## 4 Results  
Table 2 shows summary statistics (mean \(\pm\) standard deviation) of average values, per subject, of ACFL, MFDR, H1-H2, NAQ, and \(f_{0}\) from the Rainbow passage speech data, across PVH and healthy subjects, calculated with SNF, IBIF, and KF implementation of IBIF with colored noise model. Mean values are not statistically different for the three methods. Figure 10 shows box plots for some of the measures. Overall, the distribution of measures is similar when using the standard IBIF and the modified Kalman filter algorithm. From Table 3, the mean values of ACFL and MFDR from healthy subjects are not significantly different between the standard IBIF, the modified Kalman filter, and the ground-truth GVV (one-way ANOVA: \(F=1.8\), \(p=0.2\) for ACFL, \(F=2.7\), \(p=0.07\) for MFDR). Therefore, both IBIF and the modified Kalman filter have similar ACFL values comparable to the ground-truth GVV. Instead, ACFL from PVH subjects are significantly different between the standard IBIF and the ground-truth GVV (\(F=4.1\), \(p=0.02\)), while the modified Kalman does not have significant differences with the same ground-truth. Similar to ACFL from healthy subjects, MFDR from the same group do not show significantly differences between the two methods and the ground-truth GVV. However, there was a small but significantly difference between the modified Kalman filter and the ground-truth GVV for PVH subjects (\(F=3.3\), \(p=0.04\)), indicating that MFDR from the modified KF does not estimate MFDR as well as the standard IBIF, when compared to the ground-truth of that group. For all other measures, there were not significantly differences, in which either case, the modified KF or standard IBIF could provide similar mean results comparable to the ground-truth measure. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Glottal Airflow Measures** & **Description** & **Units** \\ \hline ACFL & Peak-to-peak glottal airflow & mL/s \\ MFDR & Negative peak of the first derivative of the glottal waveform & L/s\({}^{2}\) \\ H1-H2 & Difference between the magnitude of the first two harmonics & dB \\ Normalized Amplitude Quotient (NAQ) & Ratio of ACFL to MFDR divided by the glottal period & – \\ Fundamental frequency (\(f_{0}\)) & Inverse of the glottal period & Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Frame-based derived glottal airflow measures. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **ACFL** & **MFDR** & **H1-H2** & **NAQ** & \(f_{0}\) \\ \hline \multirow{3}{*}{PVH} & SNF & \(238.8\pm 74.9\) & \(279.5\pm 102.0\) & \(11.1\pm 1.30\) & \(0.19\pm 0.02\) & \(202.4\pm 20.1\) \\  & IBIF & \(306.8\pm 147.7\) & \(346.8\pm 178.6\) & \(10.3\pm 4.89\) & \(0.20\pm 0.05\) & \(202.6\pm 20.3\) \\  & Kalman & \(287.6\pm 131.3\) & \(357.3\pm 199.1\) & \(9.69\pm 5.51\) & \(0.19\pm 0.05\) & \(200.8\pm 20.1\) \\ \hline \multirow{3}{*}{Healthy} & SNF & \(184.5\pm 47.0\) & \(199.7\pm 77.8\) & \(10.7\pm 1.49\) & \(0.19\pm 0.02\) & \(204.6\pm 20.9\) \\  & IBIF & \(212.2\pm 82.9\) & \(260.0\pm 122.1\) & \(8.73\pm 3.63\) & \(0.19\pm 0.04\) & \(204.6\pm 21.0\) \\ \cline{1-1}  & Kalman & \(199.7\pm 77.8\) & \(266.1\pm 138.3\) & \(7.73\pm 3.85\) & \(0.18\pm 0.04\) & \(203.5\pm 21.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and \(\pm\) standard deviation from a pool of average values of ACFL, MFDR, H1-H2, NAQ, and \(f_{0}\) extracted from the Rainbow Passage (voiced frames only). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **ANOVA** & **ACFL** & **MFDR** & **H1-H2** & **NAQ** \\ \hline \multirow{3}{*}{Healthy} & F & 1.79 & 2.69 & 10.9 & 2.36 \\  & \(p\)-value & 0.17 & 0.07 & * \(>\)0.001 & 0.1 \\ \hline \multirow{3}{*}{PVH} & F & 4.12 & 3.27 & 1.39 & 0.74 \\  & \(p\)-value & * 0.02 & * 0.04 & 0.25 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: One-way ANOVA table with mean values of glottal flow features for both Healthy and PVH subjects when comparing the standard IBIF, the modified Kalman filter, and the ground-truth GVV (* Statistically differences: \(p<0.05\)).