## 3 Results  
A total of 1931 participants (52.6% girls; M\({}_{\text{age}}\) = 12.07 years, SD = 3.95) completed at least one subtest of Battery 1. Four hundred and thirty-one participants had no missing data on Battery 1; 433 had one missing subtest, 286--two, 233--three, 140--four, 79--five, 85--six, 51--seven, 156--eight, and 47 had nine missing subtests.  
Table 3 presents the sample descriptive statistics for each measure in Battery 1. Figure 2 shows the distribution of each subtest score. It is notable that there are multiple extreme values either on the lower tail or the higher tail of the distributions, reflecting a broad range of ability among our sample. For example, one student scored 3.84 standard deviations below the average on the approximate number system subtest, indicating possible deficits  
in quantitative reasoning. In contrast, another student scored 2.64 standard deviations above the average on equivalence, indicating potential giftedness.  
Table 4 presents the Pearson correlation coefficients between age and subtest scores. Age was positively correlated with approximate number system, equivalence, attention shifting-target, card sorting-classification, and card sorting-inference making scores. Age was negatively correlated with attention shifting-commission, attention shifting-omission, and card sorting-hypothesis testing scores. Notably, no correlations were found between age and performance on the card-sorting hypothesis-testing scores, nor between age and narrative memory. Regarding the associations between the 10 measures, the small-to-moderate effect sizes of correlations provided evidence of discriminant validity.  
Finally, we present the results of the simulation study carried out for one of the planned adaptive tests, equivalence (see Table 5). This illustrates how the data collected in the pilot exercise was used to generate the adaptive algorithm for item selection, to be implemented in the final adaptive version of the test. The results showed that compared to  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measures** & **n** & **M (SD)** & **Min** & **Max** & **Skewness** & **Kurtosis** \\ \hline
1. Approximate number system & 1636 & 0.00 (0.79) & \(-\)3.86 & 1.29 & \(-\)0.90 & 0.47 \\ \hline
2. Equivalence & 1297 & 0.00 (0.91) & \(-\)1.88 & 2.64 & 0.10 & \(-\)0.73 \\ \hline Attention shifting & & & & & & \\
3. Target & 1432 & 131.01(20.43) & 28.00 & 154.00 & \(-\)1.92 & 3.83 \\
4. Commission & 1380 & 11.63 (15.21) & 0.00 & 141.00 & 3.34 & 15.24 \\
5. Omission & 1451 & 15.55 (9.93) & 0.00 & 74.00 & 1.69 & 4.27 \\ \hline
6. Card sorting-classification & 1608 & 22.57 (1.75) & 11.00 & 24.00 & \(-\)2.00 & 5.65 \\ \hline Card sorting-hypothesis testing & & & & & & \\
7. Errors & 1341 & 9.22 (4.04) & 1.00 & 23.00 & 0.43 & \(-\)0.33 \\
8. Perseverative responses & 1341 & 15.99 (5.70) & 5.00 & 33.00 & 0.49 & \(-\)0.52 \\ \hline
9. Card sorting-inference making & 1573 & 0.00 (0.88) & \(-\)1.56 & 2.65 & 0.47 & \(-\)0.48 \\ \hline
10. Narrative memory & 1084 & 0.00 (0.65) & \(-\)1.01 & 2.12 & 0.83 & 0.24 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Descriptive statistics by subtest case examples.  
Figure 2: Score distributions of subtest case examples.  
using test length as the stopping rule, accuracy was higher and the RMSE lower when using precision as the stopping rule. The simulation results favored stopping the CAT process when a certain pre-defined precision level of ability estimate had been reached. Moreover, as compared to the stopping rule of SEM = 0.22 and 0.28, the accuracy was identical, and the RMSE was slightly lower when the stopping rule was set to SEM = 0.31. Importantly, only 14.30 items were needed on average to reach a SEM of 0.31 ([PERSON]'s alpha = 0.90), suggesting the efficiency and accuracy of developing CAT for the equivalence subtest.