Comparative Analysis Methodology.
Comparison is not placing two numbers beside each other. It is the controlled examination of equivalent units under shared boundaries, definitions and observation rules—followed by an explicit account of the differences that remain.
A comparison is valid only when its conditions are visible.
The method separates direct observations from normalized values, derived differences and interpretive conclusions. Each layer carries its own evidence state and inference boundary.
Comparative analysis methodology is the controlled examination of two or more eligible units across a declared set of equivalent dimensions, using consistent observations and explicit normalization rules to identify differences without overstating what those differences mean.
It does not independently establish why they differ or which causal mechanism produced the result.
It reflects chosen dimensions, weights and thresholds—not the complete nature of the compared units.
Change the objective, scope or weights and the comparative outcome may legitimately change.
Six controls before the first value is compared.
The contract defines the conditions under which a difference can be treated as a meaningful analytical delta rather than an artifact of mismatched inputs.
Unit identity
Define the analytical unit precisely: page, entity, query, document set, system, event or time-bound state.
Scope parity
Apply equivalent inclusion, exclusion, language, location, source and corpus boundaries.
Temporal parity
Use aligned observation windows or explicitly model time as a source of difference.
Dimension parity
Define every comparison dimension, allowed state and required evidence before observing outcomes.
Measure parity
Use the same counting unit, denominator, missing-value rule and transformation for every unit.
Evidence parity
Apply equivalent evidence requirements so one unit is not measured from richer or more permissive sources.
From question to delta without collapsing the reasoning chain.
Every stage produces an inspectable output. A failure at an early parity gate cannot be repaired later by formatting, weighting or confidence language.
Comparison claim
Specify what decision the comparison must support.
Unit registry
Resolve identities and declare the comparison class.
Shared scope
Fix corpus, source, language, location and time.
Measure model
Define dimensions, units and allowed states.
Raw matrix
Collect evidence under one observation protocol.
Comparable values
Control denominators, scale and structural size.
Delta register
Compute presence, magnitude, direction and composition.
Sensitivity test
Vary plausible rules and detect unstable outcomes.
Bounded meaning
Explain only what the evidence and design support.
Comparison manifest
Freeze rules, data, deltas, limits and provenance.
Four operations. One controlled comparison.
Each console names its input, rule, output, evidence requirement, review condition and prohibited inference. All panels remain readable even if scripting is unavailable.
Test whether units can answer the same question
Define dimensions before seeing comparative outcomes
Transform only what structural parity requires
State what changed without inventing a cause
Raw states first. Derived deltas second.
This synthetic example compares two equal-date corpora. Values are illustrative; the matrix demonstrates how direct observations, normalization and interpretive limits remain separate.
| DIMENSION | UNIT A / RAW | UNIT B / RAW | DENOMINATOR | NORMALIZED A | NORMALIZED B | DELTA | STATE |
|---|---|---|---|---|---|---|---|
| Required entity coverage | 72 supported | 81 supported | A: 90 / B: 120 | 80.0% | 67.5% | +12.5 pp A | Comparable after size control |
| Evidence traceability | 61 of 72 | 75 of 81 | Supported claims | 84.7% | 92.6% | +7.9 pp B | Comparable |
| Unresolved conflicts | 4 claims | 7 claims | Reviewed claims | 3.1% | 3.0% | −0.1 pp B | Practically aligned |
| Responsible documents | 58 entities | 63 entities | Required entities | 64.4% | 52.5% | +11.9 pp A | Comparable |
| Update latency | 12 days | 8 days | Same snapshot rule | 12 days | 8 days | 4 days faster B | Direction: lower is better |
| Source independence | Unknown | Verified | Origin trace | Not computable | Confirmed | No valid delta | Insufficient parity |
Not every difference is the same kind of difference.
The delta type determines the valid calculation and the language permitted in the final finding.
Presence
A required element is observed in one eligible unit and absent from another under the same detection rule.
A = observed · B = absentMagnitude
Both units carry numeric values expressed through the same unit and denominator.
Δ = normalized A − normalized BDirection
The values differ along an ordered state where higher or lower has a declared meaning.
direction = sign(Δ) × ruleComposition
Totals may match while the internal distribution across categories differs materially.
same total ≠ same structureSequence
The same elements occur in a different order, path or stage and therefore create a structural difference.
set(A) = set(B) · order(A) ≠ order(B)Contradiction
Equivalent evidence surfaces support mutually incompatible states for the same dimension.
A = state x · B = not-xA ranking can reverse when the decision question changes.
The example below uses the same observations under two transparent weight profiles. The reversal is not an error; hiding the dependence on weights would be.
One dataset. Two legitimate priorities. Two different outcomes.
Profile A prioritizes coverage and document ownership. Profile B prioritizes traceability and freshness. A universal winner cannot be claimed because the result depends on declared decision weights.
The correct output is a conditional statement: which unit better satisfies which objective under which model.
Six measures with explicit denominators.
Each measure answers a limited question. None independently produces a complete judgment about quality, authority or causation.
Eligibility rate
eligible units ÷ candidate unitsShows how much of the candidate set survived the declared comparability rules.
Parity completion
passed parity gates ÷ required parity gatesDescribes contract completion; critical gate failure may still invalidate comparison.
Absolute delta
Δabs = value A − value BPreserves the measurement unit and direction of the observed difference.
Relative delta
Δrel = (A − B) ÷ referenceRequires a declared reference and careful treatment when the reference is zero.
Agreement rate
matched dimension states ÷ comparable dimensionsCounts state alignment only where both units have valid comparable observations.
Decision stability
unchanged outcomes ÷ tested plausible modelsShows whether reasonable changes to thresholds or weights alter the conclusion.
Four objects. Four different comparability problems.
All examples are synthetic and demonstrate analytical decisions rather than live facts about external systems.
Eight ways a clean comparison can produce a false conclusion.
These are recorded as analytical states, not hidden in a generic disclaimer after the result.
Unit substitution
The compared objects are not instances of the same declared analytical class.
Boundary drift
Inclusion rules change across units or during collection.
Denominator mismatch
Rates appear comparable while opportunities or eligible sets differ.
Time leakage
Evidence from outside one unit’s observation window enters the matrix.
Missing-state collapse
Unknown, absent, zero and not applicable are treated as one value.
Outcome-led weights
Dimensions or weights are changed after results reveal the preferred unit.
Proxy overreach
An available measure is treated as the construct it only partially represents.
Causal inflation
A descriptive delta is presented as proof of the mechanism that caused it.
Every conclusion should be reconstructable.
The manifest connects the final finding to its units, boundaries, evidence, transformations and decision rules.
Every method node. One controlled research route.
MTH/07 establishes valid comparison. MTH/08 applies controlled coverage requirements to inspect what a content system includes, omits or leaves unsupported.