# Voice Maps as a Tool for Understanding and Dealing with Variability in the Voice
## 3 Voice Maps in Practice
### Local Gradients  
Provided that the \(\Gamma\) region extends across at least a few cells along both axes in the map, we can perform linear regression to obtain the _gradients_ along the axes of \(f_{\mathrm{o}}\) and SPL across this region, for any metric. Performing linear regression across an entire voice map is rarely meaningful, because the gradient function of a metric is typically not linear over large ranges. For a small region such as \(\Gamma\), however, a linear trend can be expected to be a fair characterization of a voice change within the speech range. Taking again an example from the data set collected for [PERSON] and [PERSON] [18], Figure 10 shows the group averages of such local gradients for three EGG metrics, for three groups of 13 adult males, 13 adult females and 20 children aged 5-7 of both sexes. (Two of the twenty-two children were excluded, because their \(\Gamma\) regions had very small extents on the \(f_{\mathrm{o}}\) axis.) In Figure 10 it can be seen that the three exemplary metrics all exhibit different trends across \(\Gamma\), when their slopes are averaged by group. Furthermore, the _individual_ slopes were extremely variable, but there is not room here to report them. Note in Figure 10c the especially dramatic SPL dependency of the inverse perturbation metric CSE, whose steep descent indicates that phonation rapidly stabilizes as vocal output power  
Figure 10: Gradients and other group-level statistics of three EGG metrics \(Q_{\mathrm{G}i}\), \(Q_{\mathrm{A}}\) and CSE, from VRPs on sustained /a:/, but evaluated only for the small \(\Gamma\) region that was derived from connected speech. Three groups of vocally healthy participants are represented: \(\blacksquare\) men, \(\bullet\) women, \(\lozenge\) children. The marker locations represent the group means. Each sloping line represents the gradient across \(\Gamma\), averaged within the group. (**a–c**) gradients versus SPL (C-weighted, re. 20 \(\mathrm{\SIUnitSymbolMicro m}\) @ 30 cm); (**d–f**) gradients versus \(f_{\mathrm{o}}\) (semitones re. 110 Hz). (Previously unpublished data, collected for [18].) by many [12; 16; 17], perturbation metrics (jitter, shimmer, CPP, etc.) are sensitive to SPL, and especially so in the rather narrow transition band between breathy and modal voice, in which VF contact is established. For the cohort of normophonic, untrained participants examined here, the habitual speech region of the voice range tended to sit right across that band. When such is the case, even small pre-post differences in _elicited_ SPL or \(f_{\text{o}}\) could easily mask the sought effects of an intervention. We conclude that the existence of steep and personal gradients in some metrics again speaks strongly in favour of making voice maps, and of comparing them only within individuals. For the same study [18], [PERSON] and [PERSON] had participants make full voice range profiles on /a:/, and then extracted the small subsets of those VRPs that were enclosed by the \(\Gamma\) regions that had been obtained from the speech task. This allowed a comparison of the variances explained by the trends, in connected speech and in productions on one vowel only. It can be seen in Figure 11 that in the vowel-only condition, much more of the total variance over \(\Gamma\) was explained by the local trends. Given that connected speech gives rise to several additional sources of variation, this is of course exactly what might be expected. The figure also shows that, in the task of traversing a range on the /a/ vowel, fully 30-50% of the total variance could be attributed to local dependencies on SPL and \(f_{\text{o}}\), even in the small \(\Gamma\) region. Again, these are group averages; individuals exhibit different personal trends. Ultimately, one's research question must dictate whether or not vocalization on /a:/ is preferable to a connected speech task. At this point, we are not recommending clinicians actually measure gradients of voice metrics.