Statistics for Categorical, Nonparametric, and Distribution-Free Data

Abstract

Researchers in applied linguistics frequently encounter data that could be considered nontraditional, including categorical data, data that does not fit a traditional parametric model, and data that may not fit any distribution (distribution free). In this chapter we describe statistical methods for handling such data. We begin by introducing methods for analyzing categorical data, including the use of basic descriptive statistics such as measures of central tendency, measures of dispersion, frequency counts, and normed rates of occurrence. We then introduce when, why, and how to use alternatives to traditional parametric statistical tests, including nonparametric analogs, permutation tests, and bootstrapping.