E2 · Publication Volume 24

Units, Nulls, Detection Limits and Qualifiers

missing versus zero, censored values and quality flags

Learning objectives

  • Explain why missing versus zero, censored values and quality flags require explicit semantic modelling.
  • Design identities, relations and constraints that preserve units, nulls, detection limits and qualifiers across exchange.
  • Separate hard release gates from diagnostic metrics and interpretation choices.
  • Produce a value-state contract with unit, limit and qualifier validation from synthetic evidence.

The lesson is complete only when the learner can defend both the model and the release decision. A neat schema without evidence, tests or declared limitations is an unverified design. The assessed artefact must make assumptions visible and distinguish source assertions from derived conclusions.

Decision context

Define a result tuple containing magnitude when present, unit, value state, qualifier, detection or reporting limit, method and quality flag. Downstream calculations must state how each state is handled; silent substitution with zero, half a limit or an arbitrary reserved code is prohibited.

Start with a decision record: name the intended use, the evidence required, the consequence of error, the accepted uncertainty and the role authorised to accept residual risk. Then ask whether the proposed model can answer the decision question without relying on filename conventions, row order, undocumented defaults or someone’s memory. This prevents technology selection from concealing a missing semantic requirement.

The same record may be fit for one use and unfit for another. A rapid exploratory view can tolerate conditions that a released exchange package cannot. Fitness is therefore stated against a use, contract version and quality gate rather than attached permanently to the data.

Core concept

A numerical field needs a value state as well as a magnitude. Zero is a measured or asserted quantity; missing means no usable value is supplied; below-detection is a censored statement; not-applicable says the property does not apply. Collapsing these states biases summaries and can reverse decisions.

The working scope is missing versus zero, censored values and quality flags. For each item in that scope, distinguish the thing itself, the label used by a source, the claim made about it and the record that carries the claim. Identity is not a display name; a value is not its unit; an observation is not a model; current is not the same as valid. These distinctions create explicit places for correction, uncertainty and competing interpretations.

A good semantic design can be explained as a set of sentences before it is encoded. Each sentence identifies a subject, a property or relationship, an object or result, and the context under which the claim holds. Physical tables and files are then projections of those sentences, not their source of meaning.

Semantic model

Separate value, unit and qualifier columns or properties. A below-limit result records the relation, the applicable limit and its unit. A quality flag qualifies a result and links to the check that produced it. Unit conversion creates a derived result with conversion rule and source link rather than altering raw evidence.

Test every proposed record against seven questions: What has identity? What type is it? Which property or relationship is asserted? Which spatial and temporal context applies? Which state or qualifier modifies the assertion? Which evidence supports it? Which version and activity produced the stored representation? Missing answers become explicit contract gaps.

Normalisation is used to separate independent facts, not to maximise the number of tables. A compact nested object can be semantically sound if the same identities, constraints and provenance remain explicit. Conversely, a highly normalised database can still be ambiguous when relationships and units exist only in documentation or application code.

Constraints and invariants

| Invariant | Executable or review test | | --- | --- | | State and magnitude agree | A missing result has no numeric magnitude; a measured result requires one. | | Limits carry units and method context | Reject a censoring qualifier without its applicable limit metadata. | | Reserved missing-value codes do not enter analytics | Translate legacy reserved codes to explicit states at ingestion. | | Raw and converted values coexist | Retain original value, unit, conversion and derived value. |

An invariant is a condition that must remain true across storage, export, correction and reprocessing. Implement it as close to the authoritative boundary as practical and repeat the check at exchange boundaries. Record rule identifier, version, severity, evaluated scope, observed value and outcome so a failure can be reproduced.

Hard gates protect identity, semantic validity, required provenance and authorised use. Diagnostic checks reveal unusual values or patterns but require interpretation. Never convert a diagnostic threshold into deletion or correction without a reviewed rule and preserved source evidence.

Quantitative reasoning

Report proportions by state, not just one missingness percentage. For state k, use p_k = n_k / n. Any estimator applied to censored data must state its substitution or censoring model and be tested for sensitivity. Unit conversion uses x_t = a x_s + b only when the dimensional quantity and scale definition permit that transformation.

Every reported ratio states its numerator, denominator, exclusions and evaluation time. Stratify results by source, entity type, contract version or processing run where aggregation could hide a local failure. Counts accompany percentages so a seemingly large change based on a tiny denominator remains visible.

Precision is part of meaning. Do not add decimal places merely because a storage type permits them, and do not round identity, interval or coordinate fields without a declared tolerance and test. Quantitative summaries support a release decision; they do not replace semantic review.

Evidence and uncertainty

Detection limits can vary by method, batch, matrix and dilution. A limit copied from a method catalogue may not be the effective limit for a particular result. Store the result-level applicable limit or a stable link to the batch-level evidence from which it is derived.

Build an evidence packet containing preserved source reference, acquisition or assertion context, applicable method, validation results, reviewer decision and links to derivatives. Classify uncertainty as observational, semantic, structural, parametric or policy-related where that distinction changes treatment. “Unknown” is a valid state when the evidence cannot justify a stronger claim.

Contradictory evidence remains available. The model may select one current assertion, but the reason, competing assertion and effective time are retained. This makes later reinterpretation possible without pretending the earlier evidence never existed.

Interfaces and storage

Contracts define allowed value states, qualifier codes, unit identifiers and permitted combinations. Text exports use separate fields rather than symbols embedded in a numeric string. Typed formats preserve numeric columns while qualifiers occupy companion columns or nested properties.

Design an interface from the logical contract outward. Specify identifiers, types, cardinalities, units, value states, coordinate and time references, version negotiation, validation behaviour and structured errors before choosing a serialisation. The physical representation then declares its mapping to those logical elements.

Storage optimisation may partition, compress, index or cache data, but it must not change identity or silently remove context. A derived representation points to immutable inputs and a processing manifest. A cache carries freshness and contract-version information and is never treated as the only evidence copy.

Governance and access

A unit registry and value-state vocabulary require versioned definitions. Changes to a qualifier’s meaning are semantic breaking changes even if the code string stays the same. Validation rules and analytic guidance must be released with the vocabulary.

Governance is expressed through named roles, review states and versioned decisions, not through references to a particular organisation. Define who may propose, validate, approve, supersede and withdraw each governed resource. The audit trail records the role and event while avoiding unnecessary personal data.

Apply least-necessary access to source evidence and derivatives. Access controls must not erase identifiers, lineage or quality metadata needed to understand an authorised release. When policy is unresolved, quarantine the output with a precise reason and escalation route.

Integration checkpoint

Measured, censored, missing and inapplicable states remain distinct
Measured, censored, missing and inapplicable states remain distinct

The diagram summarises the control flow for this lesson. Read it from source evidence through semantic structure and validation to a decision-ready artefact. Each arrow should correspond to a declared relationship or transformation; each boundary should have a contract; each released node should have an identity, version and provenance pointer.

Integrate the lesson by adding a value-state contract with unit, limit and qualifier validation to the evolving synthetic data package. Verify that earlier artefacts still resolve and that the new model does not overwrite observations, identifiers, values or versions introduced in previous lessons. Record every changed assumption.

Synthetic worked example

A synthetic result column contains 0, blank, “less than 0.01” and -999. The learner identifies a measured zero, a missing value, a censored result with a limit and a legacy reserved code. Each becomes an explicit state. A summary is then calculated twice under documented censoring treatments to show how assumptions affect the result.

Work the example in four passes:

  1. Preserve the received records and write the intended decision without correcting anything.
  2. Identify entities, claims, context, uncertainties and policy constraints; mark every unresolved item.
  3. Apply the versioned rules, create derivatives and record the exact transformation plus validation evidence.
  4. Issue an accept, reject or quarantine decision and show how an independent reviewer can reproduce it.

Because the example is entirely synthetic, its values demonstrate method only. The important result is the chain from received evidence to justified decision. If a required fact is absent, the worked solution records the gap rather than manufacturing a plausible value.

Practice task

Design a result contract for a synthetic analytical dataset. Enumerate value states and permitted field combinations, define unit conversion rules, ingest legacy reserved codes, calculate state frequencies and compare two transparent censoring treatments without replacing the preserved source values.

Use the following acceptance criteria:

  • All required identifiers and references resolve to declared types.
  • Every transformation preserves the received evidence and records its derivation.
  • Invalid, unknown and inapplicable states remain distinct and machine-testable.
  • The output identifies the contract, vocabulary and processing versions used.
  • A second reader can reproduce the validation result without private knowledge.

Submit the source snapshot, authored contract or model, validation output, derivative, manifest and a short decision record. A screenshot alone is insufficient because it cannot demonstrate the exact input, version or rule execution.

Common failure modes

  • Blank, zero and below-limit values all become zero.
  • A qualifier is embedded inside a numeric text field.
  • One global detection limit is assumed for every result.
  • Converted values overwrite the reported values.

These failures share a pattern: convenient representation is mistaken for verified meaning. Diagnose the earliest boundary at which an assumption became implicit. Correct by restoring source evidence, making the assumption a versioned field or rule, rerunning dependent transformations and superseding—not overwriting—the affected release.

Do not repair a failure by adding an undocumented default. A blocked result with a specific missing dependency is safer and more reusable than a complete-looking result whose meaning cannot be reconstructed.

Review questions

  1. Why is below-detection not the same as missing?
  2. Which metadata makes a censoring statement interpretable?
  3. How should legacy reserved codes be handled?
  4. Why must censoring assumptions accompany summaries?

For each answer, identify the governing invariant, the evidence needed to evaluate it and the appropriate release behaviour when the invariant fails. A strong answer distinguishes scientific uncertainty from missing semantics and distinguishes a recoverable warning from a hard contract violation.

Sources and further reading