## 5 Results  
### Cluster Analysis  
From the 100 participants in the initial sample, because of sporadic missing data (due to the non-recoverable absence of children on one of the two dates scheduled with the schools for testing each individual child or--less frequently--insufficient motivation or collaboration to complete the test), only 82 could be included in the cluster analysis based on the whole set of scores from the learning tests. In total, 41 (equal to 50%) of the 82 final participants were from the Typically Developing group, whose mean age was 11.22 years (SD = 1.62, range 8-14), and 41 from the SLD group (50%), whose mean values were similar (mean age = 11.80, SD = 1.76). No statistically significant differences in gender, age, or sample were observed between the two groups. After a thorough visual analysis of the different patterns emerging from the cluster analysis, the clusters emerging from the seven-group analysis were selected as the subdivision that maximized the distinctiveness and interpretability of the patterns. Three of the seven clusters were single-case clusters, indicating individuals who could not be classified as belonging to any of the other clusters. These three individuals were not taken into consideration for further analyses, thus restricting all subsequent analyses to a four-cluster solution. Indeed, as shown in Figure 5, the remaining four clusters could easily be put into correspondence with a cluster of Typically Developing children (TD, Cluster 1, \(n=41\)) having all learning scores in the positive range; a reading disordered group (RD, Cluster 2, \(n=12\)) with low scores, especially in reading accuracy but also, although less marked, in calculation (number facts and addition and subtraction); a mathematical skills disordered group (MD, Cluster 3, \(n=17\)), with low scores, especially in the number skills scores and in number reading and writing (but also, less markedly, in the reading tasks); and a reading and writing disordered group (RD + WR, Cluster 4, \(n=12\)) with low scores in both reading (especially speed) and writing tasks (but also, although less markedly, in number counting speed). As shown in Table 3, the four clusters differ in all variables except the score expressing non-word writing, as expected in a language as transparent as Italian. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Cluster** & **1** & **2** & **3** & **4** & & & \\ \hline
**N. participants** & **41** & **12** & **17** & **12** & & & \\
**Mean** & **Mean** & **Mean** & **Mean** & **Mean** & **\(F\)** & \(p\)** & _Post hoc_ \\
**Re\_Text\_rate** & 0.30 & \(-1.14\) & \(-0.81\) & \(\mathbf{-1.79}\) & 33.57 & \(<\)0.001 & 1 vs. 2, 3, 4 \\
**Re\_Text\_errors** & 0.43 & \(\mathbf{-1.95}\) & \(-0.41\) & \(-1.30\) & 17.81 & \(<\)0.001 & 1 vs. 2, 4 \\
**Re\_W\_rate** & 0.80 & \(-1.10\) & \(-0.68\) & \(\mathbf{-2.11}\) & 39.35 & \(<\)0.001 & 2 vs. 4 \\ \end{tabular}
\end{table} 
Table 3: Mean Z-scores obtained at the re-reading (W—word, Nw—non-word, text), Wr—writing (W—word, Nw—non-word, Sent—sentence), and Ca—calculation (Nu—number reading and writing, counting, Ad—addition and Subtr—subtraction, Mul—multiplication) tasks in the 4 different clusters. The multivariate ANOVA on the eight overall STM variables revealed a significant multivariate effect (Wilks' Lambda = 0.535): F(24, 203.623) = 2.236, \(p=0.001\), Partial eta2 = 0.202. The results related to each single STM variable along with post hoc tests indicating specific differences among clusters are shown in Table 4. It can immediately be observed that all overall STM variables, with the only exception being MI_VV, showed significant differences among clusters, generally indicating that the cluster of TD children performed at a higher level compared with some or all of the SLD clusters. No significant differences with respect to overall STM variables emerged among any of the SLD clusters.