## 3 Methodology
### Experimental Setup
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Language** & **VTLN Model** & **VTLN Training Dataset** & **Age Range** & **Speech Type** \\ \hline \multirow{3}{*}{Dutch} & \(\text{VTLN}_{\text{CGN}}\) & CGN-train & 18–65 & Read \\  & \(\text{VTLN}_{\text{Jas-DCDT}}\) & Jasmin-[DC, DT] & 6–18 & Read + HMI \\  & \(\text{VTLN}_{\text{Jas-DCDT}}\)nnT & Jasmin-[DC, DT, and nnT] & 6–18 & Read + HMI \\ \hline \multirow{2}{*}{German} & \(\text{VTLN}_{\text{CV}}\) & CV-train & - & Read \\  & \(\text{VTLN}_{\text{kids}}\text{TALC}\) & kidsTALC-train & 3–11 & Read + Conversational \\ \hline \multirow{2}{*}{Mandarin} & \(\text{VTLN}_{\text{SetA}}\) & SetA-train & 18–60 & Read \\  & \(\text{VTLN}_{\text{SetC1C2}}\) & SetC1C2-train,dev & 4–11 & Read + Conversational \\ \hline \multirow{2}{*}{Multiple} & \(\text{VTLN}_{\text{MultiV1}}\) & Randomly selected \(\sim\)5 h of data from different & \multirow{2}{*}{3–65+} & Read + HMI + Conversational \\  & speaker groups in Dutch, German, and Mandarin & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Overview of the different VTLN models trained on the three languages; the age ranges of the speakers; and the types of speech. Experiment 3: The Combined Effect of Augmentation and Normalization_: To study the effect of augmentation and normalization combined (i.e., the combination of the scenarios in Figure 1b,c), we combine the set-ups of Experiment 1 (the ASR models are trained with SP + SpecAug) and Experiment 2, with the difference that VTLN is applied to the ASR models in two ways:  
* _During training and testing_: Each of the VTLN models for each language is applied during training to adult training data as in Figure 1b and also applied during testing to the adults' and children's speech test sets as in Figure 1c, yielding three ASR models for Dutch and two ASR models for both German and Mandarin. * _During testing only_: Each of the VTLN models for each language is only applied during the test stage to the adults' and children's speech test sets as in Figure 1c. Moreover, in addition to the language-specific adults' and children's speech-based VTLN models, we also trained a VTLN model (VTLN\({}_{\text{MultiV1}}\)) with speech data from diverse speaker groups from all three languages. Specifically, we randomly selected around 5 h of speech from the Dutch, German, and Mandarin adults' and children's speech databases, selecting from the three available speaking styles (read, HMI, and conversational speech). The motivation for training a VTLN model on such diverse speech is that preliminary findings have shown that VTLN models can be applied cross-lingually [67]. We therefore explore the feasibility of using a common VTLN model that could work across languages. **Evaluation**: Recognition performance for the Dutch and German experiments is reported in WER and for Mandarin in Character Error Rate (CER). WER and CER are calculated as the ratio of word/character insertion, substitution, and deletion errors in the recognized transcription and the total number of spoken words/characters in the ground truth transcription [68]. We conduct an analysis of the estimated warping factors for each speaker group in the adults' and children's test sets to investigate the link between the estimated warping factors and the recognition performance. To further understand the possibilities and limitations of VTLN, we analyzed the WER results with respect to age and gender for Dutch (as this information is only available in the Dutch-Jasmin children's speech database). To assess the statistical significance of the results, we employ the procedure outlined in [69], which utilizes matched pairs sentence-segment word error (MAPSSWE) [70] to determine whether the observed differences in WER are statistically significant. We report \(p\)-values (provided in Appendix B) to indicate significant differences at the levels of \(p=0.001\) (*), \(p=0.01\) (*+), or \(p=0.05\) (*+).