Discriminant Analysis

Discriminant analyses (DA) were conducted on both dialect sets, with the two dialects being treated separately at first; they were subsequently combined to create a third dialect-independent set containing all 12 speakers for additional DA testing. The aim of DA was to determine how well individual speakers could be identified by a set of predictors. The predictors in this case were the durations of /m, n, ŋ/, and /l/.

Outliers first needed to be identified and eliminated from the data set, as DA is highly sensitive to outliers and non-normal distributions (Tabachnick & Fidell, 2007:382; further discussion of DA methodology is given in Chapter 2, §2.3.1). Identification of univariate outliers was carried out in SPSS v.17.0 by standardising the values of the predictors for each speaker independently, and eliminating any for which z>±3.29 (Tabachnick & Fidell, 2007:73). This resulted in only two tokens of /l/, one per dialect, and no nasal tokens being discarded from the data; these outliers accounted for 0.2% of the total data set.

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Single-predictor discriminant analyses were performed in SPSS using the leave-one-out method of cross-validation described in Chapter 2. The results are summarised in Table 3.7 below (SSBE and Leeds sets chance=17%; Combined chance=8%). Classification rates indicate the percentage of the total number of tokens per predictor for which group membership was correctly predicted. Tests of the six SSBE speakers generally yielded the highest classification rates, with tests of the Combined set consistently producing the lowest rates. The highest overall rate was achieved in the test of /ŋ/ within the SSBE set, with 25% of cases being correctly classified. The lowest overall rate of 8% occurred in the Combined tests of /m/ and /n/.

Classification was highest in tests of /ŋ/ across all three datasets, although it should be noted that this segment had the lowest token numbers with between five and ten per speaker. The remaining three segments performed little or no better than chance; the Leeds /l/ test in fact produced a classification rate below the level of chance (13%).

Table 3.7. Cross-validated classification rates for single-predictor DA. Predictor Correct Classification (%)

SSBE (6) Leeds (6) Combined (12)

/m/ 17 19 8

/n/ 19 19 8

/ŋ/ 25 22 15

/l/ 19 13 10

Overall, classification rates were relatively low as this analysis was based on data from a single predictor. It is hypothesised that correct classification rates will improve with the addition of more predictors, such as formant data, as

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McDougall (2004), Eriksson and Sullivan (2008), and Atkinson (2009), for example, have shown.

Table 3.8. Individual classification rates with predicted group membership for all SSBE data (in percent). Correct classifications are highlighted.

Segment Speaker Predicted Group Membership

JE JI MA MC PT TG /m/ JE 15 23 8 0 46 8 JI 0 14 0 36 29 21 MA 0 38 0 0 62 0 MC 0 57 14 0 21 7 PT 0 15 8 0 69 8 TG 0 36 7 7 43 7 /n/ JE 0 12 24 0 6 59 JI 18 12 41 0 0 29 MA 8 46 15 0 0 31 MC 6 0 24 24 0 47 PT 13 7 13 13 0 53 TG 6 0 18 18 0 59 /ŋ/ JE 33 17 0 33 0 17 JI 11 11 33 22 11 11 MA 25 13 25 0 13 25 MC 50 13 38 0 0 0 PT 38 13 0 0 0 50 TG 0 0 11 0 11 78 /l/ JE 0 14 6 22 8 50 JI 0 36 3 18 6 36 MA 0 17 0 28 8 47 MC 0 38 0 11 14 38 PT 0 23 0 9 3 66 TG 0 14 0 11 11 64

Closer inspection of individual cross-validated classification statistics revealed some interesting patterns. Tables 3.8 and 3.9 provide individual classification rates for SSBE and Leeds respectively, showing the percentage of each speaker‟s tokens that were assigned to each group. Correct classification rates

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are highlighted for each segment; all other percentages represent errors. Amongst the SSBE speakers, PT‟s /m/ tokens were classified correctly in 69% of cases, while up to 15% of other individuals‟ tokens were classified correctly. Speaker PT, along with JI, was also frequently selected incorrectly in classification of other speakers‟ tokens of /m/: 21-62% of others‟ tokens were wrongly classified as being produced by PT, and 15-57% as JI. Only one speaker (JE) was never selected incorrectly, but two (MA and MC) were never selected correctly.

A similar pattern is evident in the SSBE /n/ statistics: again two speakers were never correctly selected (JE and PT), and one achieved a high correct classification rate but was also frequently selected incorrectly. In this case, it was speaker TG who was selected correctly in 59% of cases but was also wrongly selected in classification of 29-59% of others‟ tokens of /n/. The remaining incorrect classifications were spread more evenly across all other speakers, except PT who was wrongly selected in only one case.

Speaker TG again achieved the highest individual classification rates for /ŋ/ at 78%, and for /l/ at 64%. Unfortunately, he was also selected wrongly in a large number of cases: 11-50% of /ŋ/ and 36-66% /l/ cases. Speaker JE was never selected, correctly or incorrectly, in the classification of /l/ durations. Speakers JI and TG were the only ones to have at least some tokens correctly classified for each segment.

Amongst the Leeds speakers in Table 3.9, RP stood out as the most easily classified speaker across three of the segments: 64% of /m/, 59% of /n/, and 61% of /l/ tokens were correctly classified as being produced by this speaker. In the /ŋ/ test, speaker MD achieved the highest individual classification rate. As in the SSBE set, several speakers had no correct classifications in at least one test. RP

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was the only speaker to be selected correctly for at least some cases for every segment; however, he was also frequently selected incorrectly. A high proportion of other speakers‟ cases, up to 63%, were incorrectly allocated to RP‟s group.

Table 3.9. Individual classification rates with predicted group membership for all Leeds data (in percent). Correct classifications are highlighted.

Segment Speaker Predicted Group Membership

JP JW MD RP ST SU /m/ JP 0 0 0 40 0 60 JW 15 23 0 31 0 31 MD 8 31 0 23 8 31 RP 7 0 7 64 0 21 ST 0 0 0 36 0 64 SU 8 8 25 42 0 17 /n/ JP 0 12 29 53 6 0 JW 0 0 47 35 12 6 MD 6 13 38 38 0 6 RP 6 0 24 59 6 6 ST 0 0 33 47 13 7 SU 0 0 58 42 0 0 /ŋ/ JP 33 0 44 11 11 0 JW 0 0 43 57 0 0 MD 14 0 57 29 0 0 RP 0 13 0 25 38 25 ST 20 0 40 40 0 0 SU 20 0 10 60 0 10 /l/ JP 0 5 16 47 26 5 JW 0 9 17 29 46 0 MD 3 3 0 63 28 3 RP 0 5 16 61 18 0 ST 0 10 7 28 7 48 SU 3 14 11 30 43 0

It is worthy of note that the three speakers who were correctly classified at least some of the time for every segment were also the three found to have significant results in the post-hoc comparisons for Speaker effects discussed in the

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previous section. Differences were found between JI and four of the five other SSBE speakers for /l/, and between TG and two others for /ŋ/. For Leeds /l/, comparison of RP and SU was significant, while comparison of RP and ST was approaching significance. These three speakers JI, TG, and RP were also frequently at the extremes in terms of the range of durations used, as is evident in Figures 3.9-3.12 in §3.4.3. It is clear that some speakers, in particular those who make use of either very wide or very narrow ranges of duration, are better discriminated than others.