Part II: Linear models and friends

Part II moves from the conceptual and practical foundations of statistics into the core modelling framework that underpins much of modern quantitative research in the social sciences: the family of linear models and their extensions. These chapters will show you how a single, unifying framework can encompass a wide variety of techniques — t-tests, ANOVA, regression, mixed models, and certain types of generalized linear models — and how thinking in terms of models rather than isolated “tests” makes analysis both more powerful and more coherent.

Chapter 6  Normal models begins with the normal model, introducing the logic of modelling data as coming from a distribution with parameters we estimate and test. Here, you will see how t-tests, confidence intervals, and effect sizes fit naturally into a modelling perspective. Chapter 7  Simple linear regression then moves to simple linear regression, showing how relationships between two variables can be expressed, estimated, and checked in a straightforward statistical model that links predictors to outcomes.

In Chapter 8  Multiple linear regression, the focus shifts to multiple linear regression, which allows you to include several predictors at once. This is where the advantages of the modelling approach become clearer: you can adjust for other variables, examine the unique contribution of each predictor, compare nested models, and diagnose problems like collinearity. Chapter 9  ANOVA and general linear models extends these ideas to ANOVA and the general linear model, showing that analyses traditionally taught as separate—comparing means across groups—are just special cases of regression. Factorial designs, interactions, and the combination of categorical and continuous predictors are covered in detail.

Chapter 10  Repeated measures analysis introduces repeated measures analysis, dealing with data where multiple observations come from the same individual or unit. Chapter 11  Multilevel and mixed effects models then develops this further into multilevel and mixed-effects models, which handle more complex hierarchical data structures such as students within classes or repeated measures within participants. These models allow you to account for variation at multiple levels simultaneously, making them essential for much applied research.

Chapters 12  Logistic regression and 13  Models for count data extend the linear modelling framework to situations where the outcome variable is not continuous and normally distributed. Chapter 12  Logistic regression covers logistic regression in its binary, categorical, and ordinal forms, while Chapter 13  Models for count data turns to models for count data, including Poisson, negative binomial, and zero-inflated models. These are all part of the generalized linear model family, which uses the same core principles but adapts them to fit different kinds of outcome variables.

By the end of Part II, you will see that these methods are not a disconnected set of statistical “tricks” but members of a coherent modelling family. You will have the tools to choose appropriate models for your data, fit them in R, evaluate their assumptions, interpret their parameters, and communicate your findings clearly. This part of the book equips you with the central analytical skills that many researchers rely on throughout their careers.