Quantitative Methods In Linguistics

Keith Johnson

• Publisher: Wiley-Blackwell
• Year: 2011
• ISBN:
  9781444360431
• Edition: 1
• Topic: Languages & Linguistics
• Subtopic: Linguistics
• Index: Languages & Linguistics

Quantitative Methods in Linguistics offers a practical introduction to statistics and quantitative analysis with data sets drawn from the field and coverage of phonetics, psycholinguistics, sociolinguistics, historical linguistics, and syntax, as well as probability distribution and quantitative methods.

• Provides balanced treatment of the practical aspects of handling quantitative linguistic data
• Includes sample datasets contributed by researchers working in a variety of sub-disciplines of linguistics
• Uses R, the statistical software package most commonly used by linguists, to discover patterns in quantitative data and to test linguistic hypotheses
• Includes student-friendly end-of-chapter assignments and is accompanied by online resources at available in the 'Downloads' section, below

1
Fundamentals of Quantitative Analysis

In this chapter, I follow the outline of topics used in the first chapter of Kachigan, Multivariate Statistical Analysis, because I think that that is a very effective presentation of these core ideas.

Increasingly, linguists handle quantitative data in their research. Phoneticians, sociolinguists, psycholinguists, and computational linguists deal in numbers and have for decades. Now also, phonologists, syntacticians, and historical linguists are finding linguistic research to involve quantitative methods. For example, Keller (2003) measured sentence acceptibility using a psychophysical technique called magnitude estimation. Also, Boersma and Hayes (2001) employed probablistic reasoning in a constraint reranking algorithm for optimality theory.

Consequently, mastery of quantitative methods is increasingly becoming a vital component of linguistic training. Yet, when I am asked to teach a course on quantitative methods I am not happy with the available textbooks. I hope that this book will deal adequately with the fundamental concepts that underlie common quantitative methods, and more than that will help students make the transition from the basics to real research problems with explicit examples of various common analysis techniques.

Of course, the strategies and methods of quantitative analysis are of primary importance, but in these chapters practical aspects of handling quantitative linguistic data will also be an important focus. We will be concerned with how to use a particular statistical package (R) to discover patterns in quantitative data and to test linguistic hypotheses. This theme is very practical and assumes that it is appropriate and useful to look at quantitative measures of language structure and usage.

We will question this assumption. Salsburg (2001) talks about a “statistical revolution” in science in which the distributions of measurements are the objects of study. We will, to some small extent, consider linguistics from this point of view. Has linguistics participated in the statistical revolution? What would a quantitative linguistics be like? Where is this approach taking the discipline?

Table 1.1 shows a set of phonetic measurements. These VOT (voice onset time) measurements show the duration of aspiration in voiceless stops in Cherokee. I made these measurements from recordings of one speaker, the Cherokee linguist Durbin Feeling, that were made in 1971 and 2001. The average VOT for voiceless stops /k/ and /t/ is shorter in the 2001 dataset. But is the difference “significant”? Or is the difference between VOT in 1971 and 2001 just an instance of random variation – a consequence of randomly selecting possible utterances in the two years that, though not identical, come from the same underlying distribution of possible VOT values for this speaker? I think that one of the main points to keep in mind about drawing conclusions from data is that it is all guessing. Really. But what we are trying to do with statistical summaries and hypothesis testing is to quantify just how reliable our guesses are.

Table 1.1 Voice onset time measurements of a single Cherokee speaker with a 30-year gap between recordings.

1.1 What We Accomplish in Quantitative Analysis

Quantitative analysis takes some time and effort, so it is important to be clear about what you are trying to accomplish with it. Note that “everybody seems to be doing it” is not on the list. The four main goals of quantitative analysis are:

1. 1 data reduction: summarize trends, capture the common aspects of a set of observations such as the average, standard deviation, and correlations among variables;
2. 2 inference: generalize from a representative set of observations to a larger universe of possible observations using hypothesis tests such as the t-test or analysis of variance;
3. 3 discovery of relationships: find descriptive or causal patterns in data which may be described in multiple regression models or in factor analysis;
4. 4 exploration of processes that may have a basis in probability: theoretical modeling, say in information theory, or in practical contexts such as probabilistic sentence parsing.

1.2 How to Describe an Observation

An observation can be obtained in some elaborate way, like visiting a monastery in Egypt to look at an ancient manuscript that hasn’t been read in a thousand years, or renting an MRI machine for an hour of brain imaging. Or an observation can be obtained on the cheap – asking someone where the shoes are in the department store and noting whether the talker says the /r/’s in “fourth floor.”

Some observations can’t be quantified in any meaningful sense. For example if that ancient text has an instance of a particular form and your main question is “how old is the form?” then your result is that the form is at least as old as the manuscript. However, if you were to observe that the form was used 15 times in this manuscript, but only twice in a slightly older manuscript, then these frequency counts begin to take the shape of quantified linguistic observations that can be analyzed with the same quantitative methods used in science and engineering. I take that to be a good thing – linguistics as a member of the scientific community.

Each observation will have several descriptive properties – some will be...

Table of contents

• Cover
• Dedication
• Title
• Copyright
• Acknowledgments
• Design of the Book
• 1 Fundamentals of Quantitative Analysis
• 2 Patterns and Tests
• 3 Phonetics
• 4 Psycholinguistics
• 5 Sociolinguistics
• 6 Historical Linguistics
• 7 Syntax
• Appendix 7A
• References
• Index
• End User License Agreement