Chapter 38: Statistical methods for corpus exploitation
Marco Baroni, Corso Diaz, Stefan Evert · 2006
vs. concrete nouns). As an example of a classification into multiple categories, word tokens might be classified into syntactic categories such as noun, verb, adjective, adverb, etc., with an “other” class for minor syntactic categories and problematic tokens. A chi-squared test might then be performed to compare the frequencies of these categories in samples from two genres. As another example, one might classify sentences according to the semantic class of their subject, and then compare the frequency of these semantic classes in samples of the populations of sentences headed by true intransitive vs. unaccusative verbs. It is not always obvious which characteristics should be operationalized as a classification of the tokens into types, and which should rather be operationalized in terms of different populations the tokens belong to. In some cases, it might make more sense to frame the task we just discussed in terms of the distribution of verb types across populations of sentences with different kinds of subjects, rather than vice versa. This decision, again, will depend on the linguistic question we want to answer. In corpus linguistics, lexical classifications also play an important role. In this case, types are the distinct word forms or lemmas found in a corpus (or sequences of word forms or lemmas). Lexical classifications may lead to extremely small proportions π (sometimes measured in occurrences per million words) and huge differences between populations in the two-sample setting. Article 57 discusses some of the relevant methodologies in the context of collocation extraction. The examples we just discussed give an idea of the range of linguistic problems that can be studied using the simple methods based on count data described in this Article. Other problems (or the same problems viewed from a different angle) might require other techniques, such as those mentioned in the next two Sections. For example, our study of passives could proceed with a logistic regression (see Section 8), where we look at which factors have a significant effect on whether a sentence is in the passive voice or not. In any case, it will be fundamental for linguists interested in statistical methods to frame their questions in terms of populations, samples, types and tokens. 7 Non-randomness and the unit of sampling So far, we have always made the (often tacit) assumption that the observed data (i.e., the corpus) are a random sample of tokens of the relevant kind (e.g., in our running example of passives, a sentence) from the population. Most obviously, we have compared a corpus study to drawing balls from an urn in Section 2, which allowed us to predict the sampling distribution of observed frequencies. However, a realistic corpus will rarely be built by sampling individual tokens, but rather as a collection of contiguous stretches of text or even entire documents (such as books, newspaper editions, etc.). For example, the Brown corpus consists of 2,000-word excerpts from 500 different books (we will refer to these excerpts as “texts” in the following). The discrepancy between the unit of measurement (a token) and the unit of sampling (which will often contain hundreds or thousands of tokens) is particularly obvious for lexical phenomena, where tokens correspond to single words. Imagine the cost of building the Brown corpus by sampling a single word each from a million different books rather than 2,000 words each from only 500 different books! Even in our example, where each token corresponds to an entire sentence, the unit of sampling is much larger than the unit of measurement: each text in the Brown contains roughly between 50 and 200 sentences. This need not be a problem for the statistical analysis, as long as each text is itself a random sample of tokens from the population, or at least sufficiently similar to one. However, various factors, such as the personal style of