Distributions

Distributions

The attributive or predicative use of an adjective in the comparative has an influence on the probability with which a synthetic or analytic comparative form is chosen. Consider the examples in Table 3.

Table 3a: Examples of adjectival comparatives according to syntactic function

The results of a cross-tabulation of the syntactic function of a comparative and the comparative form in a corpus-based study might yield the following distribution (see example tables for statistical analysis):

Table 3b: The choice of comparative form as a function of its syntactic function

In Table 3, the syntactic function is the independent variable, whose influence on the comparative form (the dependent variable) is being investigated.

How do you determine if this distribution is significant?

• If we say a distribution is significant at the .05 level, we mean that the probabilty of the result occuring by chance is 1 in 20 or 5 % (error probability). Similarly, if it is significant at the .01 level, the error probability is 1 in 100, and if it is significant at the .001 level, the error probability is only 1 in 1000.
• The Chi-square test can be used to estimate the significance of a cross-tabulated distribution. Excel can calculate the error probability (function: CHIQU.TEST) after you have determined the expected frequencies, i.e. the distribution of the dependent variable (form of comparative) if the independent variable (syntactic function) had no influence on its distribution. Note that the cells selected for the CHIQU.TEST function must represent arrays of adjacent cells: one for the observed distribution and one for the expected distribution.
• Attention: The Chi-square test presupposes a minimum expected frequency of 5 observations in at least 80 % of the cells. It also presupposes that all observations are independent of each other. If one or the other condition is not fulfilled, a different test or an additional correction of the test is required.

Exercise 6: In the example table for the comparative alternation (Table 3), check whether the distribution is significant and what the error probability is.