# Auditory Perception of Impulsiveness and Tonality in Vocal Fry
## 3 Results
### Perceived Binary Fry Predicted from Glottal Parameters  
The probability of perceived binary fry is modeled by logistic regression for each experiment separately. Table 1 lists z-normalized coefficient estimates and corresponding p-values of the all-listeners binomial logistic regression model. For Experiment 1, both frequency Fo and open quotient Qo are significant. The probability of perceiving binary fry increases with a decreasing Fo and a decreasing Qo. However, the coefficient values for Fo and Qo suggest that the influence of Qo is small compared with that of Fo. In addition, the area under the ROC curve (AUC, not shown) obtained with Fo as a single predictor is 0.907, and it increases only slightly to 0.91 if Qo is included as a second predictor. Table 2 lists z-normalized coefficient estimates and corresponding p-values for listener-specific binomial logistic regression models predicting the probability of perceived fry from glottal parameters. While the frequency Fo significantly affects the probability of perceived fry for the majority of listeners with equal effect directions, the open quotient Qo is significant only for 3 of 12 listeners participating in Experiment 1, when the Bonferroni-Holm correction is used [36]. Moreover, effect directions of the three listeners do not agree. In particular for Listener 8, the perception of fry increases with increasing Qo. As in Experiment 1, perceived binary fry also increases with decreasing Fo and decreasing Qo in Experiment 2 (cf. Table 1). A listener-specific binomial logistic regression analysis reveals that all eight listeners appear to be sensitive to Fo, and only two listeners are sensitive to Qo (cf. Table 2). An AUC of 0.877 is found using Fo as the predictor with a cutoff threshold estimate at 70.6 Hz. Similar to Experiment 1, the AUC (0.896) increases only slightly if Qo is included as an additional predictor. Regarding the effects of the short-term context, the influence of \(\Delta\)Fo and \(\Delta\)Qo was not found to be significant. However, \(\Delta\)Fo misses significance only marginally (\(p\) = 0.062). Its effect direction matches our hypothesis; that is, larger frequency differences favor the perception of fry. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Coefficient Estimates**} & \multicolumn{2}{c}{\(p\)**-Values**} \\ \cline{2-5}  & **Exp. 1** & **Exp. 2** & **Exp. 1** & **Exp. 2** \\ \hline Const. & 1.88 & 0.70 & \(\leqslant\)0.001 & \(\leqslant\)0.001 \\ Fo & \(\
eg\)3.51 & \(\
eg\)2.16 & \(\leqslant\)0.001 & \(\leqslant\)0.001 \\ \(\Delta\)Fo & n.a. & 0.41 & n.a. & 0.062 \\ Qo & \(\
eg\)0.20 & \(\
eg\)0.67 & 0.013 & \(\leqslant\)0.001 \\ \(\Delta\)Qo & n.a. & \(\
eg\)0.08 & n.a. & 0.484 \\ Qs & 0.05 & n.a. & 0.531 & n.a. \\ \hline \hline \end{tabular}  
* Coefficient estimates that significantly differ from 0 and \(p\)-values smaller than 0.05 (Bonferroni–Holm corrected) are highlighted in gray.  
\end{table} 
Table 1: All-listener z-normalized coefficient estimates of binomial logistic regression models designed to predict binary fry labels from glottal parameters \({}^{\text{a}}\). Figure 6 shows for Experiments 1 and 2 proportion \(\pi\)(fry) and probability P(fry) for a stimulus being labeled as fry as a function of Fo. P(fry) is predicted by binomial logistic regression. Thresholds of P(fry) equal to 5%, 50%, and 95% are shown as vertical lines. The predicted 50% threshold of Experiment 2 at 72 Hz is higher than the corresponding threshold of Experiment 1 at 66 Hz. One possible explanation for this difference is that the anchoring varied between Experiments 1 and 2. In particular, a larger maximum Fo was used in Experiment 2 than in Experiment 1 (120 Hz vs. 80 Hz), for the purpose of more efficiently sampling the fry/non-fry transition. However, differences of 50% probability thresholds obtained by the seven listeners that participated in both experiments are marginally non-significant (\(t\)-test, \(p\) = 0.06, see also Figure 7).