## ABSTRACT

Traditional approaches focused on significance tests have often been difficult for linguistics researchers to visualise. *Statistics in Corpus Linguistics Research: A New Approach *breaks these significance tests down for researchers in corpus linguistics and linguistic analysis, promoting a visual approach to understanding the performance of tests with real data, and demonstrating how to derive new intervals and tests.

Accessibly written, this book discusses the ‘why’ behind the statistical model, allowing readers a greater facility for choosing their own methodologies. Accessibly written for those with little to no mathematical or statistical background, it explains the mathematical fundamentals of simple significance tests by relating them to confidence intervals. With sample datasets and easy-to-read visuals, this book focuses on practical issues, such as how to:

• pose research questions in terms of choice and constraint;

• employ confidence intervals correctly (including in graph plots);

• select optimal significance tests (and what results mean);

• measure the size of the effect of one variable on another;

• estimate the similarity of distribution patterns; and

• evaluate whether the results of two experiments significantly differ.

Appropriate for anyone from the student just beginning their career to the seasoned researcher, this book is both a practical overview and valuable resource.

Preface

1 Why Do We Need Another Book on Statistics?

2 Statistics and Scientific Rigour

3 Why Is Statistics Difficult?

4 Looking Down the Observer’s End of the Telescope

5 What Do Linguists Need to Know About Statistics?

Acknowledgments

A Note on Terminology and Notation

Contingency Tests for Different Purposes

PART 1

Motivations

1 What Might Corpora Tell Us About Language?

1.1 Introduction

1.2 What Might a Corpus Tell Us?

1.3 The 3A Cycle

1.4 What Might a Richly Annotated Corpus Tell Us?

1.5 External Influences: Modal *Shall / Will *Over Time

1.6 Interacting Grammatical Decisions: NP Premodification

1.7 Framing Constraints and Interaction Evidence

1.8 Conclusions

PART 2

Designing Experiments With Corpora

2 The Idea of Corpus Experiments

2.1 Introduction

2.2 Experimentation and Observation

2.3 Evaluating a Hypothesis

2.4 Refining the Experiment

2.5 Correlations and Causes

2.6 A Linguistic Interaction Experiment

2.7 Experiments and Disproof

2.8 What Is the Purpose of an Experiment?

2.9 Conclusions

3 That Vexed Problem of Choice

3.1 Introduction

3.2 Parameters of Choice

3.3 A Methodological Progression?

3.4 Objections to Variationism

3.5 Conclusions

4 Choice Versus Meaning

4.1 Introduction

4.2 The Meaning of *Very *

4.3 The Choice of *Very *

4.4 Refining Baselines by Type

4.5 Conclusions

5 Balanced Samples and Imagined Populations

5.1 Introduction

5.2 A Study in Genre Variation

5.3 Imagining Populations

5.4 Multi- Variate and Multi-Level Modelling

5.5 More Texts – or Longer Ones?

5.6 Conclusions

PART 3

Confidence Intervals and Significance Tests

6 Introducing Inferential Statistics

6.1 Why Is Statistics Difficult?

6.2 The Idea of Inferential Statistics

6.3 The Randomness of Life

6.4 Conclusions

7 Plotting With Confidence

7.1 Introduction

7.2 Plotting the Graph

7.3 Comparing and Plotting Change

7.4 An Apparent Paradox

7.5 Conclusions

**8 From Intervals to Tests **

8.1 Introduction

8.2 Tests for a Single Binomial Proportion

8.3 Tests for Comparing Two Observed Proportions

8.4 Applying Contingency Tests

8.5 Comparing the Results of Experiments

8.6 Conclusions

9 Comparing Frequencies in the Same Distribution

9.1 Introduction

9.2 The Single-Sample *z *Test

9.3 Testing and Interpreting Intervals

9.4 Conclusions

10 Reciprocating the Wilson Interval

10.1 Introduction

10.2 The Wilson Interval of Mean Utterance Length

10.3 Intervals on Monotonic Functions of *p *

10.4 Conclusions

**11 Competition Between Choices Over Time **

11.1 Introduction

11.2 The ‘S Curve’

11.3 Boundaries and Confidence Intervals

11.4 Logistic Regression

11.5 Impossible Logistic Multinomials

11.6 Conclusions

12 The Replication Crisis and the New Statistics

12.1 Introduction

12.2 A Corpus Linguistics Debate

12.3 Psychology Lessons?

12.4 The Road Not Travelled

12.5 What Does This Mean for Corpus Linguistics?

12.6 Some Recommendations

12.7 Conclusions

13 Choosing the Right Test

13.1 Introduction

13.2 Tests for Categorical Data

13.3 Tests for Other Types of Data

13.4 Conclusions

PART 4

Effect Sizes and Meta-Tests

14 The Size of an Effect

14.1 Introduction

14.2 Effect Sizes for Two-Variable Tables

14.3 Confidence intervals on ϕ

14.4 Goodness of Fit Effect Sizes

14.5 Conclusions

15 Meta- Tests for Comparing Tables of Results

15.1 Introduction

15.2 Some Preliminaries

15.3 Point and Multi-Point Tests for Homogeneity Tables

15.4 Gradient Tests for Homogeneity Tables

15.5 Gradient Tests for Goodness of Fit Tables

15.7 Conclusions

PART 5

Statistical Solutions for Corpus Samples

16 Conducting Research With Imperfect Data

16.1 Introduction

16.2 Reviewing Subsamples

16.3 Reviewing Preliminary Analyses

16.4 Resampling and *p*-Hacking

16.5 Conclusions

17 Adjusting Intervals for Random-Text Samples

17.1 Introduction

17.2 Recalibrating Binomial Models

17.3 Examples With Large Samples

17.4 Alternation Studies With Small Samples

17.5 Conclusions

PART 6

Concluding Remarks

18 Plotting the Wilson Distribution

18.1 Introduction

18.2 Plotting the Distribution

18.3 Example Plots

18.4 Further Perspectives on Wilson Distributions

18.5 Alternative Distributions

18.6 Conclusions

19 In Conclusion

Appendices

A The Interval Equality Principle

1 Introduction

2 Applications

3 Searching for Interval Bounds With a Computer

B Pseudo-Code for Computational Procedures

1 Simple Logistic Regression Algorithm With Logit-Wilson Variance

2 Binomial and Fisher Functions

Glossary

References

Index