A cognitive approach to quantitative sociolinguistic variation 305The corrected mean (also known as the input value) is a measure of the rate
of ‘rule application’ or “an average frequency of occurrence of the applica-
tion value of the dependent variable” (Paolillo 2002: 76). A corrected mean
of 0.48 means that, all other things being equal, the likelihood of (th) being
realised as [f] in this corpus is around 48%. The log likelihood value meas-
ures the likelihood that a particular set of data has been generated by the
model. This is the value used when considering which combination of
factors provides the best ‘fit’ of the model to the data. The total N is sim-
ply the total number of tokens included in the final run of the analysis. Fi-
nally, the factor weight is a value that is assigned to each factor during the
analysis. It is essentially a measure of relative influence on variation. The
number ranges from 0 to 1 and it is often stated in the literature that a factor
weight of greater than 0.5 favours the application value (in this case, the
labiodental variant) and a weight of less than 0.5 disfavours the application
value).
The results of the varbrul analysis show that lexical frequency is the last
significant factor group to remain in the analysis. In other words, of all the
factors influencing variation in these data, lexical frequency has the weak-
est effect, while still remaining significant. We know that this is the case
because, of the factor groups to achieve significance, this factor group
shows the smallest range between the highest and lowest factor weights.
The next most important constraint on the variation is syllable struc-
ture/place of (th) in the word. The results for this factor group suggest that
when (th) occurs in syllable/word^12 initial position, it favors the dental fric-
ative and when it occurs syllable/word finally, the labiodental is more like-
ly to occur. The next most important constraint on the variation in (th) is
lexical category. These results support the proposition made by Stuart-
Smith and Timmins (2006) that ordinals and place names may be more
resistant to the spread of TH-Fronting than other lexical items as ordinals,
place names and proper names favor retention of the dental fricative. The
next most significant constraint on variation in (th) is the factor group
which codes for a priming effect. If the lexical item in question contains an
[f] somewhere before the variable (such as in fourth) then the variable
strongly favors the labiodental variant. Finally, the factor group ‘friendship
group membership’ substantially outranks all other constraints on the varia-
tion. There is a very strong correlation between the use of the labiodental
fricative and membership in a particular social group in this community.
The main advantage to employing a varbrul analysis is that it provides
the capability to model both social and linguistic factors simultaneously