## 4 Results
### Results for Research Objective One: Design of Open-Text Items for Assessing \"Selecting dLMs\"
Following the coding and scoring that we established and validated using the dataset from Study 1, we employed two trained coders who independently categorized the participants' responses. The inter-coder agreement was calculated separately for coding items 1-3 (see Figure 2), resulting in [PERSON]'s \(\kappa=0.86\), and item 4 (see Figure 2), \(\kappa=0.99\), placing them in a near-perfect range ([PERSON], 2016). 2.1 RQ 2.1: Can the Designed Instrument for \"Selecting dLMs\" Assess Different Levels Regarding the Number of Semesters of Study, and Are the Results Distinguishable from TPACK Self-Report Results? To address this research question, we grouped participants from Study 2 (\(n=379\)) in increments of two semesters because the number of semesters in the development stages varies between the two universities. Table 4 shows the descriptive results of the pre-service teachers' scores for \"selecting dLMs\" (external assessment) by number of semesters of study and the self-reported TPACK using the TPACK instrument by [PERSON] et al. (2016). For the external assessment, pre-service teachers achieved the highest results for \"selecting dLMs\" in semester 7 and above (\(M=2.65\), \(SD=1.51\)). To determine the items' ability to differentiate competence levels of \"selecting dLMs\", we examined the dependence of the scores on the number of semesters using one-factor ANOVA (see Table 4). The ANOVA revealed statistically significant differences between semesters (F (3375) = 8.51, \(p<0.0000\), \(\eta p^{2}=0.063\), \(n=379\)). Based on these results, we conclude that the designed items enable us to differentiate between different competence levels of \"selecting dLMs\". To analyze whether the results using the new instrument for \"selecting dLMs\" for the participants in Study 2 are distinguishable from the results of the TPACK self-report instrument by [PERSON] et al. [34], we also examined the latter concerning the number of semesters of study using the Kruskal-Wallis test (Table 4). The results revealed that the self-assessed TPACK is also influenced by the number of semesters (Chi\({}^{2}\) = 11.99, \(p\) = 0.007). The descriptive results again revealed that participants in semesters 7 and above exhibited the highest self-reported TPACK (\(M\) = 3.55, \(SD\) = 0.76). In addition, we calculated [PERSON]'s \(\alpha\) for the TPACK self-report scale, which was 0.97. This indicated excellent reliability and surpassed the 0.87 reported in the original publication by [PERSON] et al. [32]. We calculated effect sizes for each assessment to compare the results of self-reported TPACK [32] and the external assessment of \"selecting dLMs\" via the new instrument presented here. The effect size for the \"selecting dLMs\" performance assessed using the new instrument was \(f\) = 0.26. The self-reported TPACK showed an effect size of \(f\) = 0.23. Due to the smaller subgroups of pre-service teachers by study stages (primary, special education, lower, and upper secondary education), we did not investigate the stages of study of participants as done in other studies [60; 61]. For the same reasons, we did not use the universities from the two countries, Austria and Germany, as a factor, nor did we perform two-factor ANOVAs.