Stratified Rate Table¶
Comparison artifact — instantiates Conditioned Probability Frame Specification
Splits an aggregate rate into subgroup rows, each with its own denominator, so subgroup-conditioned probabilities are compared side by side without the marginal hiding them.
An aggregate rate can lie by omission: it hides that the number is very different inside each subgroup. Stratified Rate Table is the comparison artifact that breaks a single rate into rows — one per subgroup — each carrying its own denominator and its own conditioned rate, with the overall marginal shown alongside for reference. Its defining move is deliberate disaggregation for comparison: where other mechanisms protect one number, this one splits a number apart on purpose so that subgroup-conditioned probabilities can be read against each other and against the whole. It is built to make heterogeneity visible, not to hide it under an average.
Example¶
A university reports a six-year graduation rate of 68%. On its own that's a single marginal probability, and it conceals a policy-relevant story. The Stratified Rate Table breaks it out: first-generation students at 54% (denominator: 2,400), continuing-generation at 74% (denominator: 6,100), transfer entrants at 61% (denominator: 1,800), with the 68% overall shown in a "total" row. Each row is a subgroup-conditioned graduation probability — P(graduate | first-generation), and so on — with its own base, and the marginal sits beside them so nobody mistakes a subgroup rate for the whole or vice versa.
The value is that the 68% stops being a summary and becomes a comparison. The gap between 54% and 74% is exactly what an intervention would target, and it was invisible in the aggregate. The table's discipline is that each row's denominator is stated, so a reader can't quietly compare a small, noisy subgroup against a large stable one as if they were equally solid.
How it works¶
- Choose the stratifying variable. Pick the subgroup dimension that the rate plausibly depends on and that matters for the decision.
- Give every row its own denominator. Each subgroup's rate is computed over that subgroup's population, stated explicitly, so no row borrows another's base.
- Show the marginal for reference. Keep the overall rate visible as a "total" row so subgroup rates are read against the whole, not floated free.
- Label every cell as subgroup-conditioned. Mark that each rate is P(event | subgroup), not an unconditional fact, so a row is never quoted as the population rate.
Tuning parameters¶
- Stratification granularity — a few broad strata versus many fine ones. Fine strata sharpen relevance but shrink each denominator until the rates get noisy.
- Choice of stratifying variable — which dimension to split on (and whether to cross two). The wrong variable hides the real heterogeneity; crossing variables reveals interactions but fragments the sample.
- Minimum cell size — the threshold below which a subgroup is suppressed or merged. Suppression protects against noise and privacy leakage but can bury a small, important group.
- Reference row prominence — how visible the marginal is. Foregrounding it anchors comparison; hiding it invites subgroup rates to be read as totals.
When it helps, and when it misleads¶
Its strength is surfacing subgroup structure an aggregate erases — the mechanism you reach for whenever "the overall rate" is suspected of averaging over meaningfully different populations. By showing each denominator, it also lets a reader judge which comparisons are solid and which rest on a handful of cases.
Its failure mode is the reverse of aggregation's: over-stratify and every cell becomes too small to trust, so the table trades a misleading average for a wall of noise. The signature danger is Simpson's paradox — the direction of an association can flip between the stratified table and the pooled marginal, so a table and its own total row can tell opposite stories, and which is "right" depends on what's being asked.[n1] The classic misuse is stratum-shopping: slicing until some subgroup shows the rate you wanted, then quoting that row alone. The guarding discipline is to fix the stratifying variable before looking at the rates, keep the marginal in view, and enforce a minimum cell size so no row is read as signal when it's noise.
How it implements the components¶
denominator_population— every row states its own subgroup denominator explicitly; distinct bases are the table's organizing principle.base_rate_reference— the marginal "total" row keeps the overall base rate visible beside the subgroup rates.probability_type_label— each cell is labeled as a subgroup-conditioned rate, P(event | subgroup), not an unconditional fact.
It does NOT implement frame_compatibility_check — formally adjudicating whether two rates may be compared is the frame compatibility review's job; the table lays rates side by side but does not referee the comparison. Nor does it fix a single protected denominator the way the reference population note does — it splits the denominator apart on purpose.
Related¶
- Instantiates: Conditioned Probability Frame Specification — this mechanism supports subgroup-conditioned comparison within the archetype.
- Consumes: Reference Population Note supplies the total population the table stratifies.
- Sibling mechanisms: Conditional Probability Annotation · Frame Compatibility Review · Given-That Clause · Likelihood-Ratio Frame · Probability Tree · Reference Population Note · Scenario Condition Card · Two-by-Two Probability Table
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Stratified Rate Table is defined in the frozen evidence as: Splits an aggregate rate into subgroup rows, each with its own denominator, so subgroup-conditioned probabilities are compared side by side without the marginal hiding them. Its operative deployed or enacted form is therefore Analysis, Modeling & Optimization.
Nearest alternative: Representation, Specification & Plan — Representation, Specification & Plan can support this mechanism, but the evidence centers the concrete operation described above rather than the alternative family's defining operation.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Statistics & Experimental Design
Origin pattern: Single lineage
Present-day reach: Multi-domain
Rationale: Subgroup rates with denominators prevent marginal masking.
Related originating lineages:
- Data Science & Analytics — Tables operationalize disaggregation.
- Mathematics — Mathematical modeling, proof, and abstract-structure practice supplies a parallel or contributing lineage for the mechanism's defining operation: splits an aggregate rate into subgroup rows, each with its own denominator, so subgroup-conditioned probabilities are compared side by side without the marginal hiding them.
- Medicine & Healthcare — Risk rates need subgroup denominators.
Review resolution: The blind reviewers agree that statistics_experimental_design is the primary origin and differ only on alternate origin disagreement, domain reach disagreement. I preserve every independently explained alternate from both records rather than imposing a numeric cap. I retain single_lineage because the combined evidence shows one traceable formative lineage. The broader reach of multi_domain records portability separately from historical provenance; encyclopedia_synthesis=false preserves the affirmative synthesis judgment where either reviewer identified one.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] Simpson's paradox — an association present in every subgroup can reverse or vanish when the subgroups are pooled into a marginal, because the aggregate mixes populations with different base rates and different subgroup sizes. A stratified table exists partly to expose when this is happening. ↩