The Predictive Validity of Four Intelligence Tests for School Grades: A Small Sample Longitudinal Study

Abstract

Intelligence is considered the strongest single predictor of scholastic achievement. However, little is known regarding the predictive validity of well-established intelligence tests for school grades. We analyzed the predictive validity of four widely used intelligence tests in German-speaking countries: The Intelligence and Development Scales (IDS), the Reynolds Intellectual Assessment Scales (RIAS), the Snijders-Oomen Nonverbal Intelligence Test (SON-R 6-40), and the Wechsler Intelligence Scale for Children (WISC-IV), which were individually administered to 103 children (Mage = 9.17 years) enrolled in regular school. School grades were collected longitudinally after 3 years (averaged school grades, mathematics, and language) and were available for 54 children (Mage = 11.77 years). All four tests significantly predicted averaged school grades. Furthermore, the IDS and the RIAS predicted both mathematics and language, while the SON-R 6-40 predicted mathematics. The WISC-IV showed no significant association with longitudinal scholastic achievement when mathematics and language were analyzed separately. The results revealed the predictive validity of currently used intelligence tests for longitudinal scholastic achievement in German-speaking countries and support their use in psychological practice, in particular for predicting averaged school grades. However, this conclusion has to be considered as preliminary due to the small sample of children observed.

Full text

ORIGINAL RESEARCH
published: 13 March 2017
doi: 10.3389/fpsyg.2017.00375
Frontiers in Psychology | www.frontiersin.org 1March 2017 | Volume 8 | Article 375
Edited by:
Ann Dowker,
University of Oxford, UK
Reviewed by:
Chris Lange-Küttner,
London Metropolitan University, UK
Bert Jonsson,
Umeå University, Sweden
*Correspondence:
Priska Hagmann-von Arx
priska.hagmann@unibas.ch
Specialty section:
This article was submitted to
Developmental Psychology,
a section of the journal
Frontiers in Psychology
Received: 03 October 2016
Accepted: 27 February 2017
Published: 13 March 2017
Citation:
Gygi JT, Hagmann-von Arx P,
Schweizer F and Grob A (2017) The
Predictive Validity of Four Intelligence
Tests for School Grades: A Small
Sample Longitudinal Study.
Front. Psychol. 8:375.
doi: 10.3389/fpsyg.2017.00375
The Predictive Validity of Four
Intelligence Tests for School Grades:
A Small Sample Longitudinal Study
Jasmin T. Gygi, Priska Hagmann-von Arx*, Florine Schweizer and Alexander Grob
Department of Psychology, University of Basel, Basel, Switzerland
Intelligence is considered the strongest single predictor of scholastic achievement.
However, little is known regarding the predictive validity of well-established intelligence
tests for school grades. We analyzed the predictive validity of four widely used intelligence
tests in German-speaking countries: The Intelligence and Development Scales (IDS),
the Reynolds Intellectual Assessment Scales (RIAS), the Snijders-Oomen Nonverbal
Intelligence Test (SON-R 6-40), and the Wechsler Intelligence Scale for Children
(WISC-IV), which were individually administered to 103 children (Mage =9.17 years)
enrolled in regular school. School grades were collected longitudinally after 3 years
(averaged school grades, mathematics, and language) and were available for 54 children
(Mage =11.77 years). All four tests significantly predicted averaged school grades.
Furthermore, the IDS and the RIAS predicted both mathematics and language, while
the SON-R 6-40 predicted mathematics. The WISC-IV showed no significant association
with longitudinal scholastic achievement when mathematics and language were analyzed
separately. The results revealed the predictive validity of currently used intelligence
tests for longitudinal scholastic achievement in German-speaking countries and support
their use in psychological practice, in particular for predicting averaged school grades.
However, this conclusion has to be considered as preliminary due to the small sample of
children observed.
Keywords: validity, scholastic achievement, IDS, RIAS, SON-R 6-40, WISC-IV
INTRODUCTION
The primary purpose of the first intelligence test (Binet and Simon, 1905) was to predict scholastic
achievement in order to determine the best school setting for a child. Since the beginning of
intelligence assessment, the predictive validity of intelligence test scores for scholastic achievement
has been well studied. Cross-sectional and longitudinal studies indicated strong correlations,
around r=0.40–0.81, between the two (e.g., Sternberg et al., 2001; Deary et al., 2007; Mackintosh,
2011).
The association between intelligence and scholastic achievement seems to be stronger when
using standardized achievement tests compared to school grades (Sternberg et al., 2001; Rost,
2009). Standardized achievement tests represent achievement at only one point in time, whereas
school grades represent achievement over a longer period and thus may also be influenced by other
constructs such as self-control and motivation (Rost, 2009). However, school grades are crucial
for children to be promoted to the next higher grade level as well as for further scholastic and
occupational qualifications (Roth et al., 2015).

Gygi et al. Intelligence and School Grades
Focusing on school grades, a recent meta-analysis (Roth et al.,
2015) found an observed correlation of r=0.44 and an estimated
true correlation (i.e., corrected for error of measurement
and range restriction) of ρ=0.54 between intelligence and
school grades. Regarding subject domains, the correlations were
highest and comparable for mathematics/science (r=0.42,
ρ=0.49) and languages (r=0.36, ρ=0.44). The results
furthermore revealed that correlations between intelligence and
school grades in elementary school (r=0.40, ρ=0.45)
tended to be weaker than in middle and high school (r=
0.46, ρ=0.54–0.58), because intelligence deficits in elementary
school may be compensated more easily through practice than
in higher-grade levels, as the learning content is easier to
understand. This result is in contrast to previous research (e.g.,
Sternberg et al., 2001), that identified stronger correlations
between intelligence and scholastic achievement in elementary
school than in higher-grade levels, because of growing range
restrictions.
The meta-analysis performed by Roth et al. (2015) included
studies conducted in different countries. In German-speaking
countries, for example, the Culture Fair Test-20-Revision (Weiss,
2006), standardized in 2003, showed associations with school
grades in mathematics/science ranging from r=0.26 to 0.39
and in languages of r=0.23. Further, the German Cognitive
Ability Test – 4-12 – Revision (KFT 4-12+R; Heller and Perleth,
2000), standardized from 1995 to 1997, showed associations
with school grades in mathematics/science ranging from r=
0.17 to 0.60 and in languages ranging from r=0.12 to
0.14. In another study, the KFT 4-12+R and the German
version of the Wechsler Intelligence Scale for Children-III
(Tewes et al., 1999), standardized from 1995 to 1998, predicted
mathematics/science with β=0.54 and language with β=0.52
(Karbach et al., 2013). However, the meta-analysis did not include
more recently standardized intelligence tests currently used in
German-speaking countries.
Currently used intelligence tests in German-speaking
countries (e.g., Hagmann-von Arx et al., 2015) include (a) the
Intelligence and Development Scales (IDS; Grob et al., 2013),
an intelligence test for children aged 5–10 years measuring
in particular fluid intelligence; (b) the Reynolds Intellectual
Assessment Scales (RIAS; Reynolds and Kamphaus, 2003;
German version: Hagmann-von Arx and Grob, 2014), an
intelligence test for individuals aged 3 to above 90 years that
measures verbal and nonverbal intelligence, based on crystallized
and fluid intelligence, respectively. A composite intelligence
index can be computed from the values in verbal and nonverbal
intelligence; (c) the Snijders-Oomen Nonverbal Intelligence Test
Revised 6-40 (SON-R 6-40; Tellegen et al., 2012), a nonverbal
intelligence test measuring fluid intelligence in individuals
aged 6–40 years; and (d) the Wechsler Intelligence Scales for
Children, Fourth Edition (WISC-IV; Wechsler, 2003; German
version: Petermann and Petermann, 2011), an intelligence test
used worldwide to measure general intelligence (Full-Scale IQ or
FSIQ). Additionally, the WISC-IV provides four index scores:
verbal comprehension reflecting the understanding of verbal
concepts; perceptual reasoning measuring nonverbal perception
and manipulation; working memory assessing attention and
working memory; and processing speed reflecting visuospatial
speed of processing.
Nevertheless, little is known regarding the predictive validity
of these intelligence tests for school grades. Especially for
German-speaking countries and for studies independent of the
standardization samples, there is a lack of literature analyzing
predictive validity of these tests. For the IDS, Gut et al. (2013)
analyzed the predictive validity of general intelligence in children
aged 5–7 years from the standardization sample for concurrent
(n=402) and longitudinal (n=221) scholastic achievement.
Concurrent scholastic achievement was operationalized through
parents’ and teachers’ ratings in mathematics, science, and
language (German), which were averaged across subjects.
Longitudinal scholastic achievement was based on averaged
school grades in these subjects 3 years later. Results revealed
medium to large effect sizes (β=0.30–0.56) for the cross-
sectional and a small effect size (β=0.21) for the longitudinal
association. These results replicate findings of a prior study
conducted by Gut et al. (2012) showing that in an extended
sample of 263 children aged 5–10 years, IDS general intelligence
predicted school grades in mathematics, science, and language
(German) 3 years later with medium effect sizes (β=0.28–
0.34). Both studies indicate small to moderate concurrent and
predictive validity of the IDS general intelligence for averaged
school grades.
For the German version of the RIAS, we found no studies
on the predictive validity of intelligence indices on school
grades. However, the Technical Manual of the English Version
of the RIAS (Reynolds and Kamphaus, 2003) reports a cross-
sectional validation study conducted with 78 children aged
3–16 years. Results revealed strong correlations between the
composite intelligence index and a standardized achievement test
in mathematics (r=0.67) and language (r=0.64), indicating
strong concurrent validity of the RIAS composite intelligence
index for standardized achievement tests.
For the SON-R 6-40, the Technical Manual of the German
version (Tellegen et al., 2012) reports moderate to strong
correlations between the test scores and concurrent school
grades in mathematics (r=0.58) and language (r=0.49) for
182 elementary school children aged 6–11 years. These results
indicate that nonverbal intelligence measured using the SON-
R 6-40 shows moderate to strong concurrent validity for school
grades.
For the German version of the WISC-IV there are, to
our knowledge, no available studies on the predictive validity
for school grades. For the English version of the WISC-
IV, Glutting et al. (2006) studied the concurrent validity of
general intelligence and its specific indices on a standardized
academic achievement test in mathematics and reading with
a sample of 498 individuals aged 6–16 years from the WISC-
IV standardization sample. Results showed large effect sizes for
the WISC-IV FSIQ (60% variance explained) but only small
effect sizes for the specific indices (0–2% additional variance
explained). The FSIQ predicted concurrent mathematics and
reading equally well. Thus, results indicate that in particular
the WISC-IV FSIQ is correlated with concurrent standardized
academic achievement tests.
Frontiers in Psychology | www.frontiersin.org 2March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
In sum, Roth et al.’s (2015) meta-analysis revealed that
intelligence test scores correlate moderately to strongly with
school grades in mathematics and language. However, there is
only scarce evidence regarding the longitudinal prediction of
school grades with currently used intelligence tests in German-
speaking countries.
In the current study we analyzed the predictive power of
the German versions of the IDS, the RIAS, the SON-R 6-40,
and the WISC-IV for longitudinal school grades. We analyzed
the general intelligence indices only, as the Technical Manuals
(e.g., Reynolds and Kamphaus, 2003) as well as previous research
(Glutting et al., 2006) do not recommend the use of specific
indices for high-stakes decisions because of lowered reliability
and validity compared to the general intelligence indices. On
the basis of previous research (e.g., Glutting et al., 2006; Deary
et al., 2007; Gut et al., 2012, 2013; Roth et al., 2015), we expected
that the general intelligence indices would positively predict
averaged school grades as well as school grades in mathematics
and language (German) with medium to strong effect sizes.
MATERIALS AND METHODS
Participants
The sample consisted of 103 children aged 6–11 years (M=9.17
years, SD =0.93; 52% females, 48% males) enrolled in regular
schools. All children took part in an intelligence assessment.
Three years later, parents of 54 children aged 10–13 years (M
=11.77 years, SD =0.79; 52% females, 48% males) provided
information about their children’s school grades in mathematics
and language. Regarding parental education, 74% of the parents
had a non-tertiary education and 26% had a tertiary education.
This distribution indicates that parent’s educational attainment in
the present study is comparable with the general Swiss population
(Swiss Federal Statistical Office, 2016). Post hoc power analysis
using G∗Power (Faul et al., 2007) indicated that with a chance
of 80% and a 0.05 alpha level, the current study was sufficiently
powered to detect medium effect sizes (r=0.30; Cohen, 1988).
The 54 children who participated in both study waves showed
significantly higher intelligence scores in the RIAS composite
intelligence index (M=103.24, SD =8.29) as well as in the
WISC-IV FSIQ (M=107.39, SD =10.58) than the 49 children
who did not participate in the second study wave (RIAS: M=
98.98, SD =9.19, F=0.82, p<0.01; WISC-IV: M=102.12, SD
=12.78, F=1.57, p<0.05). No differences were found for the
IDS and the SON-R 6-40.
Measures
Intelligence
To assess intelligence (M=100, SD =15), the IDS, RIAS, SON-R
6-40, and WISC-IV were administered. The IDS assesses general
intelligence and five developmental domains (psychomotor
skills, social-emotional competences, mathematics, language,
and achievement motivation) in children aged 5–10 years.
For the current study, only general intelligence was analyzed.
IDS general intelligence consists of seven subtests (i.e., visual
perception, selective attention, phonological memory, visual-
spatial memory, auditory memory, abstract reasoning, figural
reasoning), which measure mainly fluid intelligence. The
administration of IDS general intelligence takes about 45 min.
The IDS was standardized from 2007 to 2008 in Austria,
Germany, and Switzerland. Reliability for general intelligence is
high with Cronbach’s α=0.92.
The RIAS is an intelligence test for individuals aged 3 to above
90 years. It comprises four intelligence subtests (i.e., guess what,
verbal reasoning, odd-item out, what’s missing), which together
constitute the composite intelligence index, CIX. The CIX can
also be divided into two indices, represented by two of the four
above mentioned subtests each: the Verbal Intelligence Index,
VIX, representing crystallized intelligence, and the Nonverbal
Intelligence Index, NIX, representing fluid intelligence. Two
additional subtests can be administered measuring verbal and
nonverbal memory resulting in a Composite Memory Index. The
memory subtests are not entered in the CIX. The assessment of
the RIAS CIX takes about 20–25 min. The German version of
the RIAS was standardized from 2011 to 2012 in Germany and
Switzerland. Reliability for the RIAS is high with Cronbach’s α=
0.95 for the CIX and α=0.93–0.94 for the VIX and NIX.
The SON-R 6-40 assesses nonverbal intelligence for
individuals aged 6–40 years. It comprises four subtests (i.e.,
analogies, categories, mosaics, patterns) that primarily measure
fluid intelligence. The administration of the SON-R 6-40
takes about 45–60 min. The German version of the SON-R
6-40 was standardized from 2009 to 2011 in Germany and
the Netherlands. Reliability for the SON-R 6-40 is high with
Cronbach’s α=0.95.
The WISC-IV is an intelligence test measuring general
intelligence for children aged 6–16 years. It includes 10 core
subtests (i.e., similarities, vocabulary, comprehension, block
design, picture concepts, matrix reasoning, digit span, letter-
number sequencing, symbol search, coding) that constitute the
FSIQ and four specific indices: the Verbal Comprehension
Index, Perceptual Reasoning Index, Working Memory Index, and
Processing Speed Index. The administration of the WISC-IV core
subtests takes about 60 min. The German version of the WISC-
IV was standardized from 2005 to 2006 in Austria, Germany, and
Switzerland. Reliability for the WISC-IV is high with r=0.97 for
the FSIQ and r=0.87–94 for the specific intelligence indices.
School Grades
Three years after intelligence assessment, parents were asked
to report on their child’s school grades in mathematics and
language (1 =poorest grade, 6 =best grade; grades 4–6 represent
the passing range) based on the school records of the latest
term (i.e., overall grades). In Switzerland, passing grades in
both mathematics and language are crucial for a child to be
promoted to the next higher grade level (Swiss Media Institute
for Education and Culture, 2016). Thus, in line with previous
research (e.g., Gut et al., 2013) school grades were additionally
averaged across subjects to obtain a composite estimate of
scholastic achievement.
Procedure
This study was carried out in accordance with the
recommendations of the Ethics Committee of Basel, Switzerland
Frontiers in Psychology | www.frontiersin.org 3March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
and with the Declaration of Helsinki. Parents gave written
informed consent prior to participation in the study, and assent
was obtained from the children. Children were recruited from
elementary schools in the German-speaking part of Switzerland
in 2011. Trained study personnel administered the tests at school
on regular school days. Each child was individually administered
the four intelligence tests (IDS, RIAS, SON-R 6-40, WISC-IV)
in counterbalanced order. Three appointments were required,
each about 2 h, including breaks (one test session for the IDS,
one test session for the WISC-IV, and one test session for the
RIAS and SON-R 6-40). The sample sizes for each intelligence
test vary somewhat, as a few children could attend only two
testing appointments (nIDS =103, nRIAS =102, nSON-R6-40
=101, nWISC−IV =103). After the study was completed, the
parents received a written report on their child’s performance in
each intelligence test. Three years later, parents were contacted
again and asked to provide information about their child’s school
grades. Two families had moved and could not be reached; in
all, 54 parents returned the requested information (resulting in a
response rate of 53%).
Data Analyses
All analyses were conducted using SPSS 23.0. Because of the small
sample size and because some of the variables showed deviations
from normality (see skewness and kurtosis in Table 1), we
used bootstrap procedures (Efron, 1979; Chernick, 2008). Bias-
corrected 95% confidence intervals (BC 95%-CI) were computed
based on 5,000 random samples. A result was considered to be
significant when the confidence interval did not include zero.
To analyze the predictive validity of each intelligence test,
separate regression analyses for each predictor (i.e., general
intelligence indices) and outcome variable (i.e., child’s school
grades) were conducted. All variables entered into the regression
analyses were z-standardized. Few children were identified as
outliers with scores more than two standard deviations from
the mean (nIDS =2, nRIAS =1, nSON-R6-40 =2, nWISC−IV =
2), and for this reason these scores were truncated to z ±2. In
the following analyses, we controlled for variables that showed
correlations with the outcome variables to some extent (i.e., sex,
age; see Table 2).
RESULTS
Table 1 gives an overview of the descriptive statistics of the
current sample. The mean scores of the intelligence tests were
somewhat higher than in the standardization samples (M=
100), and the standard deviations were somewhat lower than
in the standardization samples (SD =15). The range of school
grades is narrow (4–6) and reflects grades in the passing range.
Correlations among all variables are displayed in Table 2. The
general intelligence indices of all four tests correlated highly with
each other (r=0.63–0.80, p<0.001).
Table 3 presents the results of the prediction of longitudinal
school grades by intelligence (model a: IDS, model b: RIAS,
model c: SON-R 6-40, model d: WISC-IV) while controlling for
children’s sex and age. When school grades were averaged across
subjects, the general intelligence indices of all four intelligence
tests predicted scholastic achievement. Estimates ranged from
Estimate =0.126 (SE =0.054, BC 95%-CI =[0.019, 0.225]) for
SON-R 6-40 to Estimate =0.175 (SE =0.059, BC 95%-CI =
[0.056, 0.293]) for IDS.
Regarding mathematics, results show that IDS (Estimate =
0.376, SE =0.143, BC 95%-CI =[0.085, 0.677]), RIAS (Estimate
=0.283, SE =0.142, BC 95%-CI =[0.023, 0.544]), and SON-
R 6-40 (Estimate =0.275, SE =0.137, BC 95%-CI =[0.007,
0.519]) were significant predictors, whereas WISC-IV was not
significantly related to school grades in mathematics. Regarding
language, IDS (Estimate =0.318, SE =0.130, BC 95%-CI =
[0.066, 0.573]) and RIAS (Estimate =0.376, SE =0.153, BC 95%-
CI =[0.092, 0.699]) significantly predicted school grades. The
general intelligence indices of SON-R 6-40 and WISC-IV did not
predict school grades in language.
DISCUSSION
Our main goal was to assess the longitudinal predictive validity
of four intelligence tests currently used in German-speaking
countries for children’s school grades in mathematics, language,
and averaged across subjects.
The general intelligence indices of all four intelligence tests
showed significant predictive validity for averaged school grades
three years after intelligence assessment, which is in line with
previous studies, showing that intelligence is a positive predictor
of scholastic achievement (Deary et al., 2007; Gut et al., 2012,
2013; Roth et al., 2015). Therefore, our results support the use
of the general intelligence indices of the IDS, RIAS, SON-R 6-40,
and WISC-IV in order to make predictions of a child’s averaged
school grades.
Regarding the prediction of mathematics, IDS, RIAS, and
SON-R 6-40 were significantly associated with school grades.
IDS general intelligence includes four out of seven subtests
that tax phonological and visual-spatial working memory (i.e.,
selective attention, phonological memory, visual-spatial memory,
auditory memory). Previous research revealed that both aspects
of working memory are associated with mathematics (e.g., Dehn,
2008; Raghubar et al., 2010). The RIAS includes two out of
four subtests taxing visual-spatial abilities, while the SON-R 6-
40 assesses intelligence through subtests measuring primarily
visual-spatial abilities. Previous literature found visual-spatial
abilities to be moderately associated with mathematics (e.g.,
Wai et al., 2009; Verdine et al., 2014). The WISC-IV did not
significantly predict school grades in mathematics, although the
small effect sizes were positive; however, this contradicts the
results of previous studies that found general intelligence to be
a moderate to strong predictor of school grades in mathematics
(Roth et al., 2015). The WISC-IV includes perceptual reasoning
and phonological working memory as two out of four specific
indices, and thus measure visual-spatial abilities and working
memory to a lesser extent. This might have weakened the relation
between these general intelligence indices and school grades in
mathematics, as visual-spatial abilities (e.g., Verdine et al., 2014;
Wai et al., 2009) and working memory (Dehn, 2008; Raghubar
et al., 2010) were found to be predictors of mathematics. Thus,
Frontiers in Psychology | www.frontiersin.org 4March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
TABLE 1 | Descriptive statistics for control variables, the intelligence scores of the IDS, RIAS, SON-R 6-40, WISC-IV, and school grades in study waves 1
and 2.
Variable Study wave 1 (N=103) Study wave 2 (N=54)
Mean (SD)N(%) Range Skewness Kurtosis Mean (SD)N(%) Range Skewness Kurtosis
Sex
Female 54 (52) 28 (52)
Male 49 (48) 26 (48)
Age at Study wave 1 (years) 9.18 (0.93) 6.71–11.18 −0.19 0.26 9.04 (0.96) 6.71–11.18 −0.08 −0.14
Age at Study wave 2 (years) 11.77 (0.80) 10.25–13.60 0.43 −0.51
Parental education
Non-tertiary education 74 (72) 40 (74)
Tertiary education 29 (28) 14 (26)
IDS 103.54 (10.64) 78–134 0.15 0.41 105.19 (10.74) 79–134 0.45 0.70
RIAS 101.45 (8.99) 81–128 0.29 0.39 103.65 (8.23) 87–128 0.84 0.67
SON-R 6-40 103.27 (11.32) 79–139 0.38 0.50 103.67 (11.55) 82–139 0.62 0.61
WISC-IV 104.88 (11.91) 73–133 0.21 0.07 107.39 (10.58) 84–133 0.27 0.28
Averaged school grade 5.16 (0.42) 4–6 −0.39 −0.20
Mathematics school grade 5.15 (0.48) 4–6 −0.25 −0.71
Language school grade 5.16 (0.43) 4–6 −0.31 −0.08
IDS, Intelligence and Development Scales; RIAS, Reynolds Intellectual Assessment Scales; SON-R 6-40, Snijders-Oomen Nonverbal Intelligence Test Revised; WISC-IV, Wechsler
Intelligence Scale for Children—Fourth Edition.
TABLE 2 | Correlations among control variables, the intelligence scores of the IDS, RIAS, SON-R 6-40, WISC-IV, and school grades.
Variable N1 2 3 4 5 6 7 8 9 10
1 Sex (0 =males, 1 =females) 54 1
2 Age at Study wave 1 54 −0.09 1
3 Age at Study wave 2 54 −0.09 0.79*** 1
4 Parental education (0 =non-tertiary, 1 =tertiary) 54 −0.02 −0.14 −0.06 1
5 IDS 54 0.16 −0.34*−0.24 0.13 1
6 RIAS 54 −0.03 −0.31*−0.13 0.15 0.75*** 1
7 SON-R 6-40 52 0.05 −0.16 −0.18 0.11 0.80*** 0.63*** 1
8 WISC-IV 54 0.09 −0.27*−0.07 −0.02 0.77*** 0.67*** 0.63*** 1
9 Averaged school grade 54 0.24 −0.30*−0.37** 0.10 0.47** 0.34** 0.36*0.30*1
10 Mathematics school grade 54 0.14 −0.25 −0.28*0.13 0.43** 0.26 0.32*0.25 0.93*** 1
11 Language school grade 53 0.32*−0.30*−0.41** 0.06 0.44** 0.36** 0.32*0.30*0.91*** 0.68***
Correlations were calculated for individuals who participated at Study wave 2. IDS, Intelligence and Development Scales; RIAS, Reynolds Intellectual Assessment Scales; SON-R 6-40,
Snijders-Oomen Nonverbal Intelligence Test Revised; WISC-IV, Wechsler Intelligence Scale for Children—Fourth Edition.
*p<0.05. **p<0.01. ***p<0.001.
in the IDS, phonological and visual-spatial working memory
capacity, and in the RIAS and SON-R 6-40, visual-spatial abilities
are considered more important parts of intelligence compared
to the other intelligence tests. Therefore, it might be plausible
that in particular IDS, RIAS, and SON-R 6-40 were significantly
associated with school grades in mathematics.
Regarding the prediction of language, the general intelligence
indices of the IDS and RIAS were significantly associated with
school grades in language. The association between the IDS
and language is in line with studies revealing a moderate to
strong relationship between working memory and language (e.g.,
Dehn, 2008). The association between the RIAS and language
might be explained through the high requirements of verbal
abilities and verbal reasoning in two out of four RIAS subtests.
The other general intelligence indices showed no significant
associations with language, although the small effect sizes were
positive; however, this result contradicts the findings of previous
studies that found general intelligence to be a moderate to strong
predictor of school grades in language (Roth et al., 2015). In
contrast to the RIAS, the SON-R 6-40 focuses only on nonverbal
intelligence. Furthermore and in contrast to the IDS, the SON-R
6-40 does not include subtests taxing working memory, which is
considered as being associated with language (e.g., Dehn, 2008).
The WISC-IV includes a specific index for verbal comprehension
and working memory. However, it might be possible that
these two out of four specific indices were not sufficient to
Frontiers in Psychology | www.frontiersin.org 5March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
TABLE 3 | Regression analyses for the intelligence scores of the IDS, RIAS, SON-R 6-40, and WISC-IV predicting longitudinal school grades.
Variables Averaged school grade Mathematics Language
Estimate SE BC 95%−CI R2Estimate SE BC 95%−CI R2Estimate SE BC 95%−CI R2
Model a: IDS
Step 1 0.180* 0.092 0.251*
Sex (0 =males, 1 =females) 0.086 0.052 [−0.010, 0.176] 0.112 0.122 [−0.118, 0.324] 0.264 0.110 [0.055, 0.473]
Age −0.165 0.060 [−0.281, −0.019] −0.281 0.140 [−0.540, 0.063] −0.396 0.115 [−0.622, −0.137]
Step 2a0.318* 0.220** 0.341**
IDS 0.175 0.059 [0.056, 0.293] 0.376 0.143 [0.085, 0.677] 0.318 0.130 [0.066, 0.573]
Model b: RIAS
Step 1 0.180* 0.092 0.251*
Sex (0 =males, 1 =females) 0.086 0.052 [−0.007, 0.177] 0.112 0.120 [−0.127, 0.338] 0.264 0.112 [0.059, 0.476]
Age −0.165 0.060 [−0.266, −0.043] −0.281 0.139 [−0.518, 0.031] −0.396 0.117 [−0.621, −0.150]
Step 2a0.275* 0.148 0.347**
RIAS 0.165 0.066 [0.031, 0.298] 0.283 0.142 [0.023, 0.544] 0.376 0.153 [0.092, 0.699]
Model c: SON−R 6−40
Step 1 0.179* 0.093 0.251*
Sex (0 =males, 1 =females) 0.069 0.053 [−0.030, 0.164] 0.086 0.126 [−0.151, 0.310] 0.220 0.112 [0.013, 0.418]
Age −0.170 0.060 [−0.284, −0.031] −0.293 0.141 [−0.554, 0.072] −0.406 0.114 [−0.625, −0.165]
Step 2a0.262* 0.168* 0.301*
SON−R 6−40 0.126 0.054 [0.019, 0.225] 0.275 0.137 [0.007, 0.519] 0.217 0.116 [−0.020, 0.443]
Model d: WISC−IV
Step 1 0.180* 0.092 0.251*
Sex (0 =males, 1 =females) 0.086 0.051 [−0.013, 0.186] 0.112 0.120 [−0.114, 0.328] 0.264 0.114 [0.048, 0.476]
Age −0.165 0.060 [−0.270, −0.029] −0.281 0.140 [−0.531, 0.067] −0.396 0.115 [−0.615, −0.146]
Step 2a0.247* 0.140 0.304**
WISC−IV 0.128 0.063 [0.001, 0.266] 0.242 0.157 [−0.088, 0.590] 0.260 0.137 [−0.001, 0.553]
IDS, Intelligence and Development Scales; RIAS, Reynolds Intellectual Assessment Scales; SON-R 6-40, Snijders-Oomen Nonverbal Intelligence Test Revised; WISC-IV, Wechsler Intelligence Scale for Children—Fourth Edition. BC
95%-CI, bias-corrected 95% bootstrap confidence intervals.
aControlled for variables in step 1.
*p<0.01, ** p<0.001.
Frontiers in Psychology | www.frontiersin.org 6March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
significantly explain variance in school grades in language in the
present study. Thus, the different subtests underlying the general
intelligence indices of the IDS, RIAS, SON-R 6-40, and WISC-
IV may be responsible for the different associations with school
grades in mathematics and language. However, future studies
with larger sample sizes have to be conducted to analyze this
assumption.
It is notable that the effect sizes in the present study were
in the small to moderate range and thus somewhat lower than
we expected based on the meta-analytical results by Roth et al.
(2015). However, in a single study, the expected effects may be
smaller, as seen, for example, in Gut et al. (2012, 2013), for
several reasons. In the present study, for instance, the analyzed
sample showed slightly higher general intelligence scores than
the population and had a narrow range in school grades, which
were all in the passing range. This might have led to range
restrictions, which may have weakened the correlations between
intelligence and school grades in the present study (Sternberg
et al., 2001; Roth et al., 2015). Also, the present study analyzed
the predictive validity of intelligence tests on school grades for
elementary school children. According to Roth et al. (2015),
lower intelligence scores in elementary school might be better
compensated with practice than in higher-grade levels, which
may also have led to smaller effect sizes in the present study.
Regarding the control variables, in the present study sex
was significantly related to school grades such that girls
achieved higher scores in language than boys. This result
is in accordance with a recent meta-analyses showing that
females have advantages in school marks which are largest for
languages courses (Voyer and Voyer, 2014). Furthermore, age
was negatively related to school grades such that older children
achieved lower school grades than younger children. A possible
explanation for this relation may be that age is related to pubertal
status and that a more advanced physical pubertal status is related
to lower achievement motivation (i.e., academic self-efficacy and
valuing of school) that in turn is related to lower achievement
(Martin and Steinbeck, 2017).
In sum, our results indicate that the general intelligence
indices of the German versions of the IDS, RIAS, SON-R 6-40,
and the WISC-IV significantly predicted averaged school grades
over three years. Furthermore, the IDS and RIAS were positively
associated with longitudinal mathematics and language school
grades, while SON-R 6-40 was a predictor of mathematics school
grades. Thus, our results provide evidence for predictive validity
of these intelligence tests (Neukrug and Fawcett, 2015).
The current study has strengths and limitations. It is a
strength that we analyzed four intelligence tests currently
used in German-speaking countries, as there is a paucity of
information regarding their predictive validity for school grades.
Furthermore, we assessed intelligence three years prior to
school grades being inquired and could therefore analyze their
predictive validity longitudinally. This is especially relevant when
practitioners use intelligence scores in order to predict future
scholastic achievement. Finally, we measured a child’s scholastic
achievement in mathematics and language using school grades,
which reflect a child’s performance and effort over an extended
period of time and which are crucial for further scholastic and
occupational qualifications (Roth et al., 2015). However, the
association between intelligence and scholastic achievement may
vary with different operationalization of scholastic achievement.
In order to avoid potential errors in parental reports, future
studies analyzing currently used intelligence tests in German-
speaking countries might also consider achievement tests, which
measure specific scholastic abilities at a specific point in time
(Rost, 2009), as well as official school records obtained directly
from schools. Moreover, as school grades are considered as
indicators of achievement over a longer time period, they
may be influenced not only by intelligence but also by
other constructs (Rost, 2009). Therefore, future studies might
also consider noncognitive factors that additionally predict
scholastic achievement, such as school engagement (Reyes et al.,
2012), motivation (Steinmayr and Spinath, 2009), self-control
(Duckworth et al., 2012), personality (Poropat, 2009), and social-
emotional competencies (Gut et al., 2012).
Furthermore, the current study had a high drop-out rate
(although comparable to that of the studies conducted by Gut
et al., 2012, 2013) for the longitudinal information on the child’s
school grades. This led to a small sample size at Study wave
2. The statistical power of the present study was sufficient to
detect expected moderate associations, but there was not enough
statistical power to detect weak associations between intelligence
and school grades, as discussed above. Furthermore, the present
study examined typically developing children enrolled in regular
school with slightly higher intelligence. Thus, the conclusions
based on the current study cannot be generalized to children with
special needs or with different intelligence levels. To examine
the predictive validity of the present intelligence tests, future
studies are required with larger sample sizes and including
children with different levels of intelligence (e.g., children with
intellectual disabilities) or special needs as seen in the studies
of Canivez et al. (2014),Mayes and Calhoun (2007), as well
as Nelson and Canivez (2012). Because of these limitations,
conclusions from the current study have to be considered as
preliminary.
In conclusion, general intelligence measured with the German
version of the IDS, RIAS, SON-R 6-40, and WISC-IV was
a positive predictor of averaged school grades in the current
longitudinal study. These results support the use of the four
intelligence tests for issues raised in psychological practice
and reveal their predictive validity on longitudinal scholastic
achievement in typically developing school-aged children with
slightly higher intelligence. Furthermore, the IDS and RIAS could
predict both school grades in mathematics and language, while
the SON-R 6-40 could predict school grades in mathematics.
These results suggest that school grades in mathematics and
language can be predicted by intelligence tests depending on
their composition of subtests (e.g., working memory, verbal
abilities, visual-spatial abilities). Thus, in psychological practice,
examiners have to consider the variety of subtests included in
a particular intelligence test when making specific predictions
of mathematics and language. More studies analyzing larger
samples as well as children with different levels of intelligence or
special needs are required to replicate and generalize the findings
of the current study.
Frontiers in Psychology | www.frontiersin.org 7March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
AUTHOR CONTRIBUTIONS
JG and PH contributed to the study design, acquisition,
analysis, and interpretation of data. Drafted and revised the
manuscript, gave final approval, and agree to be accountable
for all aspects of the work in ensuring that questions related
to the accuracy or integrity of any part of the work are
appropriately investigated and resolved. FS contributed to the
study design and acquisition of data. Revised the manuscript,
gave final approval, and agrees to be accountable for all
aspects of the work in ensuring that questions related to the
accuracy or integrity of any part of the work are appropriately
investigated and resolved. AG contributed to the study design
and interpretation of data. Revised the manuscript, gave final
approval, and agrees to be accountable for all aspects of the work
in ensuring that questions related to the accuracy or integrity
of any part of the work are appropriately investigated and
resolved.
ACKNOWLEDGMENTS
We thank Anita Todd and Laura Wiles for proofreading.
REFERENCES
Binet, A., and Simon, T. (1905). Methodes nouvelles pour le diagnostic du niveau
intellectuel des anormaux. L’Anée Psychol. 11, 191–336.
Canivez, G. L., Watkins, M. W., James, T., Good, R., and James, K. (2014).
Incremental validity of WISC–IVUK factor index scores with a referred Irish
sample: predicting performance on the WIAT–IIUK .Br. J. Educ. Psychol. 84,
667–684. doi: 10.1111/bjep.12056
Chernick, M. R. (2008). Bootstrap Methods: A Guide for Practitioners and
Researchers. Hoboken, NJ: John Wiley & Sons.
Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Hillsdale,
NJ: Erlbaum.
Deary, I. J., Strand, S., Smith, P., and Fernandes, C. (2007).
Intelligence and educational achievement. Intelligence 35, 13–21.
doi: 10.1016/j.intell.2006.02.001
Dehn, M. J. (2008). Working Memory and Academic Learning.Assessment and
Intervention. Hoboken, NJ: Wiley.
Duckworth, A. L., Quinn, P. D., and Tsukayama, E. (2012). What no child left
behind leaves behind: the roles of IQ and self-control in predicting standardized
achievement test scores and report card grades. J. Educ. Psychol. 104, 439–451.
doi: 10.1037/a0026280
Efron, B. (1979). Bootstrap methods: another look at the jacknife. Ann. Stat. 7,
1–26. doi: 10.1214/aos/1176344552
Faul, F., Erdfelder, E., Lang, A.-G., and Buchner, A. (2007). G∗Power 3: a
flexible statistical power analysis program for the social, behavioral, and
biomedical sciences. Behav. Res. Methods 39, 175–179. doi: 10.3758/BF031
93146
Glutting, J. J., Watkins, M. W., Konold, T. R., and McDermott, P. A. (2006).
Distinctions without a difference: the utility of observed versus latent factors
from the WISC–IV in estimating reading and math achievement on the
WIAT–II. J. Spec. Educ. 40, 103–114. doi: 10.1177/00224669060400020101
Grob, A., Meyer, C. S., and Hagmann-von Arx, P. (2013). Intelligence and
Development Scales (IDS), 2nd Edn. Bern: Hans Huber.
Gut, J., Reimann, G., and Grob, A. (2012). Cognitive, language, mathematical,
and socioemotional skills as predictors of subsequent school performance. Z.
Pädagogische Psychol. 26, 213–200. doi: 10.1024/1010-0652/a000070
Gut, J., Reimann, G., and Grob, A. (2013). A contextualized view on long-
term predictors of academic performance. J. Educ. Psychol. 105, 436–443.
doi: 10.1037/a0031503
Hagmann-von Arx, P., Gauck, L., and Grob, A. (2015). “Intelligence assessment,”
in Handbook of School Psychology,eds K. Seifried, S. Drewes, and M. Hasselhorn
(Stuttgart: Kohlhammer), 128–139.
Hagmann-von Arx, P., and Grob, A. (2014). Reynolds Intellectual Assessment Scales
(RIAS). Bern: Hans Huber.
Heller, K. A., and Perleth, C. (2000). German Cognitive Ability Test – 4-12 -
Revision. Göttingen: Hogrefe.
Karbach, J., Gottschling, J., Spengler, M., Hegewald, K., and Spinath, F. M. (2013).
Parental involvement and general cognitive ability as predictors of domain-
specific academic achievement in early adolescence. Learn. Instr. 23, 43–51.
doi: 10.1016/j.learninstruc.2012.09.004
Mackintosh, N. J. (2011). IQ and Human Intelligence, 2nd Edn. Oxford: Oxford
University Press.
Martin, A. J., and Steinbeck, K. (2017). The role of puberty in students’
academic motivation and achievement. Learn. Individ. Differ. 53, 37–46.
doi: 10.1016/j.lindif.2016.11.003
Mayes, S. D., and Calhoun, S. L. (2007). Wechsler intelligence scale for children-
third and -fourth edition predictors of academic achievement in children
with attention-deficit/hyperactivity disorder. Sch. Psychol. Q. 22, 234–249.
doi: 10.1037/1045-3830.22.2.234
Nelson, J. M., and Canivez, G. L. (2012). Examination of the structural, convergent,
and incremental validity of the Reynolds Intellectual Assessment Scales (RIAS)
with a clinical sample. Psychol. Assess. 24, 129–140. doi: 10.1037/a0024878
Neukrug, E. S., and Fawcett, R. C. (2015). The Essentials of Testing and Assessment:
A Practical Guide for Counselors, Social Workers, and Psychologists, 3rd Edn.
Stamford, CT: Cengage Learning.
Petermann, F., and Petermann, U. (2011). WISC-IV: Wechsler Intelligence Scale for
Children—Fourth Edition (German version). Frankfurt: Pearson Assessment.
Poropat, A. E. (2009). A meta-analysis of the five-factor model of personality and
academic performance. Psychol. Bull. 135, 322–338. doi: 10.1037/a0014996
Raghubar, K. P., Barnes, M. A., and Hecht, S. A. (2010). Working
memory and mathematics: a review of developmental, individual
difference, and cognitive approaches. Learn. Individ. Differ. 20, 110–122.
doi: 10.1016/j.lindif.2009.10.005
Reyes, M. R., Brackett, M. A., Rivers, S. E., White, M., and Salovey, P. (2012).
Classroom emotional climate, student engagement, and academic achievement.
J. Educ. Psychol. 104, 700–712. doi: 10.1037/a0027268
Reynolds, C. R., and Kamphaus, R. W. (2003). RIAS, Reynolds Intellectual
Assessment Scales. Lutz, FL: PAR.
Rost, D. H. (2009). Intelligence: Facts and myths. Weinheim: Beltz.
Roth, B., Becker, N., Romeyke, S., Schäfer, S., Domnick, F., and Spinath, F. M.
(2015). Intelligence and school grades: a meta-analysis. Intelligence 53, 118–137.
doi: 10.1016/j.intell.2015.09.002
Swiss Federal Statistical Office (2016). A Portrait of Switzerland. Results from
the 2010-2014 Censuses. Available online at: https://www.bfs.admin.ch/bfs/
de/home/statistiken/bildung-wissenschaft/bildungsstand-kompetenzen/
bevoelkerung.html
Swiss Media Institute for Education and Culture, (2016). Compulsory
Education. Available online at: http://swisseducation.educa.ch/en/compulsory-
education-0
Steinmayr, R., and Spinath, B. (2009). The importance of motivation as
a predictor of school achievement. Learn. Individ. Differ. 19, 80–90.
doi: 10.1016/j.lindif.2008.05.004
Sternberg, R. J., Grigorenko, E., and Bundy, D. A. (2001). The predictive value of
IQ. Merrill Palmer Q. 47, 1–41. doi: 10.1353/mpq.2001.0005
Tellegen, P. J., Laros, J. A., and Petermann, F. (2012). Snijders-Oomen Nonverbal
Intelligence Test (SON-R 6-40). Göttingen: Hogrefe.
Tewes, U., Rossmann, P., and Schallberger, U. (1999). HAWIK-III.Hamburg-
Wechsler-Intelligenztest für Kinder – Dritte Auflage. Übersetzung und
Adaptation der WISC-III Wechsler Intelligence Scale for Children– Third Edition
von David Wechsler. Bern: Huber.
Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., Newcombe, N. S., Filipowicz,
A. T., and Chang, A. (2014). Deconstructing building blocks: preschoolers’
spatial assembly performance relates to early mathematical skills. Child Dev.
85, 1062–1076. doi: 10.1111/cdev.12165
Frontiers in Psychology | www.frontiersin.org 8March 2017 | Volume 8 | Article 375

Gygi et al. Intelligence and School Grades
Voyer, D., and Voyer, S. D. (2014). Gender differences in scholastic
achievement: a meta-analyses. Psychol. Bull. 140, 1174–1204. doi: 10.1037/a00
36620
Wai, J., Lubinski, D., and Benbow, C. P. (2009). Spatial ability for STEM domains:
aligning over 50 years of cumulative psychological knowledge solidifies its
importance. J. Educ. Psychol. 101, 817–835. doi: 10.1037/a0016127
Wechsler, D. (2003). Wechsler Intelligence Scale for Children—Fourth Edition
(WISC-IV) Administration and Scoring Manual. San Antonio, TX: The
Psychological Association.
Weiss, R. H. (2006). Culture Fair Intelligence Test Scale 2—Revision (CFT 20-R).
Göttingen: Hogrefe.
Conflict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
Copyright © 2017 Gygi, Hagmann-von Arx, Schweizer and Grob. This is an open-
access article distributed under the terms of the Creative Commons Attribution
License (CC BY). The use, distribution or reproduction in other forums is permitted,
provided the original author(s) or licensor are credited and that the original
publication in this journal is cited, in accordance with accepted academic practice.
No use, distribution or reproduction is permitted which does not comply with these
terms.
Frontiers in Psychology | www.frontiersin.org 9March 2017 | Volume 8 | Article 375