# Musical Mix Clarity Prediction Using Decomposition and Perceptual Masking Thresholds
## 4 Model Evaluation  
To evaluate the model's performance, the outputs of the clarity model variants were correlated against the MCSs obtained from the controlled listening test detailed in Section 3.3. Both [PERSON]'s correlation coefficient \(r\) and [PERSON]'s rank correlation coefficient \(rho\) were calculated, as a lack of a bivariate normal distribution or linear relationship between the two variables can cause the [PERSON]'s coefficient to provide an inaccurate measure of association. [PERSON]'s coefficient is still provided, as a non-linear relationship is suggested in cases where \(rho\) is greater than \(r\), and a linear relationship where \(r\) is greater than \(rho\). The [PERSON]'s rank coefficient is non-parametric, so is more robust, and is the focus of the following analysis. Both correlation coefficients for each model variation are given in Table 2 for the sake of comparison. When correlating the ranked L2 PM clarity model masking scores against the MCSs, a strong negative Spearman rank correlation of _rho_ = \(-0.8382\), \(p<0.01\) was achieved. This correlation is shown in Figure 3, where the box plots indicate the distribution about the MCSs obtained, ordered by rank determined by the overall masking score calculated by the proposed model. This was the highest Spearman rank correlation achieved by any implementation of the model, with most deviations from the line of best fit still within the interquartile range of the MCSs. The least well ranked stimulus, '126410', was also poorly predicted by a different mix clarity model suggested in previous work [20]. This implementation also achieved \(r=-0.7884\), \(p<0.01\), which suggests a strong and slightly non-linear parametric relationship between the model output and the subjective scores. The model was also implemented using the L3 PM, forming the L3 PM clarity model. This achieved a significant, but weaker correlation of _rho_ = \(-0.6882\), \(p<0.01\), shown in Figure 4. Again, a lesser Pearson correlation (\(r=-0.6682\), \(p<0.01\)) was seen, indicating a somewhat non-linear relationship. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measure** & \(\mathbf{r}\) & _rho_ \\ \hline L3 PM Clarity Model & \(-0.6682\) & \(-0.6882\) \\ Modified L3 PM Clarity model & \(-0.7868\) & \(-0.8088\) \\ L2 PM Clarity Model & \(-0.7884\) & \(-0.8382\) \\ \hline \hline \end{tabular} All coefficients shown are significant where \(p<0.01\).  
\end{table} 
Table 2: Pearson and Spearman rank correlations of tested metrics against MCSs. Figure 3: Spearman rank correlation between overall masking score ranks calculated using the L2 PM clarity model median clarity scores. This correlation shows some heteroscedasticity, where the stimuli given higher masking scores were predicted less accurately than those given low masking scores, though many of the interquartile ranges cross the line of best fit. The weaker correlation of this model compared to the L2 PM clarity model was somewhat unexpected, as the L3 PM is more efficient in coding applications, and the SMR values are calculated in scale-factor bands which approximate critical bands. These are more reflective of perception than the L2 PM scale-factor bands which are linearly spaced. The better performance of the L2 PM clarity model suggests a greater importance of masking occurring between higher frequency energy, due to the model calculating the overall masking of a given frame in each component as the sum of masking within the scale-factor bands (Equation (8)). Other work has suggested an importance of high frequency energy in clarity perception for some single instrument sounds [7,12]. The L3 PM also employs window switching which the L2 PM implementation does not [24]; whereby, shorter analysis windows and fewer scale-factor bands are used in determining the energy and masking thresholds of highly transient frames. For the stimuli used in the present testing, the perceptual entropy threshold was not crossed by any frames of any of the stimuli.