experimental-design

# 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

```bash
uv pip install "numpy>=1.26" "pandas>=2.0" pyDOE3
```

`pyDOE3` is the maintained successor to pyDOE/pyDOE2 and supplies factorial,
fractional-factorial, Plackett-Burman, central-composite, Box-Behnken, and
Latin-hypercube generators. The bundled scripts wrap it to return designs in real
factor units with named columns and randomized run order.

---

## 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 (more power, watch carry-over).
│   └─ You can only randomize groups, not individuals (schools, clinics)?
│         → CLUSTER-randomized design (analyze at the cluster level; 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`
- **Crossover, repeated-measures, split-plot, Latin-square, cluster, nested designs** → `references/design_types.md`
- **Sequential, group-sequential, and adaptive designs (interim analyses)** → `references/sequential_and_adaptive.md`

---

## Generating the design

Two scripts produce ready-to-use, reproducible layouts. Run them from the skill's
`scripts/` directory or add it to `sys.path`. Everything is seeded so the exact
schedule can be archived and regenerated — a requirement for trial registration
and good lab practice.

### Randomization / allocation schedules — `scripts/randomization.py`

```python
from randomization import (
    simple_randomization, block_randomization,
    stratified_block_randomization, cluster_randomization,
    assign_factorial_runs, arm_balance,
)

# Permuted blocks keep the arms balanced throughout enrollment (use for n < ~100
# or sequential intake — simple randomization can drift out of balance with small n)
sched = block_randomization(n=60, arms=["treatment", "control"], seed=42)

# Balance a prognostic variable across arms by randomizing within each stratum
sched = stratified_block_randomization({"siteA": 30, "siteB": 30},
                                       arms=["drug", "placebo"], ratio=(2, 1), seed=42)

# Randomize whole clusters, not individuals (the cluster is the unit)
sched = cluster_randomization(["clinic1", "clinic2", "clinic3", "clinic4"], seed=42)

arm_balance(sched)            # sanity-check the counts per arm
sched.to_csv("allocation_schedule.csv", index=False)
```

Choosing among them: **simple** is fine for large n but can produce imbalance with
small n; **block** guarantees balance throughout; **stratified block** additionally
balances a known prognostic factor; **cluster** is mandatory when the intervention
is delivered at a group level. See `references/randomization_and_blocking.md`.

### DOE matr