An exploratory study design was used to examine physical fitness and cognitive performance in preschoolers from a convenience sample of three kindergartens located in eastern regions of Germany [7]. Sixty-one children (boys n = 31; girls n = 30) with a mean age of 4.5 ± 0.6 years and a range of 4–6 years (i.e., 42–74 months, 58.7 ± 7.3 months) participated in the study, which was approved by the local ethics research committee (submission No. 34/2018). Additionally, the study was conducted in accordance with the latest version of the Declaration of Helsinki. Prior to the start of the study, parents or legal representatives received written information on the aims of the study and the study design including potential risks and benefits. Parents or legal representatives of all participating children provided their written informed consent before the study started. An a priori power analysis was computed using G × Power (Version 3.1.9.2, University of Kiel, Kiel, Germany [25]). The F-test family (linear multiple regression analysis) was used with a type I error of 0.05 and a statistical power of 0.80 (type II error rate) for physical fitness components (i.e., static balance, muscle strength, power, coordination) as independent (predictor) variables. With references to a study by Moradi et al. [26] who included five predictor variables (e.g., muscle strength, muscular endurance, flexibility, speed, agility) and one dependent variable (either information processing speed or inhibitory control), we included four predictor variables and one dependent variable (composite score of attention) in our statistical model. Thus, a sample size of 53 participants would be needed to explore a medium to strong effect size of F2 = 0.25 [27] for our regression analysis. In the present study we are referring to test–retest reliability using intra class coefficients (ICC) for all physical fitness and cognitive tests which were assessed in our pilot study (pre-post testing of control group n = 22; [7]). The pilot study was conducted between August and November 2018 using a quasi-experimental study design (a 2-group repeated-measures design).
Anthropometric data
Anthropometric data (body height, body mass, and BMI) was measured using standardized procedures [7]. Body mass index (BMI) was calculated using the standardized equation (mass/height [in kilograms per square meter]).
Physical fitness
Static balance, muscle strength, power, and coordination were assessed in exercise rooms located within the kindergartens by specifically trained assessors. Every child was tested individually after performing one familiarization trial and after having received standardized verbal instructions and visual demonstration regarding the test procedures.
Single-leg stance test
Static balance was evaluated by using the single-leg stance test [28]. Children had to stand barefoot with eyes opened on the dominant leg which was assessed through the ball kick tests [29]. The stopwatch was started as soon as the nondominant leg was lifted in front with hip and knee joints both flexed at 90°. Children performed one trial up to a maximum of 30 s. If they were not able to pass 2 s in the first trial, they were asked to perform a second trial [30]. A child was considered as not capable of performing the single-leg stance test if he or she performed 2 unsuccessful trials. Time was measured by a stopwatch to the nearest one-tenth of a second and was stopped if the nondominant leg touched the floor or the child started hopping to achieve stability. The interrater reliability for the single-leg- stance test from our pilot study was ICC = 0.76 [7].
Standing long jump test
As a proxy of lower limbs muscle power, standing long jump performance was assessed. Children were instructed to jump with both feet starting from a parallel standing position as far as possible in horizontal direction aiming on landing on both feet [28]. The jumping distance from start to landing was taken using a measuring tape to the nearest 1.0 cm. A trial was considered as not valid if children lost balance during landing and fell backwards. Children performed 2 trials and the best trial was used for further analysis. In our pilot study the interrater reliability was ICC = 0.89 [7].
Handgrip strength test
Muscle strength was assessed using a handheld dynamometer (Jamar plus digital with LCD display). Therefore, children performed the handgrip strength test with the dominant hand which was assessed through reports of the kindergarten teachers [31] as the preferred hand when performing fine and gross motor tasks. Prior to the handgrip strength test, the hand’s span length of each participating child (diagonal length from tip of the little finger/pinky to the tip of the thumb) was assessed. According to the span length, we used level 1 (girls 14 cm; boys 10.8 cm) or level 2 (girls 14–19.1 cm; boys 10.8–20.1 cm) to enable an individualized biomechanical position for the handgrip strength test. The Jamar handheld dynamometer has 5 notches (levels) which can be adjusted depending on the individually hand span length. While sitting on a chair with shoulders relaxed and elbows flexed at 90°, the dynamometer had to be pressed continuously at maximum effort for at least 3–4 s [32]. The best of two trials was used for further analysis. Muscle strength was measured to the nearest 0.1 kg. In children aged 4–6 years, the handgrip strength test has proven to be reliable (ICC = 0.83; [7]).
Hopping on one leg test
For the assessment of coordination, the hopping on right/left leg test [33] was operationalized and performed alternately once with each leg. Children were instructed to hop on one leg as often as possible to a maximum of 20 hops. If takeoff and landing was achieved on the same foot and at least one time, a hop was considered valid. The interrater reliability in our pilot study was ICC = 0.60 for the right and ICC = 0.88 for the left leg, respectively [7]. For further analyzes, we computed a composite score as on overall measure of coordination by using the mean z-scores from each leg (right/left).
Cognitive performance
Attention as one domain of cognition was assessed in quiet rooms in the respective kindergartens for each child individually by one specifically trained assessor.
Konzentrations-Handlungsverfahren für Vorschulkinder
We applied attention with the Konzentrations-Handlungsverfahren für Vorschulkinder [concentration-action procedure for preschoolers] (KHV-VK) [34]. Children had to sort 40 cards with familiar images as fast as possible but within a maximum time of 10 min in 4 different boxes. On every card, children had to find the key image (no, single, or double key images) in order to sort the card into the correct box. The KHV-VK measures and analyzes sorting time (working speed) as quantitative and error quote (working accuracy) as qualitative dimension of attention. The ICC in our pilot study were ICC = 0.43 for sorting time and ICC = 0.73 for correct cards [7]. Further, the test has been validated in children aged 4–6 years and proved to be sufficiently valid as a diagnostic procedure [34]. We calculated a composite score as an overall measure of attentional capacity using the mean of the z-scores of the individual dimensions of the KHV-VK (raw scores of sorting time as quantitative and error quote as qualitative dimension).
Statistical analyses
Normality of data was assessed and confirmed using the Shapiro–Wilk test. Accordingly, descriptive statistics were reported as group mean values and standard deviations (SD). The relationship between measures of physical fitness and cognitive performance were tested using two-tailed Pearson correlation coefficients for continuous variables and Spearman rank correlation for nominal variables. According to Cohen [27], a correlation coefficient of r < 0.3 is considered weak, 0.3 ≤ r < 0.5 moderate, and r ≥ 0.5 strong. We defined age, sex, body height, body mass as covariates that may influence physical fitness and cognitive performance in children. Prior to the regression analyses, key assumptions were checked. One individual case was identified as outlier and excluded from further analyses as linear regression models are not robust towards outliers. All other key assumptions of our regression models were confirmed. Single linear regression models (unadjusted vs. adjusted for potential covariates) were calculated for attention (composite score and individual dimensions—dependent variable) and the composite score of physical fitness (independent variable). Subsequently, the relation between attention (composite score and individual dimensions—dependent variable) and the four measures of physical fitness (static balance, muscle strength, power, and coordination—independent variables) were analyzed by a stepwise multiple linear regression model to find physical fitness components that predict the variance of attention in early childhood. To ascertain if a predictor variable has a practically meaningful effect, we interpreted Cohen’s F for the single linear regression models and Cohen’s F2 for the multiple linear regression model. For Cohen’s F, we calculated the square root of (R2 divided by 1-R2) considering an effect as small = 0.10, medium = 0.25, or large = 0.40. For Cohen’s F2, R2 was divided by 1-R2 considering an effect as small = 0.02, medium = 0.15, or large = 0.35 [27]. The significance level was set at p < 0.05. As no performance differences were found between boys and girls, statistical analyses were computed using pooled data. All statistical analyses were performed using SPSS version 25.0 (IBM SPSS Statistics, Armonk, NY, USA).