Frequency tables: tests, effect sizes, and explorations

Very often, the data we study as linguists are discrete in nature. That is, the linguistic elements we study come in different categories and, trivially, if two elements are labeled the same, they belong to the same category, and if they are labeled differently, they belong to different categories. In statistical approaches, this kind of scenario is usually described with the terminology of variables (or factors) and their levels. For example, when direct objects are studied, it may be interesting to describe them in terms of which part of speech the direct object's head is. In other terminology, each direct object studied is then described with regard to the variable PART OF SPEECH by assigning a particular variable level to it; depending on what the direct objects look like, the following levels are conceivable: PART OF SPEECH: LEXICAL NOUN, PART OF SPEECH: PRONOUN, PART OF SPEECH: SEMIPRONOUN, (such as matters or things), etc. Trivially, if direct objects are categorized this way, then a direct object whose head is categorized as PART OF SPEECH: PRONOUN is, for the purposes of this analysis, identical to another one whose head is categorized as PART OF SPEECH: PRONOUN and different from one whose head is categorized as PART OF SPEECH: LEXICAL NOUN. On other occasions, the observed variables are actually not discrete, but continuous, but for the purposes of an analysis they may be grouped into two or more categories such as