Statistics in the analysis of phonetic variation: application of the Goldvarb programme, by Josefina Carrera

On completion of the four phases of this initial stage, we move on to inference statistics or probabilistic analysis, where we can calculate: 1) the appearance of the dependent variable in relation to the factors of a range of explanatory or independent variables; in this case, the probability of appearance of the dependent variable (solution [a]) in an open or closed syllable, when the tonic vowel has a timbre or other quality, etc.; 2) the application of the theoretical model according to the data obtained; in this case, to observe the general probability of appearance of the vowel [a] in causes of independent variables, such as the quality of the pretonic syllable and the tonic vowel, age, studies, etc. As explained above, the final form of this part is directly related to the condition file.

The result of the iterations of all the factors, both individually and globally, is worked out by the input of the entry of the rule or application of the theoretical model, which gives the required signification by displaying whether or not the conditions chosen to explain the variation are relevant. If the input is greater than 0.5, the results generally facilitate the rule’s application; if it is less than 0.5, they do not. There are two additional operations for observation of general input and the probability of maintenance or change in the variable under study in relation to the different independent factors:

-Binomial Up & Down (U&D)
-Binomial 1 level (1L)

U&D is a process of analysis that looks for significant independent variables to find out the probability of the variable rule application. It displays regression calculations by analysing all groups of independent factors, individually at first, and then in combination, until it arrives at the most likely composition of the variable rule. The result is not the definitive probability, but rather the weight of each independent factor in terms of the other factors of the analysis. We can find out the direction in which the dependent variable will change by the weight of each linguistic or extralinguistic factor: if it is greater than 0.5, it will be influential and, if not, this factor will not have a great deal of influence on the changes of the dependent variable. The U&D calculation also presents the chosen signification of the analysis as good in terms of reasonings calculated previously – before arriving at the optimum analysis, the programme performs a number of calculations and tests such as the logarithm of likelihood and the X-square test, which measures whether the variables analysed are independent. The outcome of this test is observed by the result of p, which must be less than 0.005 to reject what statistics terms the "null hypothesis", i.e. the hypothesis that variation is not caused by the independent factors chosen to explain it.

Once the best combination of factors has been revealed, using these data, we can then move on to observe the definitive probability of each independent factor in the incidence of the variable rule (in this case, maintenance of the pretonic vowel) using the other type of analysis: Binomial 1 level (1L). 1L is a relatively quick way of revealing whether or not the set of initial parameters       -independent variables– is adequate to explain the initial rule. For example:

BINOMIAL VARBRUL, 1 step • 08/10/1•17:47 •••••••••••••••••••••••••••••••••••••
Name of cell file: 01.Cel

Using more accurate method.
Averaging by weighting factors.
One-level binomial analysis…

Run # 1, 117 cells:
Iterations: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Convergence at Iteration 15
Input 0.636

Cell	Total	App'ns	Expected	Error
tu67	8	4	3.759	0.029
tu65	17	9	10.095	0.292
tu57	21	11	12.594	0.504 (... up to 117)