows the factorial structure of the RCPM extracted by factorial studies in the

literature [53,54]. Factor I, called “continuous and discrete pattern completion through closure”,

was described by items A7, A8, A9, A10, Ab4, Ab5, Ab6, Ab7, Ab8, Ab9, Ab10, Ab11, B3, B4, and B5.

Factor II, called “closure and abstract reasoning”, was identified by items A11, A12, Ab12, B6, B7, B8,

B9, B10, B11, and B12. Factor III, called “simple pattern completion”, consisted of items A1, A2, A3, A4,

A5, A6, Ab1, Ab2, Ab3, B1, and B2.

The mean scores and standard deviations of the correct answers of the 12 age groups, considering

the item clustering by the three factors, are displayed in Table 3.

Analysing the results, according to the three factorial clusters, the factor III items were almost

completely solved from the age of six (six-years-olds’ mean score = 10.76 ± 0.72 vs. 11.5-year-olds’

mean score = 10.91 ± 0.19, out of 11 items) with no significant difference between the mean scores of

the younger and older groups (t 148 = 1.77, p = 0.08). Similarly, very low standard deviations were

detected in all the groups. Such data proves that the cognitive abilities implied in factor III already at

the age of six in normal children are sufficiently developed, and that from this age those abilities do

not discriminate between groups.

Table 1. Qualitative analysis of items: cognitive processes involved in each Raven’s Coloured Progressive Matrices (RCPM) item.

Item Cognitive Processes Involved A2 Difference, identity A3 Difference, identity, similarity B1 Difference, identity, similarity A1 Difference, identity, similarity A4 Difference, identity, similarity A5 Difference, identity, similarity Ab1 Difference, identity, similarity B2 Difference, identity, similarity Ab3 Identity, similarity, identical orientation Ab2 Identity, similarity, identical orientation A6 Difference, similarity, identical orientation B3 Similarity, symmetrical orientation, closure B4 Similarity, symmetrical orientation, closure Ab4 Similarity, symmetrical orientation, closure Ab5 Similarity, symmetrical orientation, closure Ab7 Similarity, symmetrical orientation, open symmetry A9 Difference, identity, similarity, symmetrical orientation A10 Difference, identity, similarity, symmetrical orientation A7 Difference, similarity, gestalt of completion Ab6 Closed asymmetry, symmetrical orientation, gestalt closure B5 Similarity, asymmetry, orientation towards closure A8 Difference, similarity, gestalt of completion Ab9 Open symmetry, symmetrical orientation Ab8 Closed asymmetry, orientation towards closure Ab10 Open symmetry, symmetrical orientation Ab11 Closed symmetry, symmetrical diagonal orientation B6 Asymmetrical change, asymmetrical diagonal orientation B7 Asymmetrical change, asymmetrical diagonal orientation B10 Elements addition to a changing figure A11 Difference, similarity, gestalt of completion B9 Asymmetrical change in a modified figure B11 Elements subtraction to a changing figure Ab12 Open asymmetry, asymmetrical orientation, response creation through analogy B8 Asymmetrical change in a modified figure A12 Similarity, orientation, response creation through analogy B12 Double subtraction of specific characteristics to a figure Items are displayed in descending order of the mean scores. Light grey background: completion on the basis of similarity and identity. Medium grey background: completion based on closure and directionality. Dark grey background: high abstract reasoning.

Instead, in both factors I and II, the results were largely lower than for factor III, but the performance

gradually increased with increasing age. Factor I six-year-olds’ mean score was 8.15 ± 2.83, versus

11.5-year-olds’ mean score of 14.13 ± 1.20, of the 15 items (t 148 = 17.002, p < 0.001). Factor II six-year-olds’

mean score was 1.88 ± 1.71, versus 11.5-year-olds’ mean score of 5.69 ± 2.15, out of 10 items (t 148 = 11.63,

p < 0.001). However, while in factor I, the oldest group reached a score very close to the maximum,

in factor II, no group reached the maximum score, and the lowest scores were recorded.

Considering the performance of the individual age groups, all groups reached the best scores for

factor III, with scores very close to the maximum values, while they reached lower scores for factor I

and even lower scores for factor II. Therefore, the clustering of items according to factor I, and even

more the clustering according to factor II, proves to be more difficult, while factor II was the most

difficult for each age group, suggesting that the cognitive abilities implied in these groups of items

become discriminatory in the assessment of intellectual abilities examined in the RCPM.

Finally, no difference was found between the mean scores of males and females in any age

group (Table 4).

Table 4. Mean and standard deviation of RCPM scores in the three factors, according to a breakdown of the sample by age and sex.

Factor III Factor I Factor II Total Score Age Sex n Mean ± SD Mean ± SD Mean ± SD Mean ± SD

6.0 (^) MF^3538 10.7810.75^ ±±^ 0.680.85^ 8.178.13^ ±±^ 3.052.67^ 1.891.91 ±±^ 1.571.92^ 20.8320.74^ ±±^ 3.844.

6.5 (^) MF^4236 10.7910.75^ ±±^ 0.590.66^ 8.388.39^ ±±^ 2.222.54^ 2.102.08^ ±±^ 1.801.71^ 21.1921.17^ ±±^ 3.133.

7.0 (^) MF^3840 10.8210.78^ ±±^ 0.510.69^ 8.828.85^ ±±^ 2.822.90^ 2.132.13^ ±±^ 1.942.00^ 21.7621.75^ ±±^ 3.844.

7.5 (^) MF^2936 10.7910.85^ ±±^ 0.740.49^ 9.419.44^ ±±^ 2.412.93^ 2.482.50^ ±±^ 2.182.27^ 22.6222.69^ ±±^ 4.354.

8.0 (^) MF^3747 10.8610.90^ ±±^ 0.450.49^ 10.6810.72^ ±±^ 3.272.36^ 2.812.79^ ±±^ 2.402.32^ 24.3224.38^ ±±^ 5.044.

8.5 (^) MF^4239 10.8710.91^ ±±^ 0.530.24^ 11.2911.38^ ±±^ 2.532.41^ 3.143.13^ ±±^ 2.131.95^ 25.3325.51^ ±±^ 4.133.

9.0 (^) MF^3336 10.9510.87^ ±±^ 0.270.45^ 12.0012.00^ ±±^ 2.742.66^ 3.853.81^ ±±^ 2.322.41^ 26.8526.78^ ±±^ 4.434.

9.5 (^) MF^5347 10.8810.92^ ±±^ 0.450.31^ 12.6212.68^ ±±^ 2.471.83^ 4.264.19^ ±±^ 2.592.50^ 27.8727.85^ ±±^ 4.183.

10.0 (^) MF^5441 10.8910.93^ ±±^ 0.290.22^ 13.1513.20^ ±±^ 2.511.25^ 4.134.10^ ±±^ 2.462.03^ 28.2628.27^ ±±^ 4.072.

10.5 (^) MF^3533 10.9410.90^ ±±^ 0.150.24^ 13.1113.12^ ±±^ 2.292.38^ 5.235.24^ ±±^ 2.722.40^ 29.3429.30^ ±±^ 4.454.

11.0 (^) MF^3851 10.9510.90^ ±±^ 0.160.41^ 13.4513.49^ ±±^ 1.922.00^ 5.395.35^ ±±^ 2.882.52^ 29.8229.75^ ±±^ 4.174.

11.5 (^) MF^3532 10.9410.89^ ±±^ 0.170.23^ 14.1414.13^ ±±^ 1.151.17^ 5.665.72^ ±±^ 2.142.15^ 30.8030.81^ ±±^ 2.782.

Overall 10.89 ± 0.44 11.36 ± 3.24 3.48 ± 2.62 25.85 ± 5. Legend: F = Female; M = Male.

4. Discussion

The present study aimed to verify whether a clustering of items, based on previous factorial

studies, could allow, in clinical setting, more effective diagnostic and treatment suggestions than the

overall score.

Generally, in daily clinical practice, RCPM test is widely used as one of the best general intelligence

measures, and it provides a single total score. In such a scoring system, one point is assigned to

any correct item, regardless of the cognitive process involved in that specific single item. It seems,

therefore, that the right answers exclusively result from a single factor, like Spearman’s general

intelligence. Conversely, a single total score does not consider that each item may have different

cognitive features and may be supported by different cognitive abilities. That is, the same result can

derive from responses resulting from different qualitative clusters, and therefore underlie different

cognitive abilities. This analysis of the type of cluster involved may have different diagnostic and

clinical relevance.

In the present study, a large group of typically developing children were administered RCPM

tests according to the standard procedure. Three qualitative clusters of items were identified according

to factorial studies of literature. The results of the sample were examined using the three qualitative

clusters, factorially extracted.

As expected, in each cluster, scores gradually increased with increasing age. However,

it is interesting to point out that in the factor III cluster, implying simple or discrete pattern completion,

the problems have been solved properly by almost the whole sample in every age groups. Therefore,

cluster items proved relatively simple as early as the age of six, probably because they are supported

by basic cognitive skills. These findings may be particularly suggestive in the clinical evaluation of

general cognitive function. Poor performance in such items may have a relevant clinical and treatment

prominence, suggesting an impairment in basic cognitive abilities. Similarly, any poor total score

resulting from poor performance in the problems of the factor III cluster should have a different

diagnostic value than a poor total score resulting from other combinations of wrong items.

Factor III includes items in the form of a continuous pattern, where the missing piece and pattern

have the same formal visuo-spatial features (e.g., A4, A5, Ab1, Ab2, Ab3, B1, B2). That is, the choice of

the entry is mainly mediated by selective attentional analysis, as well as visual discrimination and visual

matching processes. Therefore, the wrong answers might reflect poor selective attention and immediate

focusing on a single, main, prominent perceptual element. The factor III items evaluate the basic

skills of attentional and visuo-perceptive exploration, in terms of identity, similarity, and orientation

correspondence. Six-year-old children proved able to identify the missing element to complete

a continuous or discrete pattern, even in the presence of alternative choices as distractors, and from

an early age, visuo-spatial attentive abilities implied in attentive problems of this cluster items appears

sufficiently organised. These findings are consistent with a previous study [ 64 ] that showed that

children from the age of nine and up performed almost as well as the adult control group in a complex

visual discrimination tasks, such as Benton’s Visual Form Discrimination Test [65].

In the factor I cluster, implying continuous and discrete pattern completion and pattern completion

through closure, the results in all age groups were poorer than for factor III, and no age group reached

the maximum scores, although by increasing the age the results gradually improved. As a whole,

then, this item cluster proved to be more complex and demanding. The choice of missing element in

this item cluster implied an increasingly more complex perceptual gestalt process, requiring a selective

analysis of the single elements and a shifting from part–whole and whole–part to form a coherent

gestalt and consistent global whole (e.g., A7, A8, Ab4, Ab5, B3, B4). This cluster of items evaluates

integrated perceptual abilities involved in the closure of a coherent whole or gestalt through the

analysis of the “whole” and “parts”.

In the items of factor II, involving closure as well as concrete and abstract reasoning by

analogy, the performances were the poorest in all the age groups, especially in the younger ones.

Group performance improves with increasing age, but no group has achieved full scores. Even the

older groups showed a still-incomplete maturation of the abstractive functionality of the prefrontal

regions involved in these kinds of tasks [ 66 , 67 ]. This cluster includes homogeneous items in which the

detection of the missing piece implies a higher abstract analogical process. To understand similarities

and differences between the elements, a target figure and alternative choices must be simultaneously

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