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Statistics for Linguists


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Table of Contents

Table of contents

0. Preface: Approach and how to use this book 0.1. Strategy of the book 0.2. Why R? 0.3. Why the tidyverse? 0.4. R packages required for this book 0.5. What this book is not 0.6. How to use this book 0.7. Information for teachers 1. Introduction to base R 1.1. Introduction 1.2. Baby steps: simple math with R 1.3. Your first R script 1.4. Assigning variables 1.5. Numeric vectors 1.6. Indexing 1.7. Logical vectors 1.8. Character vectors 1.9. Factor vectors 1.10. Data frames 1.11. Loading in files 1.12. Plotting 1.13. Installing, loading, and citing packages 1.14. Seeking help 1.15. A note on keyboard shortcuts 1.16. Your R journey: The road ahead 2. Tidy functions and reproducible R workflows 2.1. Introduction 2.2. tibble and readr 2.3. dplyr 2.4. ggplot2 2.5. Piping with magrittr 2.6. A more extensive example: iconicity and the senses 2.7. R markdown 2.8. Folder structure for analysis projects 2.9. Readme files and more markdown 2.10. Open and reproducible research 3. Models and distributions 3.1. Models 3.2. Distributions 3.3. The normal distribution 3.4. Thinking of the mean as a model 3.5. Other summary statistics: median and range 3.6. Boxplots and the interquartile range 3.7. Summary statistics in R 3.8. Exploring the emotional valence ratings 3.9. Chapter conclusions 4. Introduction to the linear model: Simple linear regression 4.1. Word frequency effects 4.2. Intercepts and slopes 4.3. Fitted values and residuals 4.4. Assumptions: Normality and constant variance 4.5. Measuring model fit with 4.6. A simple linear model in R 4.7. Linear models with tidyverse functions 4.8. Model formula notation: Intercept placeholders 4.9. Chapter conclusions 5. Correlation, linear, and nonlinear transformations 5.1. Centering 5.2. Standardizing 5.3. Correlation 5.4. Using logarithms to describe magnitudes 5.5. Example: Response durations and word frequency 5.6. Centering and standardization in R 5.7. Terminological note on the term 'normalizing' 5.8. Chapter conclusions 6. Multiple regression 6.1. Regression with more than one predictor 6.2. Multiple regression with standardized coefficients 6.3. Assessing assumptions 6.4. Collinearity 6.5. Adjusted 6.6. Chapter conclusions 7. Categorical predictors 7.1. Introduction 7.2. Modeling the emotional valence of taste and smell words 7.3. Processing the taste and smell data 7.4. Treatment coding in R 7.5. Doing dummy coding 'by hand' 7.6. Changing the reference level 7.7. Sum coding in R 7.8. Categorical predictors with more than two levels 7.9. Assumptions again 7.10. Other coding schemes 7.11. Chapter conclusions 8. Interactions and nonlinear effects 8.1. Introduction 8.2. Categorical * continuous interactions 8.3. Categorical * categorical interactions 8.4. Continuous * continuous interactions 8.5. Continuous interactions and regression planes 8.6. Higher-order interactions 8.7. Chapter conclusions 9. Inferential statistics 1: Significance testing 9.1. Introduction 9.2. Effect size: Cohen's 9.3. Cohen's in R 9.4. Standard errors and confidence intervals 9.5. Null hypotheses 9.6. Using to measure the incompatibility with the null hypothesis 9.7. Using the -distribution to compute -values 9.8. Chapter conclusions 10. Inferential statistics 2: Issues in significance testing 10.1. Common misinterpretations of -values 10.2. Statistical power and Type I, II, M, and S errors 10.3. Multiple testing 10.4. Stopping rules 10.5. Chapter conclusions 11. Inferential statistics 3: Significance testing in a regression context 11.1. Introduction 11.2. Standard errors and confidence intervals for regression coefficients 11.3. Significance tests with multi-level categorical predictors 11.4. Another example: the absolute valence of taste and smell words 11.5. Communicating uncertainty for categorical predictors 11.6. Communicating uncertainty for continuous predictors 11.7. Chapter conclusions 12. Generalized linear models: Logistic regression 12.1. Motivating generalized linear models 12.2. Theoretical background: Data-generating processes 12.3. The log odd function and interpreting logits 12.4. Speech errors and blood alcohol concentration 12.5. Predicting the dative alternation 12.6. Analyzing gesture perception: Hassemer & Winter (2016) 12.6.1. Exploring the dataset 12.6.2. Logistic regression analysis 12.7. Chapter conclusions 13. Generalized linear models 2: Poisson regression 13.1. Motivating Poisson regression 13.2. The Poisson distribution 13.3. Analyzing linguistic diversity using Poisson regression 13.4. Adding exposure variables 13.5. Negative binomial regression for overdispersed count data 13.6. Overview and summary of the generalized linear model framework 13.7. Chapter conclusions 14. Mixed models 1: Conceptual introduction 14.1. Introduction 14.2. The independence assumption 14.3. Dealing with non-independence via experimental design and averaging 14.4. Mixed models: Varying intercepts and varying slopes 14.5. More on varying intercepts and varying slopes 14.6. Interpreting random effects and random effect correlations 14.7. Specifying mixed effects models: lme4 syntax 14.8. Reasoning about your mixed model: The importance of varying slopes 14.9. Chapter conclusions 15. Mixed models 2: Extended example, significance testing, convergence issues 15.1. Introduction 15.2. Simulating vowel durations for a mixed model analysis 15.3. Analyzing the simulated vowel durations with mixed models 15.4. Extracting information out of lme4 objects 15.5. Messing up the model 15.6. Likelihood ratio tests 15.7. Remaining issues 15.7.1. -squared for mixed models 15.7.2. Predictions from mixed models 15.7.3. Convergence issues 15.8. Mixed logistic regression: Ugly selfies 15.9. Shrinkage and individual differences 15.10. Chapter conclusions 16. Outlook and strategies for model building 16.1. What you have learned so far 16.2. Model choice 16.3. The cookbook approach 16.4. Stepwise regression 16.5. A plea for subjective and theory-driven statistical modeling 16.6. Reproducible research 16.7. Closing words References Appendix A. Correspondences between significance tests and linear models Appendix B. Reading recommendations

About the Author

Bodo Winter is Lecturer in Cognitive Linguistics in the Department of English Language and Applied Linguistics at the University of Birmingham, UK.

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