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The distributions of LLRs are firstly considered for each combination of formants separately. The comparative performance of the Matched and Mixed systems with

regard to validity (EER andC_llr) for the different input data is then considered.

F1, F2 and F3

Figure 5.4 displays the Tippett plot of LLRs from the Matched and Mixed systems using F1∼F3 input. There was considerable similarity in the distributions of SS LLRs across systems. The median SS LLR was +1.68 in the Matched condition and +1.49 in the Mixed condition, in both cases equivalent tomoderatesupport for the prosecution.

The two systems were also comparable in terms of the overall ranges of SS LLRs, with values extending maximally to greater than +3. However, the Matched condition (15%)

recorded a higher proportion of misses than the Mixed condition (5%). Further, the magnitude of the errors using the Matched system was marginally higher with values

approaching -1, although for both systems contrary-to-fact SS LLRs did not extend

beyondlimitedsupport for the defence.

Marked differences across the systems were found in terms of the DS LLRs. The median DS LLR for the Matched system was -5.38 (very strongsupport), which was

four orders of magnitude greater than the median for the Mixed system (-1.44;moderate support). There were also substantial differences in the maximum strength of support

for the defence with values for the Matched system extending beyond -44 compared with -16 for the Mixed system. The Mixed DS LLRs also performed considerably worse

in terms of categorical validity, with 20.7% of comparisons achieving contrary-to-fact support. For the Matched system, the false hit rate was 6.3%. Finally, the magnitude

of the errors using the Mixed system was marginally higher with values extending to +2.88.

Figure 5.4: Tippett plot of SS and DS LLRs based on F1∼F3 trajectories from /aI/ using Matched (red) and Mixed (green) system data

F2 and F3

The omission of F1 reduced some of the differences between the two systems (Figure 5.5). As with F1∼F3, the distributions of SS LLRs from the Matched and Mixed systems based on F2 and F3 overlapped considerably. The median SS LLR in the Matched condition was +1.38, compared with +1.36 in the Mixed condition. Similarly

the highest magnitude LLRs across both systems offeredmoderately strongsupport for the prosecution. Comparison with Figure 5.4 also shows that the miss rates were

more similar with the omission of F1, with 12.5% of pairs in the Matched condition and 10% of pairs in the Mixed condition offering contrary-to-fact support. For both

systems the magnitudes of the contrary-to-fact LLRs were greater without F1, although across systems their magnitudes were broadly similar.

Similar patterns in the distributions of DS LLRs are displayed in Figure 5.5 as those in

Figure 5.4. DS LLRs were generally weaker when using the Mixed system, such that the median DS LLR was -1.28 (moderatesupport) compared with -4.24 (very strong

support) using the Matched system. Further, the strongest LLRs were found using the Matched system with values extending to -40 compared with -17 for the Mixed system.

The proportion of false hits was again highest using the Mixed system (24.5%). Further, the magnitude of contrary-to-fact DS LLRs was greatest using the Mixed data with

values extending to almost +4, compared with +2.33 for the Matched system.

Figure 5.5: Tippett plot of SS and DS LLRs based on F2 and F3 trajectories from /aI/ using Matched (red) and Mixed (green) system data

F3-only

Figure 5.6 displays the Tippett plot based on F3-only input. The removal of F2 reduced

the strength of the LLRs, offering further evidence to suggest that F1 and F2 are carriers of speaker-specific information for this vowel in these varieties. The removal of F2 also

further minimised the effects of using Mixed system data compared with the Matched system. The median SS LLRs based on F3-only were very similar across systems,

although in verbal terms they were equivalent to one order of magnitude weaker than with the inclusion of F1 and F2 (difference betweenlimitedandmoderatesupport). The

overall ranges of SS LLRs were also broadly comparable, although the maximum LLR for the Mixed system (+3.01) was greater than that for the Matched system (+2.05).

Contrary-to-fact SS LLRs were of a similar magnitude with no SS pairs achieving LLRs of less than -1. Unlike with the inclusion of F1 and F2, the miss rate was lower

for the Matched system (10%) than for the Mixed (15%) system.

Figure 5.6: Tippett plot of SS and DS LLRs based on F3-only trajectories from /aI/ using Matched (red) and Mixed (green) system data

The differences between the Matched and Mixed systems were also less marked in terms of DS LLRs when using F3-only. DS LLRs for the Mixed system were generally

weaker by only one order of magnitude compared with the Matched system (difference betweenmoderately strongandmoderatesupport). In terms of the maximal support for

the defence, however, the large differences between the systems found using F1 and F2 were, to some extent, preserved using F3-only. The proportion of false hits was again

lower using the Matched system (17.2%) compared with the Mixed system (19.2%), although performance was more similar than with the inclusion of F1 and/or F2.

Overall performance

Overall system performance was assessed using EER (Figure 5.7) and C_llr (Figure

5.8). Across all three sets of input data, EER was worse for Mixed system than for the Matched system. Differences between the systems based on F1∼F3 were relatively small (ca. 1%), reflecting the fact that the Matched system produced more misses and the Mixed system produced more false hits. The biggest EER difference between

systems, however, was found when using F3-only input. This is partly due to the improvement in EER for the Matched system with the omission of F2 information.

Figure 5.7: EER (%) based on F1∼F3, F2 and F3, and F3-only input from /aI/ using Matched (red) and Mixed (green) system data

The results based onC_llrwere more systematic. Across both the Matched and Mixed

systems,Cllrincreased as the amount of acoustic input data was reduced. As with EER,

C_llr was also consistently higher using the Mixed system than the Matched system.

Interestingly, the smallest Cllr difference between the systems was found using all

three formants as input. The difference between the systems increased as F1 was

predictions about the potential lack of regional stratification in F3, since the effect of regional differences onC_llrwas greatest when using F3-only input.

Figure 5.8: Log LR Cost (Cllr) based on F1∼F3, F2 and F3, and F3-only input from /aI/

using Matched (red) and Mixed (green) system data