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Metodologia sobre la recerca sociolingüística


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


CONTINUA


The initial factors find their optimum point at the fifteenth of the programme’s twenty possible iterations. The Input of application of the pretonic vowel [a] on these factors reveals that the rule "is applied" (0.636), i.e. generally speaking, the solution [a] is maintained as it is greater than 0.5, which figure can be attributed to the appearance of both dependent factors.

Returning now to this programme’s logistic model formula, we can see how the calculations in the analysis of 1L are reached:

formula

p = Input & Weight    p0 = Input        pi  = Weight         pj  = Weight'

(i.e. probab.            the probab. of            where factor t      where factor o
of each                    all the variable          of the 1 froup is    of the 1 group is
independent factor)  rule. Here is 0.636   0.568                   0.253
                            

Returning now to this programme’s logistic model formula, we can see how the calculations in the analysis of 1L are reached:

formula

This equation gives p (Input & Weight) a value that is the probability of maintenance of [a] according to our variable rule: in the case of factor t of the 1 group, p= 0.696; if this figure is rounded up, it corresponds to the programme’s third column of results – that is, 0.70.

Thus, 1L reveals the general input of maintenance of [a] (0.636), the weight of each factor, the percentage of use of [a] according to each independent variable, which appears under the name App/Total, and lastly, the probability of maintenance of [a] in relation to these independent factors – input & weight.

Once the results are obtained, this programme displays a description of the errors between the theoretical or expected probability and the sample used. Clearly, any probabilistic analysis will involve error; if it did not, the field of study would be functional mathematics. However, probability looks for the smallest margin of error between what was expected and the real data with which it works; thus, the closer the columns that reveal frequency (App/Total) and probability (Input & Weight), the more guarantees of success of the analysis.

This part contains three tests to determine whether the theoretical conditions adapt to the study data:

-Logarithm of likelihood (Log. likelihood)
-X-square test
-Scattergram

Using the example of the previous analysis, we obtain:

Total Chi-square = 150.8532
Chi-square/cell = 1.2893
Log likelihood = -1362.634
Maximum possible likelihood = -1277.040
Fit: X-square(104) = 171.187, rejected, p = 0.0000

 

 

 


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