# Comparison of Multivariate Analysis Methods as Applied to English Speech
## 3 Results
### Factor Scores of the Three Spectral Factors
Given the prominence of the L-shape for obstruents, more detailed analyses were performed. Figure 6 shows that the distributions of voiced obstruents (Figure 6a) and voiceless obstruents (Figure 6b) indeed showed distinctive L-shapes as well. Here eight obstruents were categorized as voiced obstruents, with the number of analyzed data points in parentheses: /b/ (609), /d/ (838), /g/ (274), /v/ (467), /l/ (968), /d5/ (53), /z/ (54) and /z/ (827). Nine obstruents were categorized as voiceless obstruents: /p/ (563), /t/ (1682), /k/ (786), /j/ (226), /h/ (340), /t/j/ (195), /s/ (1389), /f/ (552), and /l/ (205). For the voiced obstruents (Figure 6a), three obstruents occupied a relatively high position on the \"low & mid-high factor\", almost parallel to the y-axis, and close to the origin on the high factor: /b/, /v/, and /l/, for which the factor scores of /v/ and /l/ were around half of /b/. By contrast, four other voiced obstruents occupied a relatively high position on the \"high factor\", almost parallel to the x-axis, and close to the origin on the \"low & mid-high factor\": /g/, /d5/and /z/, for which the factor scores of /g/ and /z/ were around half of /z/ and /d5/. Only the factor scores of /d/ were both distributed on the \"low & mid-high factor\" and the \"high factor\", yet again in an L-shape. Figure 5: The distribution of factor scores by normal factor analysis without cepstral liftering. (**a–c**) represent all possible combinations of two factors out of the three factors, and (**d**) shows a two-dimensional mapping of the three factors. The distributions of voiceless obstruents (Figure 6b),/p/,/k/,/h/, and /f/, displayed the L-shape, but they were mainly higher on the \"low & mid-high factor\". The distributions of /t/ and /@/ were also L-shaped, but they were mainly higher on the \"high factor\". The distributions of three obstruents occupied a relatively high position only on the \"high factor\", almost parallel to the x-axis, and close to the origin on the \"low & mid-high factor\": /f/,/tf/, and /s/, for which the factor scores of /s/ were about half of those of /f/ and /tf/. In sum, the voiced obstruents /b/,/v/, and /@/ were mainly related to the \"low & mid-high factor\". The voiced obstruents /z/,/z/ and /d3/ and the voiceless obstruents /f/,/tf/,/s/ were mainly related to the \"high factor\". Figure 7 shows the distributions of all the obstruents divided into fricatives/affricates and plosives on the two-dimensional configuration, again clearly showing a distinctive L-shape. Here eleven obstruents were categorized as fricatives/affricates, with the number of analyzed data points in parentheses: /@/ (205), /@/ (968), /f/ (552), /v/ (467), /s/ (1389), /z/ (827), /f/ (226), /g/ (54), /h/ (340), /tf/ (195) and /d3/ (53). Six obstruents were categorized as plosives: /p/ (563), /t/ (1682), /k/ (786), /b/ (609), /d/ (838) and /g/ (274). For the fricatives/affricates (Figure 7a), the distributions of six obstruents occupied a relatively high position on the \"high factor\", almost parallel to the x-axis, and close to the origin on the \"low & mid-high factor\": /s/, /z/, /f/, /3/, /tf/ and /d3/. The distributions of five obstruents were both located on the \"low & mid-high factor\" and the \"high factor\" in an L-shape: /@/, /@/, /f/, /v/, /h/, but they were mainly higher on the \"low & mid-high factor\". As for the distributions of plosives (Figure 7b), all of them displayed the L-shape, but /p/, /b/ and /k/ were mainly higher on the \"low & mid-high factor\", and /t/, /d/ and /g/ were mainly higher on the \"high factor\". Figure 6: The L-shaped distributions of voiced obstruents (**a**) and voiceless obstruents (**b**) in the two-dimensional space of the “low & mid-high factor” and the “high factor”. Factor scores of the three extracted spectral factors were obtained by origin-shifted factor analysis with cepstral liftering (cf. Figure 2) and the English speech samples were from three native speakers.