# Within and Across-Language Comparison of Vocal Emotions in Mandarin and English
## 3 Results
### Across-Language Comparison of Vocal Emotions: Mandarin versus English  
As mentioned above, to overcome evident biases arising from the absolute value in two languages, we adopted the method of data normalization from [21; 48] according to the following equation:  
\[\text{Normalized X}=(\text{x}-\text{N})/\text{N}\]  
where x is the absolute value of each parameter for anger, fear, happiness and sadness, respectively. N is the absolute value of each parameter for neutral. Thus, this equation produces the relative value of each parameter in each of the four emotions compared to the neutral baseline. The derived data have a positive or a negative value, depending on the relative difference with neutral.  
These derived data were analysed in a set of mixed-repeated measures ANOVAs, with Emotion (anger, fear, happiness, sadness) as a within-subject factor and Language (Mandarin, English) as a between-subject factor. [PERSON]'s tests were conducted to estimate the assumption of sphericity. Results suggested that rise (X\({}^{2}\) = 15.69, _df_ = 5, \(p\) = 0.008), rise slope (X\({}^{2}\) = 17.99, _df_ = 5, \(p\) = 0.003), fall slope (X\({}^{2}\) = 11.71, _df_ = 5, \(p\) = 0.041), H1 (X\({}^{2}\) = 13.63, _df_ = 5, \(p\) = 0.019), H2 (X\({}^{2}\) = 13.07, _df_ = 5, \(p\) = 0.024), H4 (X\({}^{2}\) = 25.02, _df_ = 5, \(p\) = 0.000), H1-A1 (X\({}^{2}\) = 25.36, _df_ = 5, \(p\) = 0.000), H1-A2 (X\({}^{2}\) = 22.04, _df_ = 5, \(p\) = 0.001), H1-A3 (X\({}^{2}\) = 19.08, _df_ = 5, \(p\) = 0.002) and CQ (X\({}^{2}\) = 11.97, _df_ = 5, \(p\) = 0.037) violated the null assumption. Therefore, the degrees of freedom were corrected for the above variables using Greenhouse-Geisser estimates of sphericity. Results are displayed in Table 4 and analysed in the order of prosodic cues, spectral cues and EGG cues.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & & \\ \cline{2-10} \multirow{2}{*}{**Measurement**} & \multicolumn{4}{c}{**Emotion (Within-Subject)**} & \multicolumn{4}{c}{**Language (Between-Subject)**} & \multicolumn{4}{c}{**Emotion \(\times\) Language**} \\ \cline{2-10}  & _F (3,24)_ & \(p\) & **n\({}^{2}\)** & _F (1,8)_ & \(p\) & **n\({}^{2}\)** & _F (3,24)_ & \(p\) & **n\({}^{2}\)** \\ \hline Mean pitch & 19.905 & 0.000 *** & 0.713 & 0.666 & 0.438 & 0.077 & 0.367 & 0.778 & 0.044 \\ Pitch range & 31.567 & 0.000 *** & 0.798 & 7.768 & 0.024 * & 0.493 & 1.285 & 0.302 & 0.138 \\ Mean absolute slope & 50.404 & 0.000 *** & 0.863 & 34.760 & 0.000 *** & 0.813 & 7.734 & 0.001 ** & 0.492 \\ Rise & 33.377 & 0.000 *** & 0.807 & 12.769 & 0.007 ** & 0.615 & 5.902 & 0.025 * & 0.425 \\ Fall & 23.507 & 0.000 *** & 0.746 & 30.419 & 0.001 ** & 0.792 & 5.158 & 0.007 ** & 0.392 \\ Rise slope & 16.980 & 0.001 *** & 0.680 & 22.950 & 0.001 ** & 0.742 & 3.210 & 0.098 & 0.286 \\ Fall slope & 27.416 & 0.000 *** & 0.774 & 22.086 & 0.002 ** & 0.734 & 5.095 & 0.023 * & 0.389 \\ Speech rate & 29.519 & 0.000 *** & 0.787 & 12.342 & 0.007 ** & 0.226 & 5.291 & 0.006 ** & 0.398 \\ Intensity & 47.668 & 0.000 *** & 0.856 & 0.851 & 0.383 & 0.096 & 2.157 & 0.119 & 0.212 \\ CPP & 18.852 & 0.000 *** & 0.702 & 2.006 & 0.194 & 0.200 & 5.101 & 0.007 ** & 0.389 \\ H1 & 3.595 & 0.051 & 0.310 & 0.004 & 0.953 & 0.000 & 4.665 & 0.637 & 0.055 \\ H2 & 7.918 & 0.010 * & 0.497 & 0.011 & 0.919 & 0.001 & 0.812 & 0.431 & 0.092 \\ H4 & 1.467 & 0.263 & 0.155 & 0.116 & 0.743 & 0.014 & 2.802 & 0.123 & 0.259 \\ H1-H2 & 0.993 & 0.413 & 0.110 & 0.048 & 0.832 & 0.006 & 2.460 & 0.087 & 0.235 \\ H1-A1 & 0.462 & 0.539 & 0.055 & 0.483 & 0.507 & 0.057 & 0.049 & 0.859 & 0.006 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of mixed repeated measures ANOVAs for each cue.