## 3 Results
### Prognostic Validity of the Prediction Methods  
In the linear discriminant analysis (see Figure 2; \(N=166\); eight children could not perform at least one test, so they were excluded from this analysis), the sensitivity could assume values of 24.1% (random result) to 100%, with a constant selection rate of 24.1%. The specificity reached values ranging from 75.9% (random result) to 84%. Thus, accordingly to Formula (8), the random (total) hit rate was 70.9% (see Formula (13)). \[\text{Random Hit Rate}=\frac{0.241\times 16+(1-0.241)\times 150}{166}\approx 0.709 \tag{13}\]  
Following Formula (9), the maximum hit rate was 0.855 (Formula (14)):  
\[\text{Maximum Hit Rate}=1-\frac{|29-5|}{166}\approx 0.855 \tag{14}\]  
For this calculation, therefore, the counter-probability is used to consider what the actual probability is if only the over-recommendations lead to an incorrect prediction. With 40 top performer predictions, 24 over-recommendations occurred, which corresponds to 14.5%--accordingly, this percentage is deducted from 100%. Finally, accordingly to Formula (11), it remains to calculate the RIOC value (Formula (15)):  
\[\text{RIOC Value}=\frac{0.795-0.709}{0.855-0.709}\approx 0.588 \tag{15}\]  
The calculations of the predictors of the other analysis methods are done analogously. All four methods revealed RIOC values in the range of 0.33-0.67 and thus illustrate a good classification result. However, the differences in the results of at least three out of four analyses were small. The results for sensitivity and specificity are very different (Table 7). The logistic regression shows a sensitivity of only 37.5% but reaches the highest specificity, with 96%. The TRS and MLP prediction methods reach 75% or more in both parameters. Considering the positive predictive values, more than every second prediction of a top performer is correct for the logistic regression (50%). The top performer predictions for the TRS and MLP analysis methods only apply to every third (TRS = 30.8% and MLP = 33.3%). However, their negative predictive values are higher than those of the other two methods. _Youden's_ J turns out to be the highest, with J = 0.59 for the MLP. This is closely followed by the TRS, with J = 0.579. Logistic regression performs worst among the four methods. Despite its high _Youden's_ J, the TRS only achieves a value of F1 = 0.437 in terms of the F1 score, which is probably related to its low positive predictive value (30.8%). Among the four methods, the MLP performs best here, with F1 = 0.462. This is not surprising because it has the highest sensitivity and also a high positive predictive value (33.3%). The RIOC values show values above 44% for all methods, with the MLP reaching the highest value of 68.1%. If, for example, a method would correctly predict the performance of another person, the RIOC value can increase between 1% and 8% depending on the performance group and method. Thus, another correct top performer prediction would increase the RIOC value of discriminant analysis from 58.8% to almost 67%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Multilayer Perceptron 1**} & \multicolumn{4}{c}{**Predicted/Recommended**} \\ \cline{2-5}  & \multirow{2}{*}{**Low Performer**} & **Top** & **Percentage** \\  & & **Performer** & **Correct** \\ \hline \multirow{3}{*}{Observed/Existing} & Top Performer & 4 & 12 & 75\% \\  & Low Performer 2 & 126 & 24 & 84\% \\  & Percentage (total) & 78.3\% & 21.7\% & 91\% \\ \hline \hline \end{tabular}  
* A 5-fold cross-validation was performed a total of five times, and the respective test results were averaged.
* Eight children could not perform at least one test, so they were excluded from this analysis.  
\end{table} 
Table 6: Sensitivity and specificity of the Neural Network (Multilayer Perceptron). Combining the predictions (union set) of the TRS with those of the MLP yields the highest sensitivity of all analyses (81.3%). Of 16 top performers, 13 are recognized as such. The selection rate is 27.7%.