## 3 Results
### Relationship between Measures of Noise Tolerance and NR Outcomes  
Pearson correlation analyses were performed to investigate the relationship between cortical and subjective noise tolerance measures and NR-driven accuracy changes. The neural SNR significantly correlated with behavioral accuracy changes (\(\Delta\)accuracy) by NR 1 (\(r\) = \(-\)0.42, \(p\) = 0.021) and NR 2 (\(r\) = \(-\)0.52, \(p\) = 0.0031), respectively, indicating that people with lower neural SNR (i.e., lower noise tolerance) may get more benefit from the use of NR algorithms (Figure 5).  
Figure 4: Post hoc comparison of behavioral accuracy between experimental conditions: Noise reduction (NR) 1 vs. NR off and NR 2 vs. NR off, respectively. The center of the box plots indicates the median, and the edges indicate the 25 th and 75 th percentiles. Solid black lines denote individuals’ performance. n.s., not significant.  
Noise-tolerance ratings that varied among participants (mean = 3.35, median = 3.05, SD = 0.93) significantly correlated with NR 2-driven accuracy changes (\(r=-0.38,p=0.041\)) but not with NR 1-driven changes (\(r=-0.10,p=0.59\)), indicating that people with lower self-reported noise tolerance may get a better chance to benefit from relatively strong NR processing (i.e., NR 2) and that subjective measure of noise tolerance might not be sensitive enough to capture changes in performance driven by relatively mild NR processing (i.e., NR 1) (Figure 6). No significant correlation was found between the neural SNR and noise-tolerance ratings (\(r=0.27,p=0.14\)).  
Stepwise Regression: Modeling the Influence of Cortical and Subjective Measures of Noise Tolerance on NR Outcomes  
Individually, both neural SNRs and noise-tolerance ratings exhibited significant correlations with NR 2-driven changes in behavioral accuracy during the preliminary correlation analyses above. Given that no correlation between neural SNR and noise-tolerance rating was found while both predictors showed potential relevance to variance in NR 2-driven accuracy changes, a multiple linear regression model was constructed stepwise. The initial model only included neural SNR as a predictor, and subsequently, another predictor (i.e., noise-tolerance rating) was added to the model to assess if additional variance in NR 2-driven changes could be explained (see Table 1).  
Figure 5: Neural signal-to-noise ratio (SNR), the cortical measures of individual noise tolerance, correlates with changes in behavioral accuracy (**Left panel**: Noise reduction (NR) 1 vs. NR off, **right panel**: NR 2 vs. NR off).  
Figure 6: Subjective rating of individual noise tolerance correlates with changes in behavioral accuracy with NR 2 (**right panel**), whereas it does not correlate with accuracy changes with NR 1 (**left panel**).  
In the initial model, the neural SNR explained a significant portion of the variance in accuracy changes by NR 2 (\(R^{2}\) = 0.273, \(F\) = 10.51, \(p\) = 0.003). When the noise-tolerance rating was added to the model, the \(R^{2}\)-value increased to 0.331, indicating that the model slightly better explained the overall variance with the secondary predictor. However, the \(F\)-value decreased to 6.69, indicating that the model became less significant. Further, the final model coefficients showed that only the neural SNR remained significant (\(p\) = 0.01), while the tolerance rating was no longer significant (\(p\) = 0.136), when both predictors were considered together, although multicollinearity was not an issue in the model given a variance inflation factor (VIF) of 1.08. These results suggest that, although the subjective ratings may explain some portion of the variance, the cortical measures of noise tolerance (i.e., neural SNR) work as the more robust driver in explaining the variance in NR benefits in speech perception.