Barnardisation¶
A statistical-disclosure-control method that pseudo-randomly perturbs nonzero interior table counts by plus one, zero or minus one according to a fixed probability rule before recomputing totals.
Core Idea¶
Barnardisation protects tabular counts by applying small randomized additive adjustments to eligible cells. Each cell independently or under a controlled scheme receives minus one, zero or plus one with declared probabilities, obscuring exact small counts while approximately preserving aggregates. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of official statistics. It is bounded count perturbation for disclosure limitation in statistical tables. That residual remains recognizable when examples, notation, scale, or implementation change, but it disappears if the carrier is mistyped, the condition that zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method fails, a neighboring object is substituted, or notation and topical resemblance replace the constitutive test.
Scope of Application¶
Barnardisation belongs to official statistics and is useful where the analyst can specify a contingency table of counts, nonzero internal cells, perturbation probability p, pseudorandom generator, plus-one or minus-one adjustments, recomputed margins, disclosure risk and utility, then evaluate zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method. The scope is broad within that domain but bounded by the need for zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Barnardisation can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Barnardisation. Barnardisation compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: a contingency table of counts, nonzero internal cells, perturbation probability p, pseudorandom generator, plus-one or minus-one adjustments, recomputed margins, disclosure risk and utility. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of official statistics because they reuse a contingency table of counts, nonzero internal cells, perturbation probability p, pseudorandom generator, plus-one or minus-one adjustments, recomputed margins, disclosure risk and utility, Each cell independently or under a controlled scheme receives minus one, zero or plus one with declared probabilities, obscuring exact small counts while approximately preserving aggregates., and type the carrier, state every parameter and convention in the definition, test that zero-cell and negative-count rules, randomization probability, repeatability policy and post-perturbation total calculation follow the published method, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Barnardisation Domain-specific
Parents (1) — more general patterns this builds on
-
Barnardisation is a kind of Randomization Prime
The proposed strict upward parent is
prime:randomization.
Hierarchy paths (6) — routes to 5 parentless roots
- Barnardisation → Randomization → Intervention
- Barnardisation → Randomization → Causality → Dependency
- Barnardisation → Randomization → Experimental Design → Comparison → Self Checking
- Barnardisation → Randomization → Probability → Measure → Set and Membership
- Barnardisation → Randomization → Probability → Measure → Aggregation → Micro Macro Linkage
- Barnardisation → Randomization → Experimental Design → Control Sample → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Barnardisation sits in a moderately populated region (52nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Statistical Dispersion & Testing (44 abstractions)
Nearest neighbors
- Count data — 0.89
- Sub-probability measure — 0.88
- Variance — 0.88
- Folded-t and half-t distributions — 0.88
- Exchangeable random variables — 0.87
Computed from structural-signature embeddings · 2026-09-08