## Appendix A  
Figure A1 illustrates and exemplifies the full processing applied to the STM scores. The details of the procedure are reported in the sections below. 1. Computation of Short-Term Memory (STM) scores. Each list was given two scores, one reflecting the number of correctly recalled items, regardless of their order (memory for item, MI), and another reflecting the number of correct items recalled in the correct order (memory for order, MO), as detailed in [51]. When computing MO, a correct item was granted 1 point even when it was recalled in a wrong position, provided that it was preceded and followed by correct items (including empty spaces on initial and final positions). Per-condition MI and MO raw scores were, respectively, the simple sums of the MI and MO scores for all the lists that were administered. These sums could range from 0 to 25, with the top score corresponding to the full recall of the three-, four-, five-, six-, and seven-item-long lists (\(3+4+5+6+7=25\)). A discontinuation rule (whose mathematical details are reported in [51]) was applied in order to avoid unnecessary frustration in children. Discontinuation could occur after the four-, five-, or six-item list. Because of this discontinuation, the raw MI and MO scores did not  
N = 581 data points were used in the analyses (all available scores from all subjects in all oral output conditions). Imputation solution (iii) showed the highest correlation with the gold standard for the MO measure, \(r\) = 0.9832; imputation solution (iv) showed the highest correlation with the gold standard for the MI measure, \(r\) = 0.98. Hence, techniques (iii) and (iv) were applied to impute discontinuation-related missing sub-scores (MO and MI, respectively). In order to obtain a perfectly homogeneous dataset, we applied the same imputation to all conditions, even to the oral output ones (in which no imputation would have been necessary because no discontinuation was ever applied). 3 Normalizing transformations for the STM indices. The distributions of atomic STM scores were often very skewed, either way in the 0-25 bounded scale. The Logit transformation [110], pp. 284-285; ref. [111], offers a theoretically founded, common solution for distributions lying anywhere along a closed scale. Indeed, in our set, there were several variables whose peak was close to, or at, ceiling = 25 and some whose peak was relatively close to floor = 0. Thus, we took each atomic STM score (0-25, after imputation), replaced 0 and 25 with 0.5 and 24.5 to avoid infinities, computed proportions p = STM/25, and, finally, obtained Logit(p) = ln[p/(1 - p)]. This normalizing transformation was applied to all atomic STM measures, leading to much more symmetrical distributions. These new Logit-transformed variables were used in all subsequent analyses. Figures 15 and 16 below report the distributions of the eight overall STM variables (obtained by averaging across multiple atomic scores), showing that the ceiling/floor effects disappeared (thanks to the Logit transformation and averaging procedure), leaving quite symmetrical patterns. The skewness values are reported in Table 17.  
4. Reliability of the eight overall STM scores. Given that the STM battery (a rather long procedure) was administered only once, we could not directly estimate the test-retest reliability level. However, we did have conditions which were empirically quite similar, so we could provide lower-bound estimates of the reliability coefficients. The logic is that the reliability coefficient of any given variable must be higher than the highest correlation coefficient recorded among a set of \"similar\" variables, under the statistical notion that the removal of any experimental difference (that is, the replacement of \"similarity\" with \"identity\") should _increase_ that top correlation. We performed this computation on the eight \"overall\" variables, and for each of them, we took the set of \"similar\" variables as the ones belonging to the same family, MO or MI.