## 3 Results
### Meta-Analysis  
To understand the overall effectiveness of AR-supported instruction and its moderating factors, we conducted a meta-analysis of the experimental research papers from 2001 to 2020. There were a total of 36 experimental research articles, but only 6 articles had reported necessary statistical information such as the mean, standard deviation, and sample size, meeting the requirements of the meta-analysis. The 6 articles included 15 separate experimental studies based on different dependent variables. The standardized effect sizes, as measured by [PERSON]'s \(g\)[59], were calculated using the random-effects model (REM). The effect size ranged from \(-2.498\) to \(3.303\). Among all the empirical studies, nine were positive effects, five were insignificantly negative effects, and one showed no effect. The REM results revealed an overall small effect size of AR-supported instruction on learning outcomes (\(g=0.268\), \(SE=0.338\), \(CI=[-0.395\), \(0.931\)], \(p=0.428\)). Furthermore, we conducted a mixed-effect analysis (MEA) to explore the potential moderators influencing the effectiveness of AR-supported instruction, and the results are indicated in Table 3. In order to avoid statistical heterogeneity and biased results, those with only one paper were not included in the calculation [60]. We examined eight potential moderators, and the MEA results revealed that there were seven variables that significantly moderated the effectiveness of AR-supported professional training. First, in terms of the training context, the results showed that discipline significantly moderated the effectiveness of AR-supported professional training (\(Q_{B}=6.43\), \(p<0.05\)), with a large positive effect in engineering (\(g=1.748\)) and an insignificantly negative effect in health and medicine. From the perspective of research design, the results revealed significant variance in effect size in terms of pedagogy (\(Q_{B}=6.843\), \(p<0.05\)) and instructional function (\(Q_{B}=13.555\), \(p<0.05\)), while effect size did not vary according to the scaffolding mode (\(Q_{B}=2.551\), \(p>0.05\)). Regarding pedagogy, the mixed pedagogy was the most effective (\(g=1.748\)) for AR-supported training, while trial-and-error generated an insignificantly negative effect (\(g=-0.246\)). In addition, instructional function, both content delivery (\(g=1.204\)) and mixed function (\(g=1.748\)), reached a large effect size; however, the results should be carefully interpreted for only showing two and three effect sizes. However, the effect size of the practice function was insignificantly negative, consistent with the effect size of trial-and-error pedagogy. Figure 7: Learning outcomes in AR-supported instruction in three disciplines. Figure 8: (**a**) Instructional function of AR-supported instruction in two periods of 2001–2015 and 2016–2020; (**b**) AR interventions by level of interactivity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Moderator** & **K** & \(g\) & **95\% CI** & \(Q_{B}\) & \(p\)**-Value** \\ \hline Discipline & & & & 6.43 ** & 0.009 \\ Engineering & 3 & 1.748 & [0.421, 3.075] & & \\ Health and medicine & 11 & \(-\)0.246 & [\(-\)0.932, 0.441] & & \\ \hline Pedagogy & & & & 6.843 ** & 0.009 \\ Mixed & 3 & 1.748 & [0.421, 3.075] & & \\ Trial-and-error & 11 & \(-\)0.246 & [\(-\)0.932, 0.441] & & \\ \hline Instructional function & & & & 13.555 ** & 0.001 \\ Content delivery & 2 & 1.204 & [0.625, 1.783] & & \\ Mixed & 3 & 1.748 & [0.421, 3.075] & & \\ Practice & 10 & \(-\)0.359 & [\(-\)1.082, 0.364] & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Moderator analysis of selected experimental studies. Regarding the technology of AR intervention, the Q-statistics indicated significant differences in the effectiveness of AR-supported professional training with devices of input modes (\(Q_{B}=12.080\), \(p<0.05\)), computing devices (\(Q_{B}=11.721\), \(p=0.003<0.05\)), output modes (\(Q_{B}=14.609\), \(p=0.001\)), and media representations (\(Q_{B}=19.417\), \(p<0.001\)).