disponível em www.scielo.br/prc
Intelligence, Age and Schooling: Data from the Battery
of Reasoning Tests (BRT-5)
Inteligência, Idade e Escolarização: Dados da Bateria
de Provas de Raciocínio (BPR-5)
Ricardo Primi*,a, Gleiber Coutob, Leandro S. Almeidac, M. Adelina Guisanded
& Fabiano Koich Miguele
a
Universidade São Francisco, Itatiba, Brasil, bUniversidade Federal de Goiás, Catalão, Brasil,
c
Universidade do Minho, Braga, Portugal,
d
Universidade de Santiago de Compostela, Santiago de Compostela, España
& eUniversidade Estadual de Londrina, Londrina, Brasil
Abstract
Intelligence is commonly divided into two distinctive areas: fluid intelligence (Gf), which is understood as
the skill of reasoning or intelligence as a process, and crystallized intelligence (Gc) that involves skills that
are more related to learning and experience (knowledge-based skills). The objective of the present work
was to investigate the effects that schooling and age exert on fluid and crystallized intelligence measuring
students’ results in sub-tests of the Battery of Reasoning Test (BRT-5). This study considered a sample
composed of 1,722 students – 603 were assessed with Form A of the battery and 1,119 with Form B. The
results show that intelligence is systematically associated with schooling and age. Some difficulties in
separating the effects of cognitive development from the effects of formal learning on students’ cognitive
performance are also emphasized.
Keywords: Intelligence, fluid/crystallized intelligence, psychometrics, schooling, age.
Resumo
A inteligência é comumente dividida em fluida (Gf), entendida como habilidade de raciocínio ou inteligência
como um processo, e cristalizada (Gc) como as habilidades mais associadas à aprendizagem e experiência
(habilidades associadas aos conhecimentos). No presente trabalho, o objetivo foi investigar os efeitos que
a escolarização e a idade exercem sobre Gf e Gc tomando os resultados dos alunos nos subtestes da Bateria
de Provas de Raciocínio (BPR-5). Este estudo considerou uma amostra composta por 1722 estudantes
respondendo 603 à forma A dessa bateria e 1119 à sua forma B. Os resultados apontam relações sistemáticas
entre inteligência, escolaridade e idade. Também se enfatiza a dificuldade em se separar os efeitos do
desenvolvimento cognitivo e da aprendizagem formal no desempenho cognitivo dos alunos.
Palavras-chave: Inteligência, inteligência fluida/cristalizada, psicometria, escolarização, idade.
Even though there is some controversy concerning the
definition and measurement of intelligence, a relative
consensus on the Cattell-Horn-Carroll hierarchical model
of cognitive abilities has been noted in the last decade
(McGrew, 1997, 2005). As its name suggests, this model
incorporates the Gf-Gc theory, which initially originated
with the work of Raymond Cattell (1963, 1971) and which
later on was developed and extended by Horn and Cattell
(1966) in articulation with the model proposed by Carroll
(1993) based on a massive meta-analysis work.
*
Endereço para correspondência: Departamento de Psicologia, Universidade São Francisco, Rua Alexandre
Rodrigues Barbosa, 45, Itatiba, SP, Brasil 13251-900. Email: rprimi@mac.com.br, gleibercouto@yahoo.com.br,
leandro@ie.uminho.pt, mariaadelina.guisande@usc.es e
fabiano@labape.com.br.
Agência de financiamento CNPq.
The psychometric theory of Cattell (Gf-Gc) initially proposed a detailed elaboration of the g factor concept of
Spearman (1927) into two components: fluid intelligence, Gf, and crystallized intelligence, Gc. On one hand,
Gf is understood as the potential for understanding and
relating information, as well as solving new problems
for which there is no available knowledge previously
stored in memory. Thus, it implies deliberate implementation and controlled and systematic mental processes
in order to find relationships between information organisation (induction) and the derivation of information
(deduction). On the other hand, Gc is understood as the
quality – in terms of its breadth and depth – of knowledge
gained from the process of acculturation, which occurs
through formal schooling and life experiences. This way,
the information base (Gc) makes it easier to understand
79
Psicologia: Reflexão e Crítica, 25 (1), 79-88.
information and solve problems that are repeated in lives
of people in a relatively automatic way using the application
of information already known.
Although postulated as two relatively distinct abilities,
these factors are highly related, because the investment
of fluid intelligence in the learning experience promotes
the development and structuring of knowledge and skills
in specific areas that lead to crystallized intelligence.
Hence, these capabilities might be highly correlated, since
high investment of Gf in learning will result in success in
various areas of knowledge that leads to a correlation with
Gc. On the other hand, besides being influenced by Gf, Gc
is also relatively more vulnerable to cultural resources
promoting learning (such as the access and quality of formal and informal educational interventions) and other individual variables such as motivation, interest and dedication. Thus, people with similar levels of Gf but distinct
socio-cultural backgrounds will differ in Gc, resulting in a
relative separation of Gf. In short, Gf can be understood
as a more “pure” general capacity that is closer to brain
maturation; a more “fluid” one, as the name denotes,
which metaphorically refers to the idea of something that
is not yet fully complete. On the contrary and despite its
historical roots in Gf, Gc reflects the sum of influences of
the experiences of an individual. In this way, the “crystallized” Gf potential is molded by the application of Gf in
varied learning experiences (Johnson & Bouchard, 2005;
Kvist & Gustafsson, 2008). In a more recent version of
that theory, seven other abilities were added besides Gf
and Gc (Carroll, 1993; Horn, 1991; Horn & Noll, 1997).
At the same time that the Gf-Gc model was evolving,
Carroll (1993) completed his seminal meta-analytical
scanning work about 60 years of investigations on intelligence and the re-analysis of 461 data sets from 1500
references, which included almost all major and classical
psychometric studies. This study resulted in a three-tier
hierarchical model of intelligence. Despite the differences
between the models of Carroll and Cattell and Horn, the
gathering of these three authors as technical advisers for
the Woodcock WJ-R test (McGrew, 2009) led to the creation of an “umbrella” terminology integrating these theories, which has since been known as the Cattell-HornCarroll (CHC) theory of cognitive abilities (Carroll, 1997;
Flanagan, Genshaft, & Harrison, 1997; Horn & Noll,
1997; McGrew & Flanagan, 1998). Some studies have
referred to the CHC model as the most consensual, complete and modern description of intelligence (Flanagan
& Ortiz, 2001; McGrew, 1999; McGrew & Flanagan,
1998; Phelps, McGrew, Knopik, & Ford, 2005; Primi &
Almeida, 2002; Stankov, 2000a, 2000b). Such contributions lead the research in the area especially that aimed at
understanding the factors measured by intelligence tests.
One central question concerning intelligence research
refers to the degree to which the educational system exerts
an impact in the development of cognitive abilities. The
origin of the primary concepts of the Gf-Gc theory has to
do with this problem, since they were originally presented
80
at a symposium back in the 1940s, which focused on the
influence of age on cognitive abilities. Two classes of influences on cognitive development were proposed at the
symposium: educational and cultural opportunities and
neurological maturational, which are obviously associated
to Gc and Gf, respectively (Horn, 1991).
These concepts were adopted by Ackerman (1996),
who proposed a theory about the cognitive development
of adults. This model refers to intelligence as a process
and intelligence as knowledge. Once again the difference
is between the ability of deductive and inductive reasoning on the one hand and knowledge and skills on the
other. In the latter case, one is facing cognitive abilities,
whose development and expression in many fields, are
the result of a long line of studies, experiences and deliberate practices and whose development is expressed
through structures of expertise. For this reason, according to Ackerman (1996), the two types of intelligence
differ in their development.
In terms of its development, Gf has its peak at the end
of adolescence and early adulthood. Thereafter, it remains
stable for a few years until it starts to decline, especially
in aspects related to processing speed, while on the contrary Gc is developed in a slow and gradual way. This
way, Gf stabilizes at the end of the early years of adulthood
and remains so for a longer period than Gc, which begins
its decline at a relatively advanced (elderly) stage. As an
example, see the analysis of McGrew and Evans (2002)
concerning the sub-tests of Woodcock Johnson III (WJIII). These differential patterns about the influence of the
age and schooling variables on cognitive abilities have
served as evidence of the validity of the approach that
presents the Gf and Gc constructs as being relatively distinct, although highly correlated.
Therefore, several studies seem to emphasize a differential impact of education on different cognitive abilities
(Almeida, 1988; Cattell, 1971; Gustafsson, 2001; McGrew
& Evans, 2002). In order to differentiate the impact of
schooling and age (development related to maturation),
the results suggest that education has an important contribution for performance in testing situations, including those
more related to fluid intelligence. Thus, there is some convergence of research, which suggests that fluid intelligence
is influenced by education, even if this influence is less
solid compared to that which occurred in tests related to
crystallized intelligence (Cahan & Noyman, 2001; Stelzl,
Merz, Eulers, & Remer, 1995).
A major methodological problem inherent in these studies concerns the separation of the influence of school in
cognitive development regardless of maturational development (Ceci, 1991; Cliffordson & Gustafsson, 2008; Stelzl
et al., 1995). In regard to children, it is frequently assumed
that the age variable is an indicator of neural maturation
and that years of study are an indicator of education and
the consequential impact of formal schooling. However,
there is a high correlation between age and schooling: age,
especially in childhood, follows maturational develop-
Primi, R., Couto, G., Almeida, L. S., Guisande, M. A. & Miguel, F. K. (2012). Intelligence, Age and Schooling: Data from the Battery
of Reasoning Tests (BRT-5).
ment and, therefore, the association between it and cognitive abilities is taken as an estimation of the influence of
biological factors in the development of intelligence.
Schooling is a variable associated with formal stimulation
and, therefore, its association with intelligence is taken
to estimate the influence of environmental factors in the
school context. Still, since age increase follows education
increase, it is difficult to separate the unique influence of
one and the other on cognitive development.
It is more plausible to conceive that maturational cognitive development, due to organic growth, is accompanied by systematic stimulation that occurs in school,
so that the two factors operate together and influence
cognitive development in an interactive way. Even so,
when analyzing the association of these variables alone
(age and education) with intelligence, there is a considerable amount of shared variance and this association
cannot be easily justified as attributable to education or
age but rather by both factors simultaneously.
A methodological strategy adopted to try to separate
the influence of these variables is based on the fact that:
children of 1 year of chronological age with the effect
of schooling held constant can be estimated from the
difference between the youngest and oldest child
within the same grade level. On the other hand, the
effect of 1 year of school attendance with chronological age held constant can be estimated from the
difference between the oldest child of any given grade
level and the youngest child of following one. (Stelzl
et al., 1995, p. 281)
Such methodology makes it possible to use a small
unique portion of variability of one variable that exists
within constant levels of the other, thus allowing the
estimation of the specific effect of each. Cliffordson and
Gustafsson (2008), as well as Stelzl et al. (1995), used
this methodology and noted that schooling has a greater
effect than age in cognitive development, which is consistent with the data reviewed by Ceci (1991). There is
also evidence that the change is greater in tests where
content resembles the domain of school syllabuses. Also
– in samples of young adults – age has a negative effect
on fluid intelligence tests, which is consistent with the
decline of Gf, despite occurring at earlier ages than traditionally observed.
In short, the literature reviewed shows evidence of the
existence of differential patterns of association between
age/education with Gc and Gf. These patterns can be used
as a reference for studies of test validation that are proposed to measure such constructs. The present study
proposes to investigate the associations of schooling and
age with scores on five sub-tests of the Battery of
Reasoning Tests (BRT-5; Primi & Almeida, 1998).
Psychometric studies of BRT-5 use traditional intra group
norms, when comparing students with the same level of
schooling. More recently, a study was developed using
the Item Response Theory to equate scores of Forms A
and B (Couto, 2005, 2007). Using a common scale for
Forms A and B, it was possible to compare the scores of
all school levels covered by BRT-5. This article is, therefore, aimed at studying the relationship between schooling
and age, as well as the equated scores of the BRT-5, as an
additional study of validity of the battery sub-tests. The
main issue investigated was whether the variable school/
age had a different association for different sub-tests due
to the composition hypothesized for these sub-tests.
Method
Sample
The data resulted from the Brazilian standardization
study of BRT-5. From the sample of 1,722 students, 603
answered Form A of the test. 30.4% of the students were
enrolled in the sixth grade (183), 29.3% in the seventh
grade (175) and 40.3% in the eighth grade (245). Students
were aged between 11 and 18 years old. 48.9% were male
(295) and 51.1% female (308). The remaining 1,119
students answered Form B. 25.2% of these students were
in their freshmen year of high school (282), 52.1% in
their second year (583) and 22.7% in their third year (254).
Students were aged between 14 and 21 years old with
42.7% being male (478) and 57.3% female (641). It is
important to clarify that the educational system in Brazil
is divided into three cycles: elementary school, which
ranges from first to eighth grade, high school, which ranges from ninth to eleventh grade and, finally, superior
education, where the number of years depends on the
chosen course (Psychology, Law, Engineering, Computing, etc.). Each school year is called a “grade,” so the
text referring to tenth grade, for example, is to be understood as the second grade of high school and so on in
respect to the other years of elementary and high school.
The Brazilian standardization study occurred during 1998
and 1999, when the two forms were applied to students
from elementary and middle schools in different cities in
the states of São Paulo (Santo André, São Bernardo, Campinas, Itatiba, Morungaba and Mogi Guaçú) and Rio Grande do Sul (São Leopoldo and Novo Hamburgo).
Instrument
The BRT-5 (Primi & Almeida, 1998) was developed
from the Differential Reasoning Tests Battery (BPRD;
Almeida, 1988). It is composed of five sub-tests: Abstract
Reasoning (AR) consisting of 25 items involving analogies with geometrical figures that have to be answered
within a twelve minute time limit; Verbal Reasoning (VR)
consisting of 25 items involving analogies between words
that have to be answered in a ten minute time limit; Numerical Reasoning (NR) consisting of 20 items in which
linear or alternating series of numbers are presented and
the student must find the rules of arithmetical progression
for each series in order to find the two numbers that complete the sequence within an eighteen minute time limit;
Spatial Reasoning (SR) consisting of 20 items that present
sets of three-dimensional cubes in motion for the student
81
Psicologia: Reflexão e Crítica, 25 (1), 79-88.
to find the type of motion from an analysis of different
faces and then choose the answer that represents the last
cube in the series, which also has to be answered in an
eighteen minute time limit; and Mechanical Reasoning
(MR), which is composed of 25 items containing pictures
of the practical contents of physics and mechanics from
which the student must choose the answer that best
represents the outcome of every situation, which has to
be answered in a fifteen minute time limit.
In Brazil there are two available forms: Form A for
students ranging in the sixth to eighth grades of elementary
school and Form B for students ranging from the first to
third grades of high school. There is an ongoing study
aiming at a first version for the first to fifth grades (Cruz,
2008). In Portugal the battery is available in three forms
according to the schooling of the students. They are for
the fifth and sixth grades, the seventh to ninth grades and
for the tenth to twelfth grades. The forms are equivalent,
have been validated in the same way in the two countries
and show adequate indices of reliability and validity (see
Primi & Almeida, 2000 for details).
The BRT-5 has its theoretical roots in psychometric
models and in cognitive psychology (Primi & Almeida,
1998). Its series, analogies and problem solving items
(practical situations involving mechanical objects) describe a measure of inductive reasoning and – through this
– the broad Gf factor. As reported in the literature, there
is strong evidence that Gf matches the g factor. Therefore,
according to this perspective, the general score of BRT-5
is supposed to reflect the g factor (Kvist & Gustafsson,
2008). The original intention of the BRT-5 was to obtain a
measure of g by means of the sum of five sub-tests with
different content but it settled on the same task of analogical inductive reasoning with g as the main factor. At
the same time, every sub-test was designed to provide
information about specific factors associated with the content of tasks; namely, Gc in the VR and NR sub-tests or Gv
(visuo-spatial intelligence) in the SR and AR sub-tests.
A number of empirical studies support these interpretations. For example, Primi and Almeida (2000) found a
one-dimensional solution explaining most of the covariance between sub-tests of the BRT-5. Cruz (2008), in
a joint factor analysis of the BRT-5 sub-tests with tests of
reading, academic classifications and Raven Progressive
Matrices, clearly found two Gf and Gc factors, and that
Raven was grouped with the sub-tests of the BRT-5 in
the Gf factor. In a correlation analysis of BRT5-6 with
the WISC-IV sub-tests, Almeida et al. (2007) found that
the VR correlates with greater magnitude in Similarities
and Comprehension sub-tests, the Cubes with AR and the
NR with the Arithmetic, Cubes and Information sub-tests.
This data is consistent with the hypothesis that these
correlations are relatively high because of specific factors
Gc, Gv (visuo-spatial intelligence) and Gq (quantative
intelligence). In terms of predicting school grades, generally there are larger magnitudes of VR and NR tests with
Portuguese and Mathematics, respectively and of AR with
82
Mathematics grades (Almeida et al., 2007; Cruz, 2008;
Lemos, Almeida, Guisande, & Primi, 2008; Primi &
Almeida, 2000). Finally, Primi and Almeida (1998) noted
that, in Portugal, students of natural sciences and arts have
higher scores on AR, SR and MR tests, whereas students
in the humanities area present lower scores. These
differences are not significant with respect to VR but these
results are consistent with the hypothesis that these tests
measure a specific Gv component, which would explain
the higher results of students in the tests with content more
related to their academic curriculum.
Procedures
BRT-5 sub-tests of Forms A and B were equated using
the common item method. A single database of all subjects
and their responses to Forms A and B was then prepared,
which assumed that the missing responses were unique
to each form. The Rasch model was applied five times –
once for each sub-test (AR, VR, NR, SR and MR) – in
order to calibrate items and estimate measures for the
subjects (Couto, 2005, 2007). Subject theta values on
Logit scale were linearly transformed into traditional
IQ scale (M = 100; SD = 15) using the average calculated for the third grade of high school, as a reference and
the standard deviation calculated for the total sample.
The average of this sub-group was chosen, because the
literature indicates that fluid intelligence tends to have
its peak around this age group. Thus, the choice of this
reference point describes the value 100 as the average
fluid intelligence peak in relation to the age of the groups
involved. The choice of the Logit standard deviation
from the total sample was made in order to try to obtain
a more reliable estimate of the dispersion of the scores
that could logically be obtained from a larger sample
instead of a sub-set of the sample.
As discussed previously, when studying the associations of age and education with cognitive measures, there
is always the problem of multi-collinearity between the
first two variables (in this study the correlation between
age and grade is r =.87). Since schooling development
goes along with age, it is difficult to separate the single
association that each variable has on intelligence. In trying
to extract the maximum amount of information from the
two variables – education and age – a series of systematic
regression analyses was used, as explained below.
Conceiving schooling as age accompanied by education, this variable was always entered as the first variable
in the regressions that had BRT-5 sub-tests as dependent
variables. Its effect is interpreted as indicating the simultaneous effect of age accompanied by progressive formal
schooling. A second predictor – called the residual age
(rAge) – was obtained from a regression having age as
the dependent variable and schooling as an independent
variable, which represents age variation that could not be
predicted by schooling. Generally speaking, this predictor
indicates age-grade distortion, where students that were
retained in a grade due to insufficient school achievement
Primi, R., Couto, G., Almeida, L. S., Guisande, M. A. & Miguel, F. K. (2012). Intelligence, Age and Schooling: Data from the Battery
of Reasoning Tests (BRT-5).
would score higher. Conversely, younger students who
are in a grade consistent with their age would score lower.
Therefore, this variable was included in the regression
analysis after age and may be interpreted as age unaccompanied by schooling.
It must be stressed that this methodology does not isolate
the unique effects of each variable, because the first one
(schooling) carries the effect of age accompanied by
schooling. Thus, the first effect contains age intertwined
with schooling. However, the second variable (residual
age) brings a unique variance associated with increase in
age that is not explained by schooling. Together these
two variables add up to the maximum information contained in both variables. The logic of using the age residual and not a school residual is based on the fact that
it is possible to observe increase in age unaccompanied
by schooling and its variance would be higher the more
pronounced are cases with age-grade distortion in the
sample. On the other hand, it is not possible to observe
an increase in school unaccompanied by age increase,
because the latter is uninterrupted.
A Repeated Measures Analysis of Variance (ANOVA)
was initially employed with normalized sub-test theta
scores as dependent variables, the type of sub-test (5) as
an intra-subject variable, school grades (SG) and the
administrative dependence (AD) of the school to which
it belonged (public and private) as between group
variables. The variable AD was included, because in all
normative studies of BRT-5 the type of educational
establishment has always been strongly associated with
performance. In Brazil, there is a very large socio-economic gap between the populations of the two educational
establishments. Therefore, this variable ended up being
an indicator of the social, economic and cultural environment of the students, although an indirect one. One
can interpret this variable as an indirect indicator of the
wealth of resources that allows the creation of a positive
environment for learning and intellectual development.
Finally, five multiple regression analyses were run using
the stepwise method in which the BRT-5 normalized subtests were defined as dependent variables with SG and
rAge being independent variables.
Table 1
Descriptive Statistics of Standardized and Equated Scores on BRT-5 Sub-tests according to Sub-tests, Grade and
Administrative Dependency of the Schools
Grade
Administration
6
Public
Private
7
Public
Private
8
Public
Private
9
Public
Private
10
Public
Private
11
Public
Private
Total
Public
Private
Total
AR
VR
MR
SR
NR
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
M
SD
65.6
16.9
83.0
16.0
69.1
17.0
85.2
17.9
80.3
16.5
89.8
16.6
84.7
16.0
94.8
15.5
88.1
14.3
94.0
13.9
86.4
13.8
105.3
12.3
63.3
13.8
80.4
15.4
68.3
12.7
83.0
14.0
74.5
15.1
87.0
14.1
82.8
13.2
91.2
11.6
87.6
12.7
94.0
12.9
87.0
14.5
104.4
12.5
77.7
9.8
85.6
10.6
79.0
11.7
85.9
10.8
81.8
12.7
91.4
12.6
85.8
13.0
96.2
13.9
90.7
13.1
95.6
12.5
87.2
13.3
106.2
13.1
76.7
12.0
87.3
12.9
79.4
9.8
90.6
13.1
84.0
11.9
95.6
14.0
87.8
12.0
98.3
14.7
88.6
13.1
94.2
12.4
86.7
10.4
104.6
13.4
66.6
16.4
84.4
18.3
75.5
13.2
84.6
17.5
81.5
18.5
92.7
14.6
83.2
13.6
90.0
13.3
85.9
14.9
91.8
12.8
86.9
14.6
103.0
12.4
M
SD
M
SD
82.2
17.2
94.3
16.5
80.4
15.8
92.9
15.6
85.7
13.5
95.7
14.4
85.6
12.7
96.3
14.3
82.0
16.2
93.1
15.6
M
SD
87.9
17.9
86.3
16.8
90.5
14.8
90.6
14.5
87.2
16.9
83
Psicologia: Reflexão e Crítica, 25 (1), 79-88.
Table 2
Results for the Analysis of Variance of BRT-5 (5 sub-tests within subject) X School Grades (SG, 6 between groups) X
Administrative Dependence (AD, two levels)
Within Subject Effect
Greenhouse-Geisser
Variable
BRT 5
BRT 5 * SG
BRT 5 * AD
BRT 5 * SG * AD
Square Sum
df
Mean Square
F
p
Eta2
29166.56
19845.48
2104.25
5622.94
4
20
4
20
7291.64
992.27
526.06
281.15
66.79
9.09
4.82
2.58
.000
.000
.001
.028
.040
.028
.003
.008
Between Subject Effect
Greenhouse-Geisser
Variable
Square Sum
df
Mean Square
F
p
Eta2
SG
AD
SG * AD
236155.40
207066.11
30944.32
5
1
5
47231.08
207066.11
6188.86
93.24
408.75
12.22
.000
.000
.000
.225
.203
.037
Results
Table 1 shows the mean and the standard deviations of
the results of BRT-5 sub-tests by school grade and administrative dependency (public or private). Figure 1 plots
the means against the same variables showing the patterns
of the data. Table 2 presents the results of the ANOVA 5
(BRT-5) X 6 (grades) X 2 (administrative dependency)
having the standardized score as a dependent variable, the
type of sub-test as a within subject variable (BRT-5), and
grade and administrative dependence as between factors.
All the main effects and interactions were significant
but they differ in magnitude. The effect of greater theoretical importance is the variable grade, which in association
with the type of school did indeed reveal greater magnitude, thus explaining 22% and 20% of the variance, respectively. In general, the scores increase with grades and
the students from private schools generally have higher
performances. There is also a significant interaction between these two variables. In general, as can be seen in
Figure 1, for students from public schools (left panel)
the increase occurs up to the eighth grade of elementary
school. In high school, the increases are much smaller or
non-existent. Amongst the students of private schools
(right panel), one continues to observe an average increase with grade in high school. In this group of students,
despite a drop between the first and second year for some
sub-tests, there is a considerable increase of performance
Figure 1. Average standardized scores in BRT-5 sub-tests (1:AR, 2:VR, 3:MR, 4:SR and 5:NR) for public (left panel) and private
(right panel) schools.
84
Primi, R., Couto, G., Almeida, L. S., Guisande, M. A. & Miguel, F. K. (2012). Intelligence, Age and Schooling: Data from the Battery
of Reasoning Tests (BRT-5).
from the second to the third year of high school. These
effects interact with the BRT-5 tests, setting different
standards depending upon the test. It is interesting to
note that the rate of increase with grade varies depending
upon the sub-test with VR displaying a pattern of steady
increase over the series.
Table 3 shows the results of multiple regression analysis
(using the stepwise procedure) in order to try to predict
the standardized scores in each sub-test from the School
Grade (SG) and the Residual Age (rAge). Data indicates
that the grade is always a significant predictor in the model
and with the greater magnitude. However, it must be
recalled that this effect carries the effect of age; in other
words, it is intertwined with the effect of age and, therefore, cannot be taken as indicative of the greater importance of grade over age.
Table 3
Results of Multiple Regression Modeling Test Performance from the School Grade (SG) and Residual Age (rAGE) for
the Five Sub-tests
B
EP
β
R, R2, ∆R2 and ANOVA
AR
SG
rAge
5.08
-3.49
.25
.38
*** 0.47
*** -0.19
R=.47; R2=.22; ∆R2=.04
***F(1,1695)=246.18
VR
SG
rAge
5.59
-2.70
.22
.33
*** 0.51
*** -0.16
R=.54; R2=.29; ∆R2=.02
***F(1,1694)=347.09
MR
SG
rAge
3.91
-0.54
.21
.31
*** 0.42
** -0.04
R=.42; R2=.17; ∆R2=.00
***F(2,1696)=178.83
SR
SG
rAge
3.06
-2.32
.21
.33
*** 0.33
*** -0.16
R=.37; R2=.13; ∆R2=.02
***F(1,1687)=130.67
NR
SG
rAge
3.78
-3.69
.24
.37
*** 0.35
*** -0.22
R=.41; R2=.17; ∆R2=.05
***F(1,1647)=169.36
Variables/Predictor variables
*** p<.001; ** p<.10
Residual age, on the other hand, has a significant effect
of smaller magnitude and in the opposite direction, that
is, the greater its value the lower the performance. To
interpret this it must be remembered, due to the procedure
that was used to calculate it, that it shows zero correlation
with age. It indicates the distortions between school grade and age, that is, it is an indicator of the time that has
been passed without the corresponding school progression. Thus, this effect indicates that the older students in
the same grade tend to have a lower performance in the
tests.
Some peculiarities are striking when analyzing the
effects of these variables in the different sub-tests of BRT5. The school grades have higher explanatory power in
the VR test (r=.51) and less explanatory power in the SR
test. The residual age has increased its explanatory power
in the NR test (r=-.22; ∆R2=.05) followed by the AR test
(r=-.19; ∆R2=.04).
Discussion and Conclusions
This study was aimed at examining the relationship
between schooling and age with the BRT-5 sub-tests by
exploring the patterns of association and their consistency
with constructs that each sub-test is supposed to measure.
In general terms, a systematic increase in performance
scores was observed throughout the grades. This increase
is slightly different depending on the type of school. In
the group of students from private schools, where it can
be generally inferred that the quality of education is due
to higher financial resources, there is a relatively more
linear increase throughout the years of schooling. This
is more noticeable in the VR test and less in the SR and
NR tests. In the group of students from public schools,
where lower availability of resources can be inferred,
there is a non-linear increase, which is higher in the first
series but decreases in high school. Once again, this
85
Psicologia: Reflexão e Crítica, 25 (1), 79-88.
pattern is less prominent in the NR and more significant
in the SR test.
Although it was not part of the goal of this study to test
the effect of the type of school, this variable stood out as
a prominent effect. The results were similar to what has
been observed in studies that investigate the association
of intelligence and/or achievement with socio-economic
status (Braun, Jenkins, & Grigg, 2006; Sirin, 2005). The
type of school is conceptually closer to education than is
age, since it indicates students of the same age but who
attended different kinds of schools. This variance might
mean differences concerning affluent neighborhoods,
level of parental education, resources, extra-curricular
activities and so on. This difference may be interpreted
as an external variable indicating more informal education
provided by parents of a higher educational level, as well
as environments with more resources. The relative magnitude of the type of school was comparable as the effect
of school grade. Therefore, it is an important variable
deserving further systematic studies that should address
the question of why it is so strongly associated with
intelligence.
The increase observed in the scores seems to represent
the influence of the combination of increased education
with the development of the basic cognitive processes
independent of learning (mostly age related) that are
accompanied by the stimulus of schooling. According to
the studies of Ackerman (1996) and McGrew and Evans
(2002), the expected results for tests that are more related
to Gf and Gv, namely AR and SR, would be to the
observance of a steady increase for the initial grades and
a more modest growth in high school. For tests more
related to Gc, namely VR and NR, one would expect to
see continuous growth, even for high school students. It
was observed that the SR and VR sub-tests present a
pattern that is closer to what one would expect, thus
corroborating that the specific component of the VR test
probably contains more Gc and the SR test more Gv. In
relation to the NR test – for which a pattern consistent
with Gc was expected – it actually showed a pattern more
consistent with Gf. In contrast, the AR test appeared to
be relatively more consistent with Gc, especially when
considering students in private school.
Regarding the NR test, although it involves mathematics
content that is required to be learned at the most basic
level in school (knowledge of arithmetical operations of
addition, subtraction, multiplication and division), it can
be inferred that this content is not complex enough to be
a specific factor (Gc or Gq) of individual differences in
samples of subjects in middle education, as is the case of
the studied sample. So one can explain that in this sample
there is a prevalence of reasoning components associated
with Gf in the numerical series presented in the NR test.
In relation to the AR test, the results are more difficult
to interpret. Although a decrease of the increase in scores
in the final grades was expected, since Gf is relatively
86
less easily influenced by schooling, the literature indicates
that this influence exists (Cahan & Noyman, 2001; Ceci,
1991; Cliffordson & Gustafsson, 2008; Stelzl et al., 1995).
within addition to this is the fact that a non-expected
pattern was observed in the group of students in private
schools, where both higher rates of developmental trajectories and also a higher quality of environmental stimulation – both formal (schools) and non-formal (family,
friends) – was expected. So in this group it is possible to
observe a continuing increase in all sub-tests.
Considering that the increase observed in the scores of
all tests is the combined effect of cognitive development
and education and that these two effects are combined in
the grade and age variables, an attempt to estimate the
effect of these two variables was made by optimizing the
whole of the information contained therein. The results
indicated that the increase in grades (carrying the impact
of age) is associated with the increase in scores and the
residual age is associated with a decrease of the scores.
This data can be interpreted in two ways. On the one hand,
if intelligence is thought to be a causal variable of achievement, these results could be interpreted as low intelligence being associated with low achievement and grade
retention. In fact, the residual age is significantly correlated with the number of grade retentions, r=.48, p<.001.
On the other hand, considering the idea of Gf, as a
consequential variable, this data may mean that the progression of intelligence is dependent on the advancement
of schooling, although it may be a slow and indirect
product of these factors. Because of the correlational
nature of the data, it is not possible to decide in favor of
one or other explanation but they can be considered as
possible interpretations and both may be valid to some
extent.
However, the methodology adopted in this study is
attractive, because differential patterns may favor one or
another hypothesis. If a test heavily influenced by school
is considered, grade and residual effects of a high magnitude and an opposite direction should be observed, since
school progression positively influences the development,
while stagnation (an increase of age without following
the progression of school) is a negative influence. Considering tests largely influenced by development and little
influenced by schooling, a relatively lower grade effect
should be observed, and it’s magnitude would depend on
how the variable is indicating age progression and the
residual effect with positive direction.
Regarding the specificity of the sub-tests, the regression
results also support the interpretation that VR has a more
specific factor associated with Gc, as it had the greater
magnitude of the grade effect. In the remaining tests, the
grade effect is relatively lower and similarly indicates a
lower presence of Gc.
In conclusion, the results are compatible with the ones
found in literature in the field (Ackerman, 1996; Cahan
& Cohen, 1989; Cahan & Noyman, 2001; Ceci, 1991;
Primi, R., Couto, G., Almeida, L. S., Guisande, M. A. & Miguel, F. K. (2012). Intelligence, Age and Schooling: Data from the Battery
of Reasoning Tests (BRT-5).
Gustafsson, 2001; McGrew & Evans 2002; Stelzl et al.,
1995), thus corroborating in part the interpretations of
the specific factors involved in the BRT-5 sub-tests. These
findings follow the logic of construct validity research,
as delineated by Cronbach and Meehl (1955), whose study
demonstrates a correspondence between a nomological
network of relationships between constructs defined by
theoretical and empirical studies in literature and the
network of empirical correlations found between the
observed variables that supposedly measure such constructs. The nomological network was elaborated by the
expectations of the relationship between the age and
educational constructs with Gf, Gc and Gv found in previous studies. Also previous researches with BRT-5,
which justified the most prevalent specific factors in each
sub-test, were presented. In the light of this nomological
model, the empirical differential relationship of the subtests with age and grade were discussed in respect to their
consistency with the expectations elaborated in the nomological network. The results were coherent for some
sub-tests, which can support construct validity.
Finally, further studies including psychological tests
most clearly associated with Gf, Gv, Gq and Gc, would
be very important in order to corroborate the findings
from the present study. This study also suggests different developmental patterns associated with the type of
schools. This result is very important and also alarming
but the cross-sectional nature of the data for the present
research limits the inferences that can be made. Therefore, a longitudinal study would be very important in this
regard. Nevertheless, the present study shows the importance of considering this variable when studying intelligence, especially in Brazilian samples.
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Recebido: 16/08/2010
1ª revisão: 16/04/2011
Aceite final: 12/05/2011
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