## 2 Materials and Methods
### Data Analysis  
A repeated measures ANOVA was conducted to investigate the development of K and CSE. We examined whether the four intervention groups showed an increase in their K and CSE following the intervention (main effect: from pre to post) and whether the increase differed according to or was dependent upon the group's design (interaction effect: group \(\times\) time).  
Moderation analysis further explored the relationships among Kpre and Kpost, and CSEpre and CSEpost. In total, 12 moderation analyses were performed using SPSS version 29.0.0.0 (IBM). The analyses were carried out with the PROCESS macro for SPSS (version 29) [70]. This analysis used a model in which the relationship between two constructs depends on another variable. This variable (the moderator) is suggested to affect the strength and/or direction of the relationship. In this case, we applied the moderator (AR or GAME) to the relationship of the pre-post variables (K or CSE development from pre to post) to unveil any potential effect said feature (AR or GAME) may have had on the participants' development (from pre to post). This choice of analysis supported the chosen research design and format of contrasting features while investigating a recorded development from before to after the intervention.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Data Set** & **Sample Size N** & **Sex** & **Age** & **Course of Study** \\ \hline \multirow{4}{*}{1 (K)} & N = 196 & & & elementary school \\  & A: n = 55 & Female = 77\% & 18–36 & education = 64.3\% \\  & B: n = 48 & Male = 23\% & M = 20.31 & secondary (WHRS) = 28.6\% \\  & C: n = 43 & Diverse = 0\% & SD = 2.434 & others = 6.6\% \\  & D: n = 50 & & & missing values = 0.5\% \\ \hline \multirow{4}{*}{2 (CSE)} & N = 177 & & & elementary school \\  & A: n = 46 & Female = 78\% & 18–36 & education = 63.3\% \\ \cline{1-1}  & B: n = 38 & Male = 22\% & M = 20.27 & secondary (WHRS) = 28.8\% \\ \cline{1-1}  & C: n = 45 & Diverse = 0\% & SD = 2.441 & others = 7.3\% \\ \cline{1-1}  & D: n = 48 & & & missing values = 0.6\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics of data sets 1 and 2.  
AR and GAME were tested for their potential moderating effects on CSE and K gains. A significant moderating effect would imply that the variable in question--in this case, the intervention design conditions AR/non-AR/GAME/non-GAME--is associated with the direction and/or the intensity of the relationship between pre-post variables--in this case, the development of knowledge/computer self-efficacy. To contrast the interventions by AR or GAME, the groups were merged to form AR/non-AR and GAME/non-GAME groups. Moderation analyses were applied to each of the total samples of K (data set 1 N = 196) and CSE (data set 2 N = 177) as well as to the merged groups. An overview of the performed moderation analyses is shown in Table 2.  
Due to the lack of normal distribution, the variables Kpre, Kpost, CSEpre, and CSEpost were Box-Cox transformed to perform moderation analyses. The optimal lambdas for transformation were rounded to one decimal. The following lambdas were used for Box-Cox transformation: Kpre \(\lambda\) = 3.2; Kpost \(\lambda\) = 4.9; CSEpre \(\lambda\) = 3.5; and CSEpost \(\lambda\) = 4.4.