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Learning objectives

Source: vignettes/objectives.Rmd
objectives.Rmd

Overview

This course is an introduction to study design and quantitative data analysis, including statistics, as commonly employed in linguistics, using the R software.

We will cover the following topics:

  • The basics of quantitative data analysis.
  • Study design.
  • The principles of data visualisation.
  • Statistical modelling.
  • Statistical inference using Null Hypothesis Significance Testing.

Examples from different branches of linguistics will be used to provide you with hands-on experience in quantitative data analysis and Open Research practices.

At completion of the course you will have gained the following skills:

  • Effectively address the intended research questions with quantitative methods.
  • Using compelling visualisations to communicate a specific message about patterns in the data.
  • Master linear models for different types of data (continuous measures, counts, accuracy data, reaction times).
  • Correctly interpret p-values and confidence intervals and avoid common interpretation pitfalls.

Weekly breakdown

The following sections report the learning objectives more in detail, broken down by week.

For each week, you can find a set of questions that you should be able to answer at the end of the week and a set of skills that you will practice during the week.

Week 1: Quantitative methods and uncertainty

Questions:

  • What are knowledge and data?
  • What is quantitative data analysis?
  • How can we talk about uncertainty?
  • Which are the limits of quantitative methods?

Skills:

  • Think critically about “data”.
  • Interpret basic numeric summaries and plots.
  • Use R to perform simple calculations and obtain numeric summaries.
  • Master the basics of the programming language R Learn how to manage your analyses with scripts and RStudio.

Week 2: Data visualisation

Questions:

  • What are the principles of good data visualisation?
  • Which are the main components of a plot?
  • Which are the appropriate plots for different types of data?
  • How can we visualise uncertainty?

Skills:

  • Create common types of plots with ggplot2.
  • Use colour and shape to effectively convey meaning.
  • Describe a plot in writing and comment on observable patterns.
  • Write dynamic reports and generate publication-quality image files.

Week 3: Linear models: Basics I

Questions:

  • What are statistical models useful for?
  • What are statistical populations, samples and distributions?
  • What are statistical variables and which type of relationships exist between variables?
  • What is a linear model and which are its components?

Skills:

  • Perform basic data wrangling in R (filtering and mutating data).
  • Fit a linear model with one continuous outcome variable and one continuous predictor with lm().
  • Interpret the summary of the model and understand the meaning of the reported coefficients.
  • Plot and diagnose the model and describe the model specification and results in writing.

Week 4: Linear models: Basics II

Questions:

  • How can we use linear models with categorical (rather than continuous) predictors?
  • Why do we need to code categorical predictors as numbers?
  • And which are the most common coding methods?
  • How can we represent a linear model using a formula?
  • How do you interpret a linear model with both continuous and categorical predictors?

Skills:

  • Read data into R and obtain grouped summaries.
  • Master contrast coding in R for categorical predictors.
  • Fit, interpret and plot linear models with continuous and categorical predictors.
  • Advanced reporting of model specification and results.

Week 5: Linear models: Discrete outcomes

Questions:

  • Is Gaussian data that common?
  • How can we model non-Gaussian data?
  • Which are the properties of binary outcomes (‘yes/no’, ‘true/false’) and counts?
  • Why do linear models use log-odds and odds instead of probabilities?

Skills:

  • Fit, interpret and plot linear models with binary outcome variables, using the Bernoulli/binomial distribution family.
  • Fit, interpret and plot linear models with count outcome variables, using the Poisson distribution family.
  • Convert between log-odds, odds and probabilities.
  • Recognise different types of outcome variables.

Week 6: Catch-up Week

There will be no class this week. Instead, you will be asked to catch up with the materials covered that far, complete a short formative assessments, and participate in class discussions on Piazza.

Week 7: Linear models: Basics III

Questions:

  • What makes data “tidy”?
  • And what makes it “untidy”?
  • Why is centering and/or scaling continuous variables helpful?
  • What are z-scores?
  • How do you model interactions between two or more variables?

Skills:

  • Tidy messy data in R with dplyr and tidyr.
  • Centre, scale and z-score continuous predictors.
  • Fit, interpret and plot linear models with interactions (continuous * continuous, continuous * categorical, categorical * categorical).
  • Reporting of models with interactions.

Week 8: Linear models: Hierarchical data

Questions:

  • What makes data hierarchical?
  • Can we pool information from different groups in the data?
  • How are fixed and varying effects related to pooling?
  • What is shrinkage and when is it useful?

Skills:

  • Fit, interpret and plot a linear model with varying effects using lmer().
  • Understand varying intercepts and slopes as variance coefficients.
  • Deal with model convergence and singularity issues.
  • Report models with varying effects.

Week 9: Significance Testing I

Questions:

  • What is statistical inference?
  • What is Null Hypothesis Significance Testing?
  • What are p-values?
  • What are they not?
  • Are p-values a guarantee of “truth”?

Skills:

  • Define the statistical population and sample.
  • Obtain and interpret p-values.
  • Recognise and avoid common misconceptions of p-values.
  • Report p-values.

Week 10: Significance testing II

Questions:

  • How much are we willing to risk getting a false positive result?
  • What is statistical power and how is it related to false negative results?
  • What are Questionable Research Practices (QRP) and how do we avoid them?
  • Why is it important to know the required minimal sample size?

Skills:

  • Understand alpha, beta and statistical power.
  • Understand Type-I, II, M and S errors.
  • Master Open Research practices and prevent QRPs.
  • Run power analyses with simr to calculate the required minimal sample size.