# Smart-Median: A New Real-Time Algorithm for Smoothing Singing Pitch Contours
## 5 Results  
This section provides the results of the comparisons between the Smart-Median algorithm and the other 35 contour smoothers mentioned in Section 3.3. Three groups of data were obtained for evaluation. These groups were 1--the ground truth pitch contour (GT), 2--the original estimated pitches (ES), and 3--the smoothed contour. The metrics explained in Section 3.5 were employed to compare these data groups. The data series were compared two by two, i.e., GT with ES, GT with SM, and ES with SM.  
Tables A4-A8 show the accuracy of each of the pitch detector algorithms, and the accuracy of contour-smoother algorithms applied to the estimated pitch contours to bring them closer to the ground truth pitch contour. The GT-ES columns show the initial difference between ground truth and the original estimated pitch contour. Next, the differences between ground truth and the smoothed contours are shown in the GT-MS columns. Finally, the results of comparing the initially estimated pitch contour and the smoothed pitch contour are provided in the ES-SM columns. The metrics comparing GT and SM are more important than those comparing GT-ES and ES-SM, because the values of GT-SM illustrate the resulting improvement supplied by each algorithm. For example, in the Specacd column in Table A7, the first row (smoother algorithm with code 00) shows that according to the FFE metric GT-ES = 40, GT-SM = 48, and ES-SM = 61. That is, 40 per cent of the pitches estimated by the Specacd algorithm were correct. Then, the smoother algorithm improved this to 48 per cent acceptable data. Finally, 61 per cent of the values in the estimated pitch and smoothed contour remained in the same range; i.e., the smoother algorithm significantly changed 39 per cent of the values.  
According to Tables A4-A7, the Smart-Median was the best algorithm for all pitch contours estimated by Specacd, FComb, MComb, Yin, or YinFFT. However, the best accuracy for the pitch contours calculated by Praat was recorded by the contour smoother code 33 (standard median). However, there was no agreement between the metrics employed to select the best smoother of pitch contours generated by Schmitt or PYin.  
Table A8 aggregates all the data in Tables A4-A7. It can be observed in Table A8 that all the metrics agree that the Smart-Median worked better than the other smoother algorithms.  
Only the GT-SM column was considered to have found significant differences between the accuracy of the algorithms. All the algorithms in the range of the column average plus/minus standard deviation were considered to exhibit a similar accuracy. The algorithms with values outside this range were considered to be in the best or worst category, as shown in Table 2. There were certain agreements and disagreements between the metrics employed to find the best and worst algorithms. For example, the smoother code 07 was in the worst category based on the metrics MAE and RMSE, but in the best category based on the FFE metric. These agreements and disagreements are discussed in Section 6.  
An ANOVA test was used to check the accuracy of the smoother algorithms. For all the metrics, the \(p\)-value calculated for each smoother algorithm was 0. That means that the accuracy of all the smoother algorithms depended on errors that occurred in the pitch contours, i.e., the smoother algorithms did not work with the same accuracy when each pitch contour was affected by different sources of error.