Effect of timing of school enrollment on physical fitness in third graders

Abstract

Timing of initial school enrollment may vary considerably for various reasons such as early or delayed enrollment, skipped or repeated school classes. Accordingly, the age range within school grades includes older-(OTK) and younger-than-keyage (YTK) children. Hardly any information is available on the impact of timing of school enrollment on physical fitness. There is evidence from a related research topic showing large differences in academic performance between OTK and YTK children versus keyage children. Thus, the aim of this study was to compare physical fitness of OTK (N = 26,540) and YTK (N = 2586) children versus keyage children (N = 108,295) in a representative sample of German third graders. Physical fitness tests comprised cardiorespiratory endurance, coordination, speed, lower, and upper limbs muscle power. Predictions of physical fitness performance for YTK and OTK children were estimated using data from keyage children by taking age, sex, school, and assessment year into account. Data were annually recorded between 2011 and 2019. The difference between observed and predicted z-scores yielded a delta z-score that was used as a dependent variable in the linear mixed models. Findings indicate that OTK children showed poorer performance compared to keyage children, especially in coordination, and that YTK children outperformed keyage children, especially in coordination. Teachers should be aware that OTK children show poorer physical fitness performance compared to keyage children.

Full text

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Eect of timing of school
enrollment on physical tness
in third graders
Thea Fühner *, Urs Granacher, Kathleen Golle & Reinhold Kliegl
Timing of initial school enrollment may vary considerably for various reasons such as early or delayed
enrollment, skipped or repeated school classes. Accordingly, the age range within school grades
includes older-(OTK) and younger-than-keyage (YTK) children. Hardly any information is available on
the impact of timing of school enrollment on physical tness. There is evidence from a related research
topic showing large dierences in academic performance between OTK and YTK children versus
keyage children. Thus, the aim of this study was to compare physical tness of OTK (N = 26,540) and
YTK (N = 2586) children versus keyage children (N = 108,295) in a representative sample of German
third graders. Physical tness tests comprised cardiorespiratory endurance, coordination, speed,
lower, and upper limbs muscle power. Predictions of physical tness performance for YTK and OTK
children were estimated using data from keyage children by taking age, sex, school, and assessment
year into account. Data were annually recorded between 2011 and 2019. The dierence between
observed and predicted z-scores yielded a delta z-score that was used as a dependent variable in the
linear mixed models. Findings indicate that OTK children showed poorer performance compared to
keyage children, especially in coordination, and that YTK children outperformed keyage children,
especially in coordination. Teachers should be aware that OTK children show poorer physical tness
performance compared to keyage children.
e importance of physical tness for children’s health is undisputed1. According to Caspersen etal.2, physical
tness can be categorized as health- (e.g., cardiorespiratory endurance, muscular endurance, muscular strength,
body composition, and exibility) or skill-related tness (e.g., agility, balance, coordination, speed, [muscle]
power, and reaction time). ere is evidence from original research3, systematic reviews, and meta-analyses4,5
that cardiorespiratory endurance and muscular strength are positively associated with markers of physical health
(e.g., body mass index, waist circumference, skinfold thickness, cardiovascular disease risk score) in youth.
Accordingly, it is important to regularly monitor and evaluate children’s physical tness to identify potential
decits in physical tness as early as possible. Recent studies on global secular trends in youth physical tness
indicated physical tness declines particularly for measures of cardiorespiratory endurance. is trend addition-
ally emphasizes the relevance of physical tness testing6,7.
Physical tness tests represent an easy-to-administer, reliable, and valid means to assess and evaluate chil-
dren’s physical tness in large scale studies conducted in sport clubs or schools8. Several studies from around the
globe8–17 showed developmental increases in physical tness from childhood to adolescence8,10–12,15,17. Irrespective
of age, boys outperform girls in most components of physical tness9–17, except for balance10,17 and exibility9–15,17.
e available studies on physical tness development have been conducted in youth aged 5–18years. In these
studies, children and adolescents were matched into 1-year age groups. is age grouping system is also evident
in many settings of children’s everyday life. For instance, children are matched in 1-year age teams within sport
clubs or in grades within schools. However, this age grouping system is not without limitations because of dif-
ferences in relative age depending on the specic cut-o date under consideration. For schools in general, the
cut-o date of initial school enrollment is specic to the country under investigation. For instance, in the Federal
State of Brandenburg, Germany the ocial and initial school enrollment date is September 30th. Accordingly,
children are enrolled to school (i.e., rst grade) if they are aged between 6years and 0months and 6years and
11months on September 30th of the respective year (i.e., keyage children in rst grade). us, children who are
born on September 30th or slightly later are at the extreme end, i.e., almost 1 year older than their classmates
who are born in August. ese dierences in the birthdate may have an impact on anthropometrics (e.g., body
height, body mass) and physical tness (e.g., muscular strength, power, cardiorespiratory endurance, or speed)18
OPEN
Division of Training and Movement Sciences, Faculty of Human Sciences, University of Potsdam, Am Neuen Palais
10, Building 12, 14469 Potsdam, Germany. *email: fuehner@uni-potsdam.de
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because physical tness performance increases with age from childhood to adolescence8,10–12,15,17. us, within
a 1-year age-group, the relatively older children (i.e., born near the cut-o date) may outperform their relative
younger classmates (i.e., born later to the cut-o date) because of their relatively older age18,19. In fact, a previous
study conducted with keyage third graders (i.e., children aged 8years and 0months to 8years and 11months) has
shown that physical tness increased linearly with chronological age20. Furthermore, even within the single ninth
year of life, the relatively older children (i.e., aged 8years and 6months to 8years and 11months) signicantly
outperformed the younger children (i.e., aged 8years and 0months to 8years and 5months) in physical tness20.
Within one school-grade, there are keyage children as well as younger- (YTK) or older-than-keyage (OTK)
children. is is due to early or late school enrollment, skipping or repetition of a school year. With reference to
our data, age ranged from 5years and 11months to 14years and 5months for our study sample that included
YTK and OTK children. Given that there are already large dierences in physical tness within the group of key-
age children20, the question arises as to physical tness performance of YTK and OTK children. To the authors’
knowledge there is hardly any information available in the literature on dierences in physical tness of YTK and
OTK children versus keyage children. A major goal of physical education is to create a learning setting for each
child according to his/her individual needs to ensure a holistic development. us, ndings on physical tness
performance of YTK and OTK children provide valuable information to promote physical tness according to
the child´s individual needs. For instance, children who show delayed physical tness development should receive
additional health and tness programs to compensate their decits in physical tness. Furthermore, given that
grading systems are only available for keyage children, ndings of this study can be used to individually grade
physical tness according to age, sex, and timing of school enrollment.
Information from a related research topic shows large dierences in academic performance between OTK
and YTK children versus keyage children21–23. For instance, in a study including 1144 German primary school
children, Urschitz etal.23 reported that especially OTK children aged > 9years compared with keyage children
showed poor academic performance in terms of grades in mathematics, science, reading, spelling, and hand-
writing. In a study including 3,684 Australian high school students aged 14years, Martin22 reported that YTK
children scored signicantly better in academic performance (i.e., performance in literacy and numeracy) than
keyage children. However, as already mentioned this has not yet been examined for physical tness. erefore,
the aim of this cross-sectional study was to compare physical tness of OTK and YTK children versus keyage chil-
dren in a sample of German primary school children taking age, sex, school, and assessment year into account.
With reference to the relevant school-based studies on dierences in academic performance of OTK and YTK
children versus keyage children21–23, we hypothesized that OTK children show poorer and YTK children better
physical tness performance compared with keyage children.
Methods
Experimental approach. is cross-sectional study is part of the ongoing EMOTIKON research project
(www. uni- potsd am. de/ en/ emoti kon). Physical tness tests were conducted every year between September and
November starting in 2011. Physical tness tests were also administered in 2009 and 2010, but later in the
school year that is between March and April. Due to the seasonal variation in physical tness these data were
not included.
Population. Since 2009, all third graders living in the Federal State of Brandenburg, Germany were tested
annually for their physical tness. is cross-sectional study was mandated and approved by the Ministry of Edu-
cation, Youth and Sport of the Federal State of Brandenburg, Germany. e Brandenburg School Law requires
that parents are comprehensively informed prior to the start of the study. Consent is not needed given that the
tests are obligatory for both, children and schools24. None of the authors included in the author list had access
to personally identiable information on the children. e authors received the data absolutely anonymized
from the Ministry of Education, Youth and Sport of the Federal State of Brandenburg, Germany. Research was
conducted according to the latest Declaration of Helsinki25.
To compare physical tness development of YTK and OTK children with that of keyage children, we used
physical tness data recorded between 2011and 2019.
• 2586 YTK children aged 7years and 0months to 7years and 11months
• 108,296 keyage children aged 8years and 0months to 8years and 11months
• 26,540 OTK children aged 9years and 0months to 9years and 11months
Selection into keyage, OTK, and YTK groups was strictly based on children’s birthdate relative to the legal
date for school enrollment (i.e., September 30th in the Federal State of Brandenburg for all assessment years).
us, on September 30th, keyage third graders ranged between 8years and 0months to 8years and 11months.
YTK children were younger, and OTK children were older.
e selection of keyage children has been described in a previous publication of our research group20. Data
from an earlier study were used as a reference for OTK and YTK children. Initially, 30,253 OTK children were
included in the data base: 2842 were excluded due to age. e excluded third-graders ranged from 10years and
1month to 14years and 5months. Another 27 students were excluded due to adverse health events as reported
by the responsible teacher (e.g., physical disability, autism spectrum). Finally, 844 students were considered
outliers and outside + /− 3 SD of their group x sex x test cell. Finally, 26,540 OTK children were included in
the analyses (88.7%). For YTK children, initially 2654 YTK were eligible to be included in the data base. From
this initial sample, 28 were excluded due to age because they ranged from 5years and 11months to 6years and
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11months. Moreover, 40 children were considered outliers and beyond + /− 3 SD in their group × sex × test cell.
Finally, 2586 YTK children were included in the analyses (97.4%).
Physical tness tests. Physical tness was assessed using the specic EMOTIKON test battery20. ese
tests evaluated cardiorespiratory endurance (i.e., 6-min-run test), coordination (i.e., star-run test), speed (i.e.,
20-m linear sprint test), lower (powerLOW [i.e., standing long jump test]), and upper limbs muscle power (i.e.,
powerUP [ball-push test]). e EMOTIKON test battery ocially includes six tests. In 2016, the assessment of
exibility (i.e., stand-and-reach test) was stopped and the assessment of balance (i.e., single-leg balance test with
eyes closed) was included26. Due to the much smaller number of scores and their confound with assessment year,
these two tests were not included in the analyses.
Physical tness tests were administered by qualied physical education teachers and conducted during the
regular physical education classes. All physical education teachers received standardized test instructions for the
assessment (www. uni- potsd am. de/ en/ emoti kon/ proje kt/ metho dik—for further information on the test proto-
cols). Furthermore, all physical education teachers participated in advanced training programs about standard-
ized physical tness assessment. Tests were always conducted in the morning between 8 and 12 am. Prior to
testing, all third-graders performed a standardized warm-up program consisting of dierent running exercises
(e.g., side-steps) and small games (e.g., playing tag).
Cardiorespiratory endurance. Cardiorespiratory endurance was assessed using the 6-min-run test. Participat-
ing children had to run the furthest distance during the 6 min test time around a volleyball eld (54m) at a self-
paced velocity. e test instructor provided split times every minute. Aer the 6min, maximal distance covered
in meters to the nearest nine meters was recorded and used as dependent variable. High test–retest reliability
was reported for the 6-min-run test with an intraclass correlation coecient (ICC) of 0.92 in children aged 7–11
years27.
Coordination. Coordination under time pressure was evaluated using the star-run test. During the star-run
test, the participating children had to complete a parkour with dierent running techniques (i.e., running for-
wards, running backwards, side-steps) as quickly as possible. e star shaped parkour (9m × 9m) consisted
of four spikes. Each spike and the center of the star were marked with a pylon. e participants started in the
middle of the star. First, they had to run forward to the rst pylon and backward to the middle. Next, they had
to do side-steps to the second pylon on the right side and side-steps back to the middle. en, they had to run
backward to the third pylon and forward to the middle. Finally, they had to do side-steps to the fourth pylon on
the le side and side-steps back to the middle. e participants had to touch each pylon within the parkour with
the hand. e whole covered distance was 50.912m. Time for test completion in seconds to the nearest 1/10s
was taken using a stopwatch and used as dependent variable in the analysis. e participants had two test trials of
which the best test trial in terms of time until test completion was kept for analysis. e star run test was reliable
(test–retest) for children aged 8–10years with an ICC of 0.6828.
Speed. Speed was assessed using the 20-m linear sprint test. e participating children started from a standing
position with one foot right behind the starting line. Aer an acoustic signal, they had to sprint as fast as possible
over a distance of 20m. Time for test completion in seconds to the nearest 1/10s was taken using a stopwatch
and used as dependent variable in the analysis. e participants had two test trials of which the best trial was
taken for further analysis in terms of the time until test completion. Test–retest reliability has been reported to
be high for children aged 7–11years with an ICC of 0.9027.
Lower limbs muscle power (PowerLOW). PowerLOW was assessed through the standing long jump test. e
participating children had to jump as far as possible from a frontal position. Arm swing prior to and during the
jump was allowed. Jump distance in centimeters between the starting line and heel of the posterior foot was
recorded to the nearest one centimeter using a measuring tape. e participants had two test trials of which
the best trial in terms of the longest jump distance was taken for further analysis. e standing long jump test
showed high test–retest reliability for children aged 6–12years with an ICC of 0.9429.
Upper limbs muscle power (PowerUP). Power up was evaluated with the ball-push test. From a standing posi-
tion, the participating children had to push a 1kg medicine ball that was held tight right in front of the chest.
e participants had to push the ball at maximal eort with both hands. e pushing distance in meters was
recorded to the nearest ten centimeters using a measuring tape. e participants had two test trials of which the
best test trial in terms of the longest pushing distance was taken for further analysis. e ball-push test was reli-
able (test–retest) for children aged 8–10years with an ICC of 0.8128.
Statistics. Pre- and post-processing of data were carried out in the R environment of statistical computing30
using the tidyverse package31. For statistical inference we relied on Linear Mixed Model analyses (LMM) with the
MixedModels package32 in the Julia programming language (v 1.7.1)33.
For measures of cardiorespiratory endurance (i.e., 6min run test), powerLOW (i.e., standing long jump test)
and powerUP (i.e., ball push test), higher scores indicate better physical tness. For measures of coordination
(i.e., star run test) and speed (i.e., 20-m linear sprint test), a Box-Cox distributional analyses indicated that a
reciprocal transformation brought scores in line with the assumption of a normal distribution34. erefore, we
converted scores from seconds to meters/seconds (i.e., pace scores; star run test = 50.912 [m]/time [s]; 20-m linear
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sprint test = 20 [m]/time [s]). ese transformations had the advantage that a large value was indicative of good
physical tness for all ve tests. Finally, z-scores were computed in two stages. In the rst stage, we calculated
z-scores within the test (i.e., 6-min-run test, star-run test, 20-m linear sprint test, standing long jump test, ball-
push test) × sex (male, female) × group (YTK, OTK) cells and removed observations exceeding + /− 3 SDs (i.e.,
outliers). is is in accordance with a previous publication from the same research group20. In the second stage,
we used means and SDs of the ve tness tests for keyage children from a previous study20 and computed the
respective z-scores that were included in Figs.1 and 2.
To compare YTK and OTK children`s development of physical tness with that of keyage children, we pre-
dicted the physical tness performance for ages 7years and 0months to 7years and 11months and 9years and
0months to 9years and 11months using LMM parameter estimates of the 108,295 keyage children (i.e., grey
lines in Fig.1), reported in Fühner etal20. rough this predication analyses we received the information about
physical tness performance of keyage children at the ages 7years and 0months to 7years and 11months and
9years and 0months and 9years and 11months. e model parameters comprised xed eects for age, tests,
sex, and their interactions, variance components (VCs) and correlation parameters (CPs) for GM and four test
contrasts for the random factor child, VCs and CPs for GM, four test contrasts, sex, and age for the random factor
school, and VCs for test and, age for the random factor assessment year. Details about model specication for
these predictions are provided in Fühner etal.20 and in script: fggk22_lmm_pred.jl in the repository.
rough physical tness testing in EMOTIKON, we obtained the actual physical tness status of YTK children
aged 7years and 0months to 7years and 11months and OTK children aged 9years and 0months to 9years and
11months. Please note that the classication of children into YTK, keyage, or OTK groups is based solely on
children’s birthdate whereas children’s age is the dierence between the date of test and their birthdate. erefore,
some YTK children were slightly older than 8years and some OTK children were slightly younger than 9years
at the time of testing. Results did not change if non-keyage children aged between 8 and 9years were excluded.
e dierence between observed (i.e., obtained through physical tness testing) and predicted z-scores (i.e.,
predicted data from keyage children [grey lines in Fig.1]) yielded a delta z-score that was used as dependent vari-
able in the following LMMs to compare physical tness development of YTK and OTK children (i.e., obtained
scores through physical tness testing) with that of keyage children (i.e., predicted data).
We analyzed the data with separate LMMs for OTK and YTK children. e xed eects included in the start-
ing LMM were similar to the one reported by Fühner etal.20. Specically, there were four sequential-dierence
xed-eect contrasts for the ve tests: (H1) coordination versus cardiorespiratory endurance, (H2) speed versus
coordination, (H3) powerLOW versus speed, and (H4) powerUP versus powerLOW. We additionally included the
eect of age (centered at 8years and 6months) as a second-order polynomial trend, the eect of sex (boys–girls),
and all interactions between contrasts, age, and sex. We used a two-sided z-value > 2.0 as signicance criterion
for the interpretation of xed eects.
e random eect structure included VCs and CPs of the delta z-scores for the ve tests related to grouping
(random) factors of child, school, and assessment year. Tests varied within children, schools, and assessment
years; age and sex varied between children, but within schools and within assessment years. erefore, in prin-
ciple, VCs and CPs also include eects of age and sex for the factors school and assessment year.
LMM for older-than-keyage (OTK) children. e initial LMM included child (N = 26,540), school (N = 513),
and assessment year (N = 9) as three random factors; the total number of observations (i.e., max = 5 per child)
was 128,198. With three random factors, there was a need for selecting a random-eect structure that included
theoretically relevant and reliable VCs and CPs but was also still supported by the data (i.e., was not overparam-
eterized).
Parsimonious model selection occurred in two major steps without knowledge or consideration of xed-eect
estimates35; details are provided in script: fggk22_lmm_otk.jl in the repository. e random-eect structure of
the parsimonious LMM of delta z-scores was expected to be simpler than the one for the LMM of Fühner etal.20
because the much smaller number of children and, importantly, because most of the school- and assessment-year-
related random eects as well as xed eect of age and sex were included in the predicted z-scores. We started
with a model estimating VCs and CPs between delta z-scores of the ve tests for children and VCs of delta z-scores
for the ve tests, age, and sex for school, and only varying intercept (GM) for assessment year. is LMM was
well supported by the data. Increasing the complexity of the random-eect structure by adding CPs for school
or adding VCs for assessment year did not improve the goodness of t. Moreover, the school-related VC for sex
and high-order xed-eect interactions between test, age, and sex could be removed without loss of goodness of
t. As in Fühner etal.20, we also estimated the nal model with an alternative post-hoc LMM parameterization
to test main xed eects of sex and age separately for each tness test (i.e., we specied sex and age as nested
within the ve levels of the factor test).
LMM for younger-than-keyage (YTK) children. e LMM included child (N = 2586), school (N = 437), and
assessment year (N = 9) as three random factors; the total number of observations (i.e., max = 5 per child) was
12,590. In the model selection process, we followed the model of OTK described above.
Parsimonious model selection occurred without knowledge or consideration of xed-eect estimates35; details
are provided in script: fggk22_lmm_ytk.jl in the repository. First, we applied the LMM of OTK to the data of
YTK. is model was not supported by the data (i.e., overparameterized) because of the relatively small sample
size of YTK (N = 2586) compared to OTK (N = 26,540). Indeed, the data supported only a LMM with a strongly
reduced complexity, comprising (a) xed eects on delta z-scores for the four contrasts of test, (b) VCs for the
ve delta z-scores for school and child, and (c) CPs for the ve delta z-scores of child. us, there was no statistical
support for xed or random eects of age and sex for YTK children relating to delta z-scores.
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Results
Table1 summarizes descriptive statistics for the three subsamples of third-graders. Statistics about keyage chil-
dren refer to the sample reported in Fühner etal.20. Statistics about YTK and OTK children refer to the samples
of this study.
Figure1 displays the observed (points) and predicted (lines) physical tness development for YTK boys and
girls aged 7years and 0months to 7years and 11months and OTK boys and girls aged 9years and 0months
to 9years and 11months. e predicted z-scores for keyage children aged 8years and 0months to 8years and
11months are located on the predicted lines. ere is a slight overlap between groups at 8- and 9-year boundaries
due to birthdate determining the classication of children into keyage groups and age being measured as the
dierence between age at test and birthdate.
Figure2 displays the delta z-scores between observed and predicted physical tness development for YTK
boys and girls aged 7years and 0months to 7years and 11months and OTK boys and girls aged 9years and
0months to 9years and 11months. e delta z-scores for keyage children aged 8years and 0months to 8years
and 11months are represented in the horizontal zero line. e z-scores for OTK and YTK children will be
described in the next sections.
Physical tness of older-than-keyage children (OTK). Table2 displays statistics for xed eects of
age (linear and quadratic) and sex as well as their interactions with the four test contrasts for LMM of OTK
children.
e overall negative linear trend for age (z = − 6.68) and positive quadratic trend of age (z = 4.50) were signi-
cant. e positive quadratic trend of age indicates that the dierence between predicted and observed physical
tness becomes more negative initially, but plateaus with even a slight reduction of delta z-scores for the oldest
children (see Fig.2).
Furthermore, the main eect of contrast H1 was signicant (z = 2.51) indicating that the main eect was larger
for coordination than for cardiorespiratory endurance. e LMM tested the interactions of linear and quadratic
age with the four test contrasts, that is whether slopes in neighboring panels in Fig.2 (averaged across sex) were
parallel. e slope can be equated with the developmental rate. Indeed, one of four interaction was signicant
(see second and third block of Table2) the linear age developmental rate was larger for cardiorespiratory endur-
ance than coordination (H1; z = − 3.38) and the quadratic age developmental rate was larger for coordination
than cardiorespiratory endurance (H1; z = 2.73).
ree of the test contrasts interacted with sex. First, the delta z-score was more negative for boys than girls
for cardiorespiratory endurance and more negative for girls than boys for coordination (z = 3.41, see Table1).
e post-hoc LMM revealed signicantly less severe delta z-scores for girls (− 0.14) than boys (− 0.18) for cardi-
orespiratory endurance (z =− 2.30). ere was no signicant sex dierence for the delta z-score for coordination
Figure1. Observed z-scores for physical tness development for boys (closed circles) and girls (open circles)
aged 7.00–10.0years. e lines represent the predicted z-scores for physical tness development for boys (grey
line) and girls (dashed grey line). Data were z-transformed. Endurance = cardiorespiratory endurance (i.e.,
6-min-run test), Coordination = star-run test, Speed = 20-m linear sprint test, PowerLOW = lower limbs muscle
power (i.e., standing long jump test), PowerUP = upper limbs muscle power (i.e., ball-push test). Note that delta
z-scores for younger-than-keyage boys and girls were aggregated over 7.00–7.99years and that delta z-scores for
older-than-keyage boys and girls were aggregated over 9.50–9.99years. Points are binned observed child means.
Coordination and speed times were converted from seconds to meters/seconds (i.e., pace scores; star-run
test = 50.912 [m]/time [s]; 20-m linear sprint test = 20 [m]/time [s]). ese transformations have the advantage
that a large value is indicative of better physical tness and that they remove skew in the distributions.
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(z = 1.38). Second, the negative dierence between boys and girls in the delta z-score was larger for powerLOW
than speed (z = 3.38). e post-hoc LMM revealed a signicant sex dierence (favoring boys) only for power-
LOW (z = 3.90; boys: − 0.23, girls: − 0.29; see Table1). ere was no signicant sex dierence for speed (z = 1.19).
ird, the same powerLOW sex dierence was the source of the signicant interaction for the fourth contrast
(z = − 2.80). ere was no signicant sex dierence for powerUP (z = 1.12).
Table3 lists estimates of VCs for children and for school. e delta z-scores VCs were large for children
(0.88–0.94) and small for schools (0.06–0.09).
Physical tness of younger than keyage (YTK) children. Table4 displays estimates and test statis-
tics for xed eects of the four test contrasts. Figure2 displays the delta z-scores between observed and pre-
dicted physical tness development for YTK boys and girls aggregated over 7years and 0months to 7years and
11months.
e grand mean was signicant (z = 5.09). Furthermore, three of the four main eects of contrasts were
signicant: the main eect was larger for coordination than cardiorespiratory endurance (H1; z = 3.05), larger
for coordination than speed (H2; z = − 2.49) and larger for powerUP than powerLOW (H4; z = 2.47), which can
also be seen in Fig.2.
Table5 lists estimates of VCs between delta z-scores for children and for school. e delta z-scores VCs were
large for children (0.83–0.89) and small for schools (0.09–0.12).
Discussion
e aim of this cross-sectional study was to examine physical tness of YTK and OTK children versus keyage
children in a representative sample of German primary school children. Our ndings indicate that (1) OTK chil-
dren showed poorer performance compared to keyage children, especially for coordination, (2) OTK girls outper-
formed OTK boys, and (3) YTK children showed better results than keyage children, especially for coordination.
Several studies conrmed a linear increase in physical tness performance with chronological age9–11,15. For
instance, in a study with 424,328 Greek children and adolescents aged 6–18years, Tambalis etal.15 reported a
linear increase in physical tness performance with age for cardiorespiratory endurance (i.e., 20-m shuttle run
test), lower limbs muscle power (i.e., standing long jump test), exibility (i.e., sit-and-reach test), muscular
strength (i.e., sit-ups test), and agility (i.e., 10 × 5m shuttle run test). e development of physical tness of
keyage children (see predicted gray lines in Fig.1) is in accordance with the above reported results. For keyage
children, physical tness performance increased linearly with age. However, the development of physical t-
ness for OTK children is dierent. Poor performance was found in OTK children aged 9years and 0months
to 9years and 11months compared with age-matched keyage children for all components of physical tness,
especially for coordination. is could be due to the fact that third graders aged 9years and 0months to 9years
Figure2. Delta z-score between observed and predicted physical tness development for boys (closed
circles) and girls (open circles) aged 7.00–10.0years. Data were z-transformed. Endurance = cardiorespiratory
endurance (i.e., 6-min-run test), Coordination = star-run test, Speed = 20-m linear sprint test,
PowerLOW = lower limbs muscle power (i.e., standing long jump test), PowerUP = upper limbs muscle power
(i.e., ball-push test). Note that delta z-scores for younger-than-keyage boys and girls were aggregated over 7.00–
7.99years and that delta z-scores for older-than-keyage boys and girls were aggregated over 9.50–9.99years.
Points are binned delta child means. Coordination and speed times were converted from seconds to meters/
seconds (i.e., pace scores; star-run test = 50.912 [m]/time [s]; 20-m linear sprint test = 20 [m]/time [s]). ese
transformations have the advantage that a large value is indicative of better physical tness and that they remove
skew in the distributions.
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and 11months (i.e., OTK children) are not representative for the “average” age-matched keyage child which is
why we observed a deviation from the typically reported tness development with age in this cohort9–11,15. We
do not know the exact circumstances which lead to the delayed enrollment into rst grade or to the repetition
of a school year. According to our results, we can only speculate that maybe a delay in cognitive development
might be the reason why children are late enrolled into rst grade or must repeat a school class. ese results
are in line with a study of Urschitz etal.23 who examined dierences in academic performance. ese authors
observed that poor academic performance signicantly increased with age for mathematics, science, reading,
spelling, and handwriting in a sample of 1144 German third graders. Of note, children who repeated a school
class were more prone to poor academic performance. ese results were conrmed by other studies for academic
performance21,22. Interestingly, in our study OTK girls showed better performance compared to OTK boys which
is in accordance with Urschitz etal.23. ese authors reported that except for mathematics, boys showed a larger
prevalence for poor academic performance compared with girls23. As girls mature approximately two years earlier
than boys, the better performance of girls compared to boys might be inuenced by biological maturation. Girls
enter the adolescent growth spurt at approximately ten years of age and peak height velocity at 12years, whereas
boys enter the growth spurt on average at age 12 and peak height velocity at 1436.
In contrast, YTK children outperformed keyage children especially in tests requiring motor coordination.
Again, we do not know the exact circumstances which resulted in early enrollment into rst grade or reasons
for skipping a school year. According to our results, we speculate that accelerated cognitive development could
be a reason why early enrolled children skip a school year. is is supported by the fact that in this study, YTK
Table 1. Descriptive statistics for younger-than-keyage, keyage, older-than-keyage children. N = sample
size, SD = standard deviation, delta = dierence between observed (i.e., obtained through physical
tness testing) and predicted z-scores (i.e., predicted data from keyage children [grey lines in Fig.1]),
Endurance = cardiorespiratory endurance (i.e., 6-min-run test), Coordination = star-run test, Speed = 20-m
linear sprint test, PowerLOW = lower limbs muscle power (i.e., standing long jump test), PowerUP = upper
limbs muscle power (i.e., ball-push test), OTK = older-than-keyage children (i.e., aggregated over 9years and
0months to 9years and 11months), YTK = younger-than-keyage children (i.e., aggregated over 7years and
0months to 7years and 11months). Coordination and speed times were converted from seconds to meters/
seconds (i.e., pace scores; star-run test = 50.912 [m]/time [s]; 20-m linear sprint test = 20 [m]/time [s]). ese
transformations have the advantage that a large value is indicative of better physical tness.
Sample Physical tness component Sex N schools N child Mean age [years] SD age [years] Mean s core SD score Mean delta SD delta
Keyage Endurance [m] Boys 513 51,116 8.56 0.28 1041.38 154.03 0 0.4
Keyage Endurance [m] Girls 511 52,821 8.55 0.28 967.72 132.50 0 0.3
Keyage Coordination [m/s] Boys 512 51,023 8.56 0.28 2.08 0.30 0 0.4
Keyage Coordination [m/s] Girls 510 52,886 8.55 0.28 2.01 0.27 0 0.3
Keyage Speed [m/s] Boys 513 51,700 8.56 0.28 4.58 0.42 0 0.4
Keyage Speed [m/s] Girls 512 53,259 8.55 0.28 4.45 0.39 0 0.4
Keyage PowerLOW [cm] Boys 513 52,141 8.56 0.28 129.41 19.53 0 0.4
Keyage PowerLOW [cm] Girls 509 53,856 8.55 0.28 122.00 18.44 0 0.4
Keyage PowerUP [m] Boys 514 52,254 8.56 0.28 3.99 0.70 0 0.4
Keyage PowerUP [m] Girls 512 54,070 8.55 0.28 3.50 0.63 0 0.3
OTK Endurance [m] Boys 511 14,870 9.35 0.25 1017.86 166.33 − 0.18 1.1
OTK Endurance [m] Girls 499 10,519 9.35 0.26 950.97 140.53 − 0.14 1.0
OTK Coordination [m/s] Boys 509 14,808 9.35 0.25 2.06 0.31 − 0.28 1.1
OTK Coordination [m/s] Girls 502 10,542 9.35 0.26 1.99 0.29 − 0.30 1.1
OTK Speed [m/s] Boys 511 15,010 9.36 0.25 4.58 0.44 − 0.17 1.1
OTK Speed [m/s] Girls 503 10,644 9.35 0.26 4.44 0.41 − 0.19 1.1
OTK PowerLOW [cm] Boys 511 15,137 9.35 0.26 127.83 21.08 − 0.23 1.2
OTK PowerLOW [cm] Girls 502 10,699 9.35 0.26 119.42 19.45 − 0.29 1.1
OTK PowerUP [m] Boys 511 15,236 9.36 0.25 4.13 0.75 − 0.22 1.1
OTK PowerUP [m] Girls 503 10,733 9.35 0.26 3.62 0.67 − 0.23 1.0
YTK Endurance [m] Boys 350 1087 7.85 0.19 1042.92 149.54 0.036 1.0
YTK Endurance [m] Girls 384 1408 7.88 0.18 973.11 132.88 0.035 1.0
YTK Coordination [m/s] Boys 350 1091 7.85 0.19 2.05 0.29 0.10 1.1
YTK Coordination [m/s] Girls 382 1397 7.87 0.18 1.99 0.26 0.10 1.0
YTK Speed [m/s] Boys 349 1097 7.85 0.19 4.51 0.40 0.035 1.1
YTK Speed [m/s] Girls 385 1423 7.87 0.18 4.42 0.39 0.070 1.0
YTK PowerLOW [cm] Boys 350 1112 7.85 0.19 128.54 18.48 0.082 1.1
YTK PowerLOW [cm] Girls 384 1433 7.87 0.18 121.77 18.06 0.078 1.0
YTK PowerUP [m] Boys 348 1111 7.85 0.19 3.79 0.70 0.12 1.0
YTK PowerUP [m] Girls 384 1431 7.88 0.18 3.33 0.61 0.14 0.9
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children showed the best performance in the coordination test which has an inherent large cognitive demand.
Moreover, ndings from Martin22 point in a similar direction by showing that in a cohort of 3684 Australian
high school students, YTK children outperformed keyage children in academic performance.
Our study is not without limitations. First, anthropometric factors such as body mass, body height, and
sitting height were not assessed in this study so that associations between anthropometric factors, biological
maturation, and physical tness could not be calculated. ese factors would have provided additional insight
as there is strong evidence that children’s physical tness is associated with anthropometric characteristics37–39
and biological maturation36. One explanation of the deviation of YKT and OKT children might be a dierence
between chronological and biological age. It appears plausible to argue that YKT children may be more mature
and that OKT children are biologically somewhat younger than indicated by their chronological age. us, in a
hypothetical plot of performance over biological age, the linear trend may well hold for all children. Second, we
predicted the performance of the YTK and OTK children based on a linear extrapolation recently reported by
Fühner etal.20. However, we do not know if this linear extrapolation exactly ts to the data of keyage children
aged 7years and 0months to 7years and 11months/9years and 0months to 9years and 11months as we do
not have such longitudinal data. ird, we cannot parse out the exact number of OTK children that were late
enrolled or repeated a school class.
To sum up, this study is the rst study that examined dierences in physical tness development of YTK and
OTK children compared to keyage children. Our study ndings complement results reported in the literature
on the development of academic performance in youth21–23. Politicians and decision makers, schools, (physical
education) teachers, and parents should be aware that OTK versus keyage children showed poorer physical tness
performance. is is a novel and somehow unexpected result. erefore, OTK children should be specically
promoted through additional health and tness programs to compensate their decits in physical tness to enable
a holistic development. Furthermore, the assessment of physical tness should be performed regularly to tailor
the contents of physical education classes based on the results of physical tness assessments (e.g., data driven
physical education classes). More specically, the physical tness status of OTK children should be monitored
regularly over time to evaluate whether e.g., additional health and tness programs already helped to compensate
the observed decits in physical tness.
Given that reference values for the grading of physical tness is only available for keyage children, raw data
from this study can be used to calculate age-, sex-, and timing of school enrollment-specic percentile values.
Table 2. Fixed-eect estimates of linear mixed model for older-than-keyage (OTK) children. H1–
H4 = hypothesis 1–4, endurance = cardiorespiratory endurance (i.e., 6min run test), coordination = star run
test, speed = 20-m linear sprint test, powerLOW = lower limbs muscle power (i.e., standing long jump test),
powerUP = upper limbs muscle power (i.e., ball push test), * = z-value > 2.0, linear mixed model random
factors: assessment years (9), schools (513), children (26,540), observations = 128,198 (missing = 3.4%). For
estimates of variance components and correlation parameters see Table3.
Source of variance Fixed-eect estimates Standard error z-values
Main eects
Grand mean (intercept) 0.348 0.068 5.08*
H1: coordination versus endurance 0.230 0.091 2.51*
H2: speed versus coordination − 0.025 0.083 − 0.30
H3: powerLOW versus speed 0.029 0.075 0.39
H4: powerUP versus powerLOW − 0.022 0.094 − 0.23
Age (linear) − 1.014 0.152 − 6.68*
Age (quadratic) 0.357 0.079 4.50*
Sex 0.015 0.011 1.43
Age (linear) × Fitness component
H1: coordination versus endurance − 0.693 0.205 − 3.38*
H2: speed versus coordination26 0.180 0.187 0.96
H3: powerLOW versus speed − 0.181 0.168 − 1.08
H4: powerUP versus powerLOW 0.089 0.211 0.42
Age (quadratic) × Fitness component
H1: coordination versus endurance 0.294 0.108 2.73*
H2: speed versus coordination − 0.034 0.098 − 0.34
H3: powerLOW versus speed 0.059 0.088 0.67
H4: powerUP versus powerLOW − 0.014 0.111 − 0.13
Sex × Fitness component
H1: coordination versus endurance 0.052 0.015 3.41*
H2: speed versus coordination − 0.001 0.014 − 0.10
H3: powerLOW versus speed 0.042 0.012 3.38*
H4: powerUP versus powerLOW − 0.044 0.016 − 2.80*
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e respective data should be useful for (physical education) teachers or researchers to individually evaluate and
grade children´s physical tness development.
e EMOTIKON test battery is easy-to-administer, cost eective, and it requires only minimal equipment
that is usually available in gyms (e.g., stopwatch, measuring tape, medicine ball, pylons). erefore, physical
education teachers, coaches, or researchers can use the EMOTIKON test battery to evaluate children’s physical
tness and use the results to promote health- and skill-related physical tness during physical education.
Data availability
e datasets generated and analyzed during the current study as well as Julia and R scripts are available in the
Open Science Framework (OSF) repository: https:// osf. io/ dmu68/? view_ only= 240bd ab8f1 be4d8 384ac f9356
ee50f 8b.
Received: 29 November 2021; Accepted: 26 April 2022
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Acknowledgements
e authors thank Paula Teich for helpful comments.
Author contributions
T.F., R.K., and U.G.: made substantial contributions to conception and design; K.G. and T.F.: contributed to data
collection; T.F. and R.K.: carried out data analysis; T.F., R.K., and U.G.: interpreted the data; T.F.: wrote the rst
dra of the manuscript and all authors were involved in revising it critically for important intellectual content;
all authors provide nal approval of the version to be published and agreed to be accountable for all aspects of
the work and agreed with the order of presentation of the authors.
Funding
Funded by the Deutsche Forschungsgemeinscha (DFG, German Research Foundation) – Projektnummer
491466077.Open Access funding enabled and organized by Projekt DEAL. e study was commissioned and
supported by the Ministry of Education, Youth, and Sport of the Federal State Brandenburg. e funders had no
role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Reinhold
Kliegl was supported by the Center for Interdisciplinary Research, Bielefeld (ZiF)/Cooperation Group “Statistical
models for psychological and linguistic data”.
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Competing interests
e authors declare no competing interests.
Additional information
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