• Basic motor competencies (BMCs; children tests):

To measure BMCs, we used the MOBAK test instruments for preschool (MOBAK-KG) and the first two years of primary school (MOBAK-1-2). The MOBAK instrument is a curriculum-valid instrument that measures the level of BMC and can be used easily in PE lessons [1,32]. Moreover, it is oriented toward the elementary learning goals of PE (e.g., [5]). The BMCs in the two competence areas of self-movement and object movement (Table 1; for details, see [1,32]) are measured via four items each. A standardized task with corresponding evaluation criteria is described per item. The children performed two trials per test item (six trials for the throwing and catching items). Both attempts were rated dichotomously (0 = fail, 1 = successful). The individual results per test item were summed up to calculate the final item score (0 points = no successful attempts, 1 point = one successful attempt, 2 points = two successful attempts). The throwing and catching scores were calculated differently. In these cases, 0–2 successful attempts were scored as 0 points, 3–4 successful attempts as 1 point, and 5–6 successful attempts as 2 points. For each competency domain, a maximum sum score of eight points could be achieved (for details, see [1,32]). The data collection took 30–40 min and was carried out during a regular PE lesson of 45 min duration. The classes were split up and an examiner led three to four children through the eight test stations and gave a standardized explanation and one demonstration of each test item.

**Table 1.** Descriptions of the test items (see Herrmann, 2018 (p. 15) and 2020 (p. 8–9) [1,32]). Note: 0 = no attempt completed, 1 = task completed once, 2 = task completed twice.


### **Table 1.** *Cont.*


The factorial validity of the MOBAK instruments for preschool and primary education has already been investigated and confirmed in various studies (e.g., [33,34]).

• Social integration (PIQ; teacher questionnaires):

The teachers measured the children's social integration using the subscale of the perception of inclusion (PIQ) questionnaire [15]. The teachers rated the children individually via four items (e.g., "He/she gets along very well with his/her classmates.") on a fourpoint scale. The teachers received the questionnaire for each child in advance along with the information on the study. We asked the teachers to complete the questionnaire and bring it with them on the day of the MOBAK test. The Cronbach's alpha of the scale was calculated for preschool (0.82) and primary school (0.83) and showed satisfactory internal consistency [35]. The factorial validity of the instrument was confirmed in a validation study by Venetz and colleagues. [15].

• General health-related quality of life (general HRQoL; parent questionnaires):

The low reading literacy of children, especially in early childhood, has led to the development of instruments that measure children's HRQoL via parental assessments [36]. General health-related quality of life (HRQoL) was measured via the KIDSCREEN-10 instrument [36,37] in a subsample of N = 943 preschool children and the total sample of N = 880 primary school children (subsample 1), with a short version used in one canton due to the construction of the questionnaire. This instrument contains ten items (e.g., "Has your child felt sad?") and provides a valid measure of a general HRQoL factor. Moreover, the parents filled out the children's date of birth and gender. The parents received the questionnaire along with the declaration of consent, both of which were collected by the teachers. The internal consistency of the KIDSCREEN-10 instrument was acceptable, with a Cronbach's alpha of 0.73 for preschool and 0.76 for primary school (overall 0.74) [35]. For the analyses, the sum score (10–50) was transformed into the t-value (mean: 50, standard deviation: 10). Higher values indicate a higher general HRQoL [36,37].

• Physical well-being (parent questionnaires):

In a subsample of N = 348 preschool children (subsample 2), the physical well-being subscale of the KIDSCREEN-27 instrument [36] was used exploratively. The subscale consists of five items (e.g., "Has your child felt fit and well?") and had an acceptable Cronbach's alpha of 0.71. For the analyses, the sum score (5–23) was transformed into the t-value (mean: 50, standard deviation: 10). Higher values indicate higher physical well-being [37].

runs back backwards.

Running

### *2.3. Data Analysis* est. In addition to the 95% confidence intervals, Cohen's d was calculated to examine the

The child runs forward along a corridor (0.6 m × 4.0 m) to a wall, touches it with his/her hand, and then

*2.3. Data Analysis*

SPSS 28 was employed for the data editing, descriptive statistics, t-tests, and Cronbach's alpha estimations [38]. Descriptive statistics were calculated for all variables. T-tests were used to calculate differences between boys and girls in the variables of interest. In addition to the 95% confidence intervals, Cohen's d was calculated to examine the strength of the differences. Therefore, effect sizes were interpreted following Cohen (1988) as small (d = 0.10), medium (d = 0.50), and large (d = 0.80) [39]. We used Mplus 8.4 to perform multivariate analyses [40]. We calculated interclass correlations (ICCs) to test the influences of the multilevel structure (pupils from different classes) due to class associations. A high ICC value means that there are large differences between classes for the corresponding characteristics, the cause of which is to be sought at the class level (e.g., class composition). Raudenbush and Bryk (2002) recommend accounting for the multi-level structure of the data for advanced analyses with ICCs > 0.05 [41]. strength of the differences. Therefore, effect sizes were interpreted following Cohen (1988) as small (d = 0.10), medium (d = 0.50), and large (d = 0.80) [39]. We used Mplus 8.4 to perform multivariate analyses [40]. We calculated interclass correlations (ICCs) to test the influences of the multilevel structure (pupils from different classes) due to class associations. A high ICC value means that there are large differences between classes for the corresponding characteristics, the cause of which is to be sought at the class level (e.g., class composition). Raudenbush and Bryk (2002) recommend accounting for the multilevel structure of the data for advanced analyses with ICCs > 0.05 [41]. *Model 1:* In this first model, we used structural equation models to examine the relationships between the two MOBAK factors self-movement and object movement, social

Note: 0 = no attempt completed, 1 = task completed once, 2 = task completed twice.

SPSS 28 was employed for the data editing, descriptive statistics, t-tests, and

T-tests were used to calculate differences between boys and girls in the variables of inter-

The child moves sideways from one cone to another

placed at a distance of 3 m from each other.

*Int. J. Environ. Res. Public Health* **2022**, *19*, x 5 of 14

*Model 1:* In this first model, we used structural equation models to examine the relationships between the two MOBAK factors self-movement and object movement, social integration, and general HRQoL, with age as a covariate. Self-movement and object movement, as well as social integration, were included as latent factors. integration, and general HRQoL, with age as a covariate. Self-movement and object movement, as well as social integration, were included as latent factors. Following Ravens-Sieberer and colleagues, we summed up general HRQoL, transformed it into the t-value, and included it as a manifest variable in the model [37] (Figure

Following Ravens-Sieberer and colleagues, we summed up general HRQoL, transformed it into the t-value, and included it as a manifest variable in the model [37] (Figure 1). This model was separately examined for both age groups of interest (MOBAK-KG, model 1a; MOBAK-1-2, model 1b). Since KIDSCREEN-10 was not used (in its entirety) at all study locations, model 1 was calculated for a subsample of N = 943 preschool children and N = 880 primary school children (subsample 1). 1). This model was separately examined for both age groups of interest (MOBAK-KG, model 1a; MOBAK-1-2, model 1b). Since KIDSCREEN-10 was not used (in its entirety) at all study locations, model 1 was calculated for a subsample of N = 943 preschool children and N = 880 primary school children (subsample 1).

**Figure 1.** Model 1. Structural equation model with object movement, self-movement, general HRQoL, and social integration with the covariate age. **Figure 1.** Model 1. Structural equation model with object movement, self-movement, general HRQoL, and social integration with the covariate age.

*Model 2:* Next, we re-calculated model 1 as a multigroup model to investigate the correlations between the model components separately for boys and girls. This allowed for a model test for boys and girls. All parameters were estimated freely. Only the factor structure was kept equal between boys and girls [42–44]. This served to ensure that the factor structure (numbers and types of latent factors and loadings) was the same for boys *Model 2:* Next, we re-calculated model 1 as a multigroup model to investigate the correlations between the model components separately for boys and girls. This allowed for a model test for boys and girls. All parameters were estimated freely. Only the factor structure was kept equal between boys and girls [42–44]. This served to ensure that the factor structure (numbers and types of latent factors and loadings) was the same for boys and girls. We calculated model 2 separately for both MOBAK-KG (model 2a) and MOBAK-1-2 (model 2b).

*Model 3:* In a subsample of N = 384 preschool children (subsample 2), we used the physical well-being subscale of the KIDSCREEN-27 instrument (5 items [36]) to assess the children's physical well-being from the parents' perspective. The sum score of the five

Self-movement <sup>a</sup>

Social integration <sup>a</sup>

4.5

13.5

[4.4; 4.7] 0.05 4.3

[13.4; 13.7] 0.19 13.4

[4.1; 4.5]

[13.2; 13.5]

items was t-transformed into a manifest variable. We used structural equation models to calculate the relationship between the latent factors self-movement, object movement, and social integration and the manifest variable physical well-being. Age was included as a covariate (Figure 2). calculate the relationship between the latent factors self-movement, object movement, and social integration and the manifest variable physical well-being. Age was included as a covariate (Figure 2).

and girls. We calculated model 2 separately for both MOBAK-KG (model 2a) and

items was t-transformed into a manifest variable. We used structural equation models to

*Model 3:* In a subsample of N = 384 preschool children (subsample 2), we used the

*Int. J. Environ. Res. Public Health* **2022**, *19*, x 6 of 14

MOBAK-1-2 (model 2b).

**Figure 2.** Model 3. Structural equation model showing object movement, self-movement, physical well-being, and social integration with the covariate age. **Figure 2.** Model 3. Structural equation model showing object movement, self-movement, physical well-being, and social integration with the covariate age.

*Model 4:* We then re-calculated model 3 as a multigroup model for boys and girls. We examined the configural invariance in a multiple group model. This allowed for a model *Model 4:* We then re-calculated model 3 as a multigroup model for boys and girls. We examined the configural invariance in a multiple group model. This allowed for a model test for boys and girls simultaneously.

test for boys and girls simultaneously. In all models, we treated the MOBAK test items as ordinal-scaled and the question-In all models, we treated the MOBAK test items as ordinal-scaled and the questionnaire items as interval-scaled data. Accordingly, we applied the mean- and variance-adjusted weighted least squares (WLSMV) estimator.

naire items as interval-scaled data. Accordingly, we applied the mean- and variance-adjusted weighted least squares (WLSMV) estimator. The "type = complex" function for nested datasets implemented in Mplus was needed to correct the standard error and ensure that dependencies within the multilevel structure (0.01 ≤ ICC ≤ 0.19; Table 2) were accounted for in all model estimations [41]. The The "type = complex" function for nested datasets implemented in Mplus was needed to correct the standard error and ensure that dependencies within the multilevel structure (0.01 ≤ ICC ≤ 0.19; Table 2) were accounted for in all model estimations [41]. The goodness of fit of the models was assessed using fit indices proposed in the literature [45]. Effect sizes were interpreted as small (r > 0.10, β > 0.05), medium (r > 0.30, β > 0.25), and large (r > 0.50, β > 0.45) [39,46].

goodness of fit of the models was assessed using fit indices proposed in the literature [45]. Effect sizes were interpreted as small (r > 0.10, β > 0.05), medium (r > 0.30, β > 0.25), and **Table 2.** Descriptive analyses of sum scores of the motor competency domains, social integration, general HRQoL, and physical well-being.

[4.6; 5.0] 0.21 4.9

[4.8; 5.1] 0.14 4.8

[13.6; 13.8] 0.25 13.5

[4.6; 5.0]

[13.3; 13.8]

5.1

13.9 [13.7; 14.1] 0.15

[4.9; 5.3] 0.14


4.8

13.7


Note: M = mean, 95% CI = 95% confidence interval. Point ranges: object movement (0–8), self-movement (0–8), social integration (5–20), KIDSCREEN-10 sum score (10–50), KIDSCREEN physical well-being (5–25). <sup>1</sup> The sum score (range: 10–50) was transformed into t-values (mean: 50, standard deviation: 10). Higher values indicate better general health-related quality of life or physical well-being [37]. <sup>a</sup> Complete sample (preschool: N = 1163, primary school N = 880), <sup>b</sup> subsample 1 (preschool: N = 943, primary school N = 880), <sup>c</sup> subsample 2 (preschool: N = 384).

We accounted for missing values by generating model estimates using the full information maximum likelihood (FIML) procedure. This procedure prevents bias in the sample composition by preventing a reduction in the sample size [47].
