Construct Design Matrix

---
name: construct-design-matrix
description: "Construct a balanced/randomized/orthogonal experimental design matrix appropriate to the chosen design mode."
---

# construct-design-matrix

## Purpose

Construct a balanced/randomized/orthogonal experimental design matrix appropriate to the chosen design mode.

## Input contract

```yaml
required: [factor_schema, design_mode, run_budget, randomization_constraints]
optional: [evidence, assumptions, prior_results]
constraints: [use named scientific objects; retain provenance and missingness; $\alpha$ = 0.05 and power = 0.8 where applicable]
```

## Procedure

1. Validate the typed inputs and state the decision this operation must support.
2. Apply the declared operation to the named object; record intermediate values that affect interpretation.
3. Check boundary conditions and counterexamples, then emit the result with uncertainty and source links.

If the design cells are fixed but their outcomes and estimands are not, consider `specify-metrics` as the next tactic.

## Output contract

```yaml
produces: [construct_design_matrix_result, evidence_trace, uncertainties]
delta_fields: [evidence_updates, uncertainties]
```

## Quality gates

- Inputs are named scientific objects with compatible schemas.
- Every material result has a derivation or source reference.
- Fixed statistical criteria remain exact where applicable: $\alpha$ 0.05 and power 0.8.

## Failure and counterexamples

Return a failed operation with the violated precondition when inputs are incomplete, assumptions are unsupported, or a counterexample defeats the result.

## Provenance map

- intermediate: experiment-execution/design-matrix-construction