Conventions

This page summarizes the visual conventions used throughout the book.

Code

R code appears in syntax-highlighted blocks. Output is prefixed with #> to make the boundary between input and output explicit:

mean(c(1, 2, 3, 4, 5))
#> [1] 3

Code blocks are display-only: they are not executed when the book is rendered, so numeric output shown after #> is the output observed when the block was written, not a value regenerated at build time. Blocks that report simulation results state the number of replicates and the seed so that the reader can reproduce them.

Inline code is in monospace. Function calls always include parentheses (mean() rather than mean) so that they are unambiguously functions. Package-qualified calls (gsDesign::gsDesign) appear when the function is not universally known, when there is name-collision risk, or when the chapter is teaching package usage.

Callouts

Three callout types appear:

TipTip

A small practical recommendation.

A short question testing comprehension of the just-read material. Click to expand the answer.

WarningWarning

A pitfall the reader may otherwise hit.

Cross-references

Within this book, sections, figures, and tables are referenced by their Quarto label (@sec-randomization-human, @fig-boundary, @tbl-comparison). These resolve to clickable links in HTML and proper section numbers in PDF.

References to the companion volumes use prose pointers rather than Quarto cross-references, because cross-references do not resolve across separate books. For example: ‘see the Survival Analysis chapter of the companion Statistical Computing in the Age of AI volume’.

Mathematical notation

Conventional notation throughout. Vectors are bold lower-case (\(\mathbf{x}\)); matrices are bold upper-case (\(\mathbf{X}\)); scalars and parameters are non-bold. Estimators carry hats (\(\hat\theta\)). Total sample size is \(N\); per-arm sample size is \(n\); the number of randomization strata is \(S\); the number of measurement occasions in a longitudinal trial is \(J\). Treatment assignment is \(Z \in \{0, 1\}\) with \(Z = 1\) denoting the experimental arm. Potential outcomes are \(Y(1)\) and \(Y(0)\).

Trial-specific conventions: \(\alpha\) is the one-sided type I error rate unless stated otherwise (the convention in confirmatory drug trials, where the two-sided 0.05 test is usually described as one-sided 0.025); \(1 - \beta\) is power; \(\Delta\) is a non-inferiority margin; \(\delta\) is the targeted treatment effect.

Chapter structure

Every content chapter follows the same template:

  1. Learning objectives. What you will be able to do after reading.
  2. Orientation. A short prose framing.
  3. The statistician’s contribution. What no tool can automate. The judgments at the center of the chapter.
  4. Content sections with Check-your-understanding callouts at natural pauses.
  5. Worked example. One trial, carried through.
  6. Collaborating with an LLM on the chapter topic. Prompt / Watch for / Verification triples for AI assistance.
  7. Principle in use. Two or three habits to carry forward.
  8. Exercises. The work.
  9. Further reading. Where to go next on the topic.

The pattern repeats deliberately. By the third chapter you know where to find each component.

The advanced-topic chapters

Chapters 11 through 28 differ from the ten course chapters in one respect: each is built on a specific research compendium from the author’s own methodological work, and each reports simulation results from that compendium. Those chapters carry an additional Provenance section naming the compendium so that a reader can trace every number back to the code that produced it.