Experimental Design

Overview

The design of a study — how units are assigned to conditions, what is held constant, what is varied, and in what structure — determines what questions the data can answer. No analysis can rescue a confounded or pseudoreplicated design after the fact. This skill is about the decisions made before data collection: picking a design that isolates the effect of interest, randomizing to license causal claims, blocking to remove known nuisance variation, and structuring multi-factor experiments so effects are estimable rather than tangled together.

The three ideas behind almost every good design (Fisher's principles):

• Randomization — assign treatments at random so that confounders, known and unknown, are balanced in expectation. This is what turns a comparison into a causal claim.
• Replication — independent repetition at the right level, so you can estimate variability and your effects aren't artifacts of a single unit. The most common fatal error is pseudoreplication: counting repeated measurements on the same unit as independent replicates.
• Blocking / local control — group similar units (by batch, day, site, litter) and randomize within blocks, removing that nuisance variation from the error term instead of letting it inflate noise.

This skill helps you choose among design types, generate the actual randomization or DOE layout (with reproducible scripts), and avoid the structural mistakes that make data uninterpretable.

When to Use This Skill

• Planning any comparative experiment or trial and deciding how to assign units
• Randomizing subjects/samples to arms (simple, blocked, stratified, or cluster)
• Removing nuisance variation by blocking or stratification
• Designing multi-factor experiments: full or fractional factorial, screening designs
• Optimizing a response over continuous factors (response-surface designs)
• Within-subject / repeated-measures, crossover, split-plot, or Latin-square designs
• Cluster- or group-randomized designs (sites, clinics, classrooms, litters)
• Deciding the number and level of replicates and avoiding pseudoreplication
• Sequential, group-sequential, or adaptive designs with interim analyses
• Laying out plates/batches and randomizing run order to defeat drift

Installation

uv venv --python 3.13 .venv-design
uv pip install --python .venv-design/bin/python "numpy==2.5.3" "pandas==3.0.6" "pydoe==1.5.0"

pyDOE3 was archived in May 2026; active development returned to pydoe. The bundled wrappers target pydoe==1.5.0, imported as lowercase pydoe, and return designs in real factor units. All seven DOE wrappers and both script demos were executed with Python 3.13, NumPy 2.5.3, pandas 3.0.6, and SciPy 1.18.1. On Windows, the environment interpreter is .venv-design/Scripts/python.exe. Archive the environment versions and exported schedules: a seed alone does not promise identical output across package or script upgrades.

Choosing a design

Start from the question and the structure of your units, not from a favorite design.

What are you trying to learn?
│
├─ Compare a few predefined conditions (A vs B vs C)?
│   ├─ Units independent, possibly with a known nuisance factor (day, batch, site)?
│   │     → Completely randomized (no nuisance) or RANDOMIZED BLOCK design.
│   ├─ Each unit can receive every condition in sequence (washout possible)?
│   │     → CROSSOVER / repeated-measures design (watch carry-over and correlation).
│   └─ You can only randomize groups, not individuals (schools, clinics)?
│         → CLUSTER-randomized design (account for clustering; see pseudoreplication).
│
├─ Screen MANY factors (5+) to find the few that matter?
│     → FRACTIONAL FACTORIAL or PLACKETT-BURMAN screening design.
│
├─ Quantify main effects AND interactions among a handful of factors?
│     → FULL 2^k FACTORIAL design.
│
├─ Find the settings that OPTIMIZE a response (curvature matters)?
│     → RESPONSE-SURFACE design: central composite or Box-Behnken.
│
└─ Explore a simulation/computer model over a continuous space?
      → SPACE-FILLING design: Latin hypercube.

Detailed guidance per branch:

• Randomization, blocking, stratification, controls → references/randomization_and_blocking.md
• Factorial, fractional-factorial, screening, response-surface, DOE concepts (aliasing, resolution) → references/factorial_and_doe.md

…