Phonetic Detail in the Perception of Ethnic Varieties of US English 299multivariate signi¿ cance is compared to the individual signi¿ cance values
(using signi¿ cance levels and r^2 correlation coef¿ cients). This comparison is
the test of whether the multivariate analysis is stronger than parallel univari-
ate analyses: the closer the univariate and multivariate squared correlation
coef¿ cients are to each other, the less likely the multivariate approach pro-
vides insight into the distinction between groups. Canonical coef¿ cients of
the linear combination of the measures are then computed. Assuming that the
multivariate approach provides a stronger account of the variation in the data
(by a higher squared coef¿ cient value), the Mahalanobis distance between the
means of the voicing categories is calculated. This distance accounts for the
statistical distribution of the data based on the correlation between the acous-
tic measures used by the model.
Even though the canonical discriminant analysis only ¿ nds one factor
among the acoustic measures because there are only two voicing categories,
we can explore the reduction of dimensions using principal component analysis
from the basis of the four most signi¿ cant measures themselves. This difference
in analysis is one of perspective: if the analysis proceeds from the number of
categories, then only one factor is possibly considered (canonical discriminant
analysis); if the analysis proceeds from the number of measures in the model,
then the goal of the analysis is to account for the most variation within the cat-
egories (principal component analysis). This third analytical procedure, then,
informs our interpretation of which factors might be active within the voiced
or voiceless categories. The result of this step allows us to understand the dif-
ferences between voiced and voiceless tokens at different stages over time and
with varying temporal distance to immigrant language inÀ uences.
It will be assumed that the within-category weights contribute to the
across-category weight. In other words, we could expect that two measures
contribute to one factor among voiceless tokens, while two different measures
contribute to a factor distinguishing voiced tokens. However, two assump-
tions simplify the cross-category interpretation: the same four measures are
used for both voiced and voiceless models within each group; and, binary
grouping of the four measures are assumed to fall consistently into the same
two (and only two) principal components for both the voiced and voiceless
tokens. The criteria for the binary grouping proceed by an examination of
the strongest correlation for all of the voiced and voiceless components for
any one measure (four values compared per measure; see Table 13.6). Plots of
the two measures along the two component dimensions, multiplied by their
individual eigenvector (i.e., weight), provide graphic insight into how well the
voiced and voiceless tokens may be distinguished from each other (Figures
13.3 through 13.8).