298 Thomas C. Purnell
Because independence of acoustic characteristics of postvocalic obstruent
voicing is inconsistent, the statistical analysis examining overlapping mea-
sures proceeded in three stages. The heart of the analysis is the use of canoni-
cal coef¿ cients, which explain the relation between distinct acoustic variables
(predictors) in a many-to-many fashion. This multivariate approach differs
sharply from a univariate analysis of several measures.
I n t e r m s of wh ich a cou st ic me a su re s m a ke a sig n i¿ cant contribution to the
perception of obstruents, predictors were ¿ rst identi¿ ed using a discriminant
analysis of voicing by speaker group based on a forward stepwise procedure.
Typically, a forward stepwise analysis uses only those measures conserva-
tively below the 0.15 signi¿ cance level. Although Costanza and A¿ ¿ (1979)
recommend using signi¿ cance levels where 0.10 < p < 0.20, they note that the
point of raised signi¿ cance levels is to widen the scope of important variables
unless it was known that few variables stopped the procedure early. Such
signi¿ cance levels, as will be seen, yield an uneven number of potentially
signi¿ cant measures across groups. In order to facilitate a between-group
comparison and to allow for the inclusion of several low-frequency properties
previously claimed to be important to postvocalic voicing, a predetermined
number of steps were set to four. In other words, the model used only the ¿ rst
four measures in order to identify the most inclusive subset of variables from
which we assume the perceptual cues will come. Adding and taking away
insigni¿ cant variables in a stepwise fashion involved using variables with
univariate signi¿ cance over the Į limit of 0.05 in all groups (maximally 0.12,
0.77, 0.36, 0.35, and 0.06, respectively across groups 1 through 5 in Table
13.3). Again, the reason for considering variables above 0.05 is that the pool
of perceptual cues includes the strongest, albeit not entirely strongly signi¿ -
cant, acoustic variables. While inclusion of more measures over fewer works
against the criterion of parsimony, the multivariate analysis technique has the
ability to identify more border-line variables that would not be found using a
univariate analyses of several measures, allowing con¿ rmation of whether the
strongest acoustic characteristics are in fact the strongest perceptual cues.
The second step in the analysis is a canonical discriminant analysis reduc-
ing the top four variables for each group to one dimension. Rather than trying
to understand the voicing distinction on a fairly obtuse four-dimensional rela-
tion, we can reduce the dimensions to one less than the number of contrasts;
a canonical discriminant analysis can only yield an n-1 category analysis.
Assuming that voicing is phonetically distinctive at some level by a binary
feature (e.g., [spread glottis] for aspirating languages such as English, and
[slack vocal folds] for voicing languages such as Spanish; see Iverson and
Salmons 2003), then only one dimension is possible.^12 For each group, the