Randomization, Blocking, Stratification, and Controls

These are the tools of local control: removing or balancing nuisance variation so the comparison you care about is clean. Randomization handles the unknown confounders; blocking and stratification handle the known ones; controls and blinding handle the systematic biases.

Randomization — why and how

Randomization assigns treatments to units by chance, so that in expectation every confounder (measured or not, known or unknown) is balanced across arms. This is the foundation of causal inference: without it, an observed difference could always be due to some variable that happened to track the grouping.

Use a seeded, reproducible schedule (see scripts/randomization.py) and follow it exactly. Record the seed. "I randomized somehow" is neither auditable nor reproducible.

Methods (and when each is right)

Method	What it does	Use when
Simple	Independent random assignment per unit	n is large (≳100); simplicity matters; imbalance is tolerable
Permuted block	Within each block, arms appear in fixed ratio; order shuffled	You need balance throughout enrollment, or n is small/moderate, or intake is sequential
Stratified block	Separate blocks within each level of a prognostic factor	A known covariate (site, sex, stage) must be balanced across arms
Cluster	Whole groups (clinics, classes) assigned to arms	The intervention is delivered at a group level
Minimization	Adaptively assign to minimize imbalance across several covariates	Many prognostic factors and small n (specialized; not in the script)

Simple randomization caveat: with small n it behaves like flipping a few coins — you can easily get 12 vs. 8 instead of 10 vs. 10, and worse for subgroups. Blocking fixes this.

Block size: must be a multiple of the ratio unit (e.g. for 1:1, sizes 2, 4, 6). Smaller blocks balance more tightly but are more predictable in unblinded trials (a clinician who knows the block size can guess the last allocation). Vary block size or keep it concealed when predictability is a concern.

Blocking — removing known nuisance variation

A block is a group of units expected to be similar (same day, batch, litter, plate, instrument run). You randomize treatments within each block. The nuisance variation between blocks is then removed from the error term, so the treatment comparison is more precise — often dramatically so.

Block on anything that (a) you can identify before the experiment and (b) you expect to affect the response but isn't of interest itself:

• Time: day, week, session, processing batch.
• Space: plate, plate position/edge, shelf, cage rack, field plot.
• Material: reagent lot, animal litter, cell passage, donor.
• People/instruments: technician, machine, sequencing run.

Rule of thumb: "Block what you can, randomize what you cannot." If you suspect a factor matters but can't block it, at least randomize across it and record it as a covariate.

Randomized complete block design (RCBD): every treatment appears once in every block. This is the workhorse design — analyze with treatment + block in the model.

Stratification vs. blocking vs. covariate adjustment

These overlap; the distinction is about when you control the variable:

• Stratify / block at design time when the factor is known before assignment and you want guaranteed balance (the safest, since it doesn't rely on a model).
• Adjust as a covariate at analysis time (ANCOVA, regression) when the factor is continuous or measured after assignment. Often you do both: stratify on the big ones, adjust for the rest.

A few strata are better than many: stratifying on too many factors at once leaves strata with too few units to block effectively. For many covariates and small n, minimization is the alternative.

Controls

A comparison needs a concurrent baseline. Match the control to the threat you're ruling out:

• Untreated / standard-of-care control — isolates the treatment effect from time.
• Vehicle / sham control — isolates the active ingredient from the delivery (injection stress, vehicle solvent, sham surgery).
• Positive control — a treatment known to produce the effect, to confirm the assay can detect one at all.
• Concurrent, not historical — controls run at the same time as the treatment; historical controls reintroduce time confounding.

Blinding

Blinding prevents expectation from biasing measurement and behavior:

• Single-blind: the subject doesn't know the assignment.
• Double-blind: neither subject nor experimenter/assessor knows.
• Blinded outcome assessment: at minimum, whoever measures the outcome shouldn't know the group — cheap and high-value even in animal/bench work. Allocation concealment (the person enrolling can't foresee the next assignment) is distinct from blinding and just as important; a sealed seeded schedule provides it.

Batch effects and plate layout (especially omics / HTS)

Batch effects are systematic technical differences between processing groups and are a leading cause of irreproducible high-throughput results.

• Never let batch align with the biological condition. If all cases are in batch 1 and all controls in batch 2, condition and batch are perfectly confounded and no normalization can separate them.
• Randomize or block sample-to-batch and position-within-plate. Spread each condition across all batches and across plate positions.
• Avoid edge effects: evaporation and thermal gradients make outer wells differ; don't load all controls into edge columns. Randomize positions, or include replicates spanning edge and interior.
• Include anchor/reference samples in every batch to estimate and correct batch shifts.
• Use assign_factorial_runs() / the randomization functions to generate a randomized processing order and position map.

Documentation

Record, and ideally pre-register: the randomization method, the seed, block sizes, stratification factors, the schedule itself, and the planned analysis (which must include block/stratum/cluster terms). This is what makes the study auditable and the primary analysis confirmatory rather than exploratory.