60 Jen Hay and Margaret Maclagan
relatively high and low Euclidean distances, respectively, to give a sense of
the variation here. The places where the targets were taken are marked. For
each speaker, we then calculated their average Euclidean distances, to get an
overall index of the degree to which their /au/ tends to be monophthongal.
We t hen ¿ t a logistic regression model, over just the plough paradigm,
attempting to predict the likelihood that /r/ would be produced. We found
signi¿ cant effects of gender and social class, as well as a signi¿ cant effect of
the degree of monophthongization of the /au/ vowel.
The model statistics are given in Tables 2.8 and 2.9. Figures 2.13–2.15
plot the effects from the model. Males were signi¿ cantly more likely to use
intrusive /r/ after /au/ (Figure 2.13), and there is a signi¿ cant effect of social
class, such that individuals from higher social classes do not use /r/ after
/au/ at all, but then rates of intrusive /r/ increase with decreasing social class
(Figure 2.14). These two effects are as one would expect from the previous
analysis—they work the same way as those described in section 3.1, in the
analysis of the entire data-set. Figure 2.15 shows the effect of monophthon-
gization of /au/. Speakers with highly diphthongal /au/ are very unlikely to
produce /r/ after /au/. Speakers with an /au/ which contains less movement are
much more likely to produce intrusive /r/ after /au/.
Note that there are no speakers for whom /au/ is entirely monophthongal.
That is, it is not merging with a second vowel (such as /a:/), and thus becom-
ing eligible for intrusive /r/. Rather this phonetic change in the quality of the
vowel is making it eligible for participation in a phonological rule.
Table 2.8 Wald Statistics for Model Predicting the Likelihood of /r/-insertion
After /au/
Factor Chi-Square d.f. P
Gender 5.08 1 0.0242
Social class 14.45 1 0.0001
Monophthongization of /au/ 10.2 1 0.0014
TOTAL 15.72 3 0.0013Table 2.9 Coef¿ cients for Model Predicting the Likelihood of /r/-insertion After /au/
Coef
Intercept -6.83224
gender=Male 1.89032
Social class 1.01736
Monophthongization of /au/ -0.01296