## 4 Discussion  
The previous results show that 13 single-graph and 16 full-model metrics are statistically significant in that they report on the complexity of the PROforma models. It is interesting to remark that four out of the 16 full-model metrics deemed significant, namely, percentage of single node plans (\(p1\%\)), average size plan (\(\hat{t}\)), percentage of plans over average (\(p50\%\)), and structuredness (\(\phi_{uggr}\)), can only be calculated over the full model, i.e., the corresponding single-graph metric does not exist. Then, the global number of metrics deemed significant is similar when the analyses are limited to those metrics that have a definition for the single graph and the full model. Among the relevant metrics, the ones showing a significance level below 0.05, only eight of them are statistically significant in both analyses, namely, density (\(\Delta\)), coefficient of connectivity (\(CNC\)), average connector degree (\(\overline{d_{C}}\)), maximum connector degree (\(\widehat{d_{C}}\)), separability (\(\Pi\)), sequentiality (\(\Xi\)), and depth (\(\Lambda\)). In other words, these eight metrics are statistically significant when they are calculated over the single graph but also when they are calculated over the full model with the aggregation formula. In most of cases (12 out of the 16 cases (eight metrics \(\times\) two analyses)), the metrics show a significant correlation for the pooling including all exercises. However, the behavior is different for the other two poolings of exercises. For the pooling including only the analysis exercises, the statistical results suggest that the relevant metrics fit better when they are calculated over single graphs, as five out of eight single-graph metrics are statistically significant. In contrast, only two out of eight full-model metrics are statistically significant. For the pooling including only the modifiability exercises, the statistical results suggest the opposite, i.e., the relevant metrics fit better when they are calculated over the full model. For this kind of exercises, three out of eight single-graph metrics are statistically significant, whereas seven out of \begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Cat.** & **Metric \& Fixed Effect** & **Alls** & **Ana.** & **Mod.** \\ \hline \hline \multirow{2}{*}{Size} & Diameter: \(Diam_{uggr}\times Difficulty\) & **0.014** & 0.050 & 0.055 \\ \hline \multirow{7}{*}{Density} & Density: \(\Delta_{uggr}\times Difficulty\) & 0.296 & 0.212 & **0.032** \\ \cline{2-5}  & Coef. of connectivity: \(CNC_{uggr}\times Difficulty\) & **0.008** & 0.114 & **0.025** \\ \cline{2-5}  & Avg. connector degree: \(\overline{d_{C_{uggr}}}\times Difficulty\) & **0.012** & **0.032** & **0.030** \\ \cline{2-5}  & Max. connector degree: \(\overline{d_{C_{uggr}}}\times Difficulty\) & 0.217 & 0.093 & **0.027** \\ \cline{2-5}  & Density of plans: \(\overline{p}\times Difficulty\) & 0.068 & **0.021** & 0.095 \\ \cline{2-5}  & Perc. single node plans: \(p1\%\times Difficulty\) & **0.031** & **0.039** & 0.374 \\ \cline{2-5}  & Avg. size plan: \(\overline{l}\times Difficulty\) & **0.007** & **0.026** & **0.043** \\ \cline{2-5}  & Perc. plans over average: \(p50\%\times Difficulty\) & **0.002** & 0.061 & **0.038** \\ \cline{2-5}  & Decision density: \(\delta_{D}\times Difficulty\) & **0.005** & **0.005** & **0.044** \\ \hline \multirow{7}{*}{Partitionability} & Separability: \(\Pi_{aggr}\times Difficulty\) & **0.016** & 0.087 & **0.030** \\ \cline{2-5}  & Sequentiality: \(\Xi_{aggr}\times Difficulty\) & **0.017** & 0.090 & **0.048** \\ \cline{2-5}  & Structuredness: \(\phi_{uggr}\times Difficulty\) & **0.037** & **0.031** & **0.043** \\ \cline{2-5}  & Depth: \(\Lambda_{aggr}\times Difficulty\) & **0.026** & **0.032** & 0.051 \\ \cline{2-5}  & Model depth: \(\mathrm{Y}\times Difficulty\) & 0.119 & **0.047** & 0.151 \\ \hline Conn. Interplay & Number of preconditions: \(S_{Prelcond}\times Difficulty\) & 0.304 & **0.042** & 0.204 \\ \hline \hline \end{tabular}
\end{table}