---
slug: magnitude_vs_significance
name: Magnitude vs. Significance
one_liner: "Separate how large an effect is from how certain we are that it is nonzero — a scale-free measure of the size of a relationship, reported independently of the evidence that it exists at all."
type: prime
schema_version: 2
status: density_v2_draft
categories: [epistemic, structural]
origin_domain: statistics_and_inference
alternate_origin_domains: [epidemiology, economics, meta_science]
aliases: [effect_magnitude, size_vs_detectability, standardized_magnitude, practical_vs_statistical_significance]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-05 generalization) — the proposed GENUS of `effect_size` (lift: strip the frequentist-statistics frame and the specific standardized-mean-difference metric, keeping the bare separation of magnitude from detectability). Discovered in the op-05 pilot sweep 2026-07-03. Tier B candidate. STATUS: HOLD pending owner keep/cut. Domain-instance risk: candidate may still be tethered to statistics rather than a genuinely lifted structure."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Phase-C action: re-similarity-check vs `effect_size` and the named nearest primes; confirm it is a genuine genus (covers the input AND the named siblings) and not a domain instance or a restatement of the input; draw a subsumption edge input→candidate + sibling edges at incorporation; sync one_liner to a v1 draft per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 3
  domain_breadth: 3
  structural_abstraction: 4
  transfer_evidence: 3
  reasoning: 'The bare structure — hold two orthogonal quantities apart, "how big is the effect" and "how sure are we it is not zero," and refuse to let evidence-of-existence stand in for size — is a clean epistemic distinction that recurs wherever a quantity is estimated from noisy data. It shows up in epidemiology (an odds ratio is a magnitude; its confidence interval is the certainty), in meta-analysis (standardized mean differences pooled separately from their precision), and in economics (an elasticity is a magnitude reported apart from its standard error). Structural abstraction is fairly high because the move is a pure conceptual separation, but domain breadth and transfer are held near 3 because in practice the distinction lives inside quantitative-estimation settings and inherits the vocabulary of statistics; it is not obviously a scheduling- or graph-grade medium-neutral relation. A lifted candidate should still score above its framed input `effect_size`.'
similarity_to_nearest_existing_prime:
  slug: effect_size
  similarity: 0.6
structural_framed:
  label: framed
  aggregate: 0.58
  criteria: {vocab_travels: 0.5, evaluative_weight: 0.4, institutional_origin: 0.6, human_practice_bound: 0.6, import_vs_recognize: 0.7}
  rationale: 'The distinction is a conceptual/epistemic one rather than a value-laden doctrine, which keeps evaluative weight modest, but its native vocabulary (significance, effect, power, confidence) is statistical and it originates as a methodological corrective inside inferential-statistics practice. It is imported as a named distinction more than recognized as a bare structure, though the underlying "size is not the same as sureness" skeleton does travel. On balance it reads mildly framed, and whether the lift truly de-frames it (vs. remaining an effect-size doctrine) is the central keep/cut question.'
phase_b_passes_completed: []
---
# Magnitude vs. Significance

## Core Idea

Magnitude-versus-significance is the epistemic structure that *keeps two orthogonal questions about an estimated quantity strictly apart*: "how large is the effect?" and "how confident are we that the effect is not zero?" The genus is reached from the input `effect_size` by stripping the one constraint that ties that prime to a specific frame — the frequentist-statistics apparatus and its particular standardized metrics (Cohen's d, r, and their kin). What remains once that frame is removed is a bare relational commitment: a magnitude lives on one axis, and the strength of evidence that the magnitude is real lives on a second, and the two must never be collapsed into each other.

The load-bearing anatomy has three parts. First, a *magnitude* — a size, on some scale-free or interpretable scale, of the relationship or difference in question. Second, a *detectability / certainty* quantity — how strongly the available evidence rules out "no effect at all," which is a function of sample, noise, and precision rather than of size. Third, the *orthogonality claim*: these two can vary independently, so a tiny effect can be established with overwhelming certainty (large sample) and a large effect can remain wholly uncertain (thin data). The characteristic payoff is that it blocks a pervasive inferential error — mistaking "we are sure something is there" for "what is there is big," and vice versa — and lets a decision-maker ask the substantive question (is this effect large enough to matter?) separately from the evidential one (is it there at all?). The characteristic failure is the collapse itself: reporting only a significance verdict and letting readers infer importance, or reporting only a magnitude and letting readers infer certainty.

Read structurally, the same separation recurs across methodologically unlike settings. In *epidemiology* an odds ratio or relative risk is a pure magnitude of association, reported alongside — but never fused with — a confidence interval that carries the certainty; a modest odds ratio can be rock-solid and a dramatic one can be noise. In *meta-analysis* the whole machinery pools standardized mean differences (magnitudes) weighted by precision (certainty), explicitly holding the two apart so that many small-but-consistent studies and one large-but-shaky study are treated correctly. In *economics* an elasticity is a magnitude of responsiveness reported apart from its standard error. These are not the same statistic; they share the structure — a size and a sureness on separate axes, and a standing prohibition on reading one off the other.

## Notes

**Provenance.** Produced by operator 05 (generalization / lift) as the proposed genus of `effect_size`, lifting away the frequentist-statistics frame and the specific standardized-difference metric to leave the bare magnitude-vs-detectability separation. Surfaced in the op-05 pilot sweep on 2026-07-03. It claimed the siblings *odds ratio* (epidemiology), *standardized mean difference across meta-analyses*, and *elasticity* (economics). Manifest tier: B.

**For owner evaluation (keep/cut).** The case FOR: the "size is not sureness" separation is a genuinely load-bearing epistemic distinction that recurs well beyond the frequentist frame `effect_size` is stated in, and the three named siblings are structurally unlike instances of it (an odds ratio, a pooled SMD, an elasticity), which is the signature of a real lift rather than a restatement. The RISKS Kurt should weigh: (1) **domain-instance / restatement risk (the flag: "stats-domain risk; weak")** — the candidate may not actually escape statistics; if the genus reads as "effect size, told generally," it collapses back into the input and should be cut. The sharp test: does the candidate cover the siblings *because* they share the magnitude/certainty split, or only because they are all statistics? (2) **Tier-B / near-coinage caution** — this is a B-tier candidate flagged *weak*; the one-liner and genus were composed for a single input, so keep-rate expectation is lower. (3) **Alias risk** — if the corpus has or adds a broader "distinguish two orthogonal quantities" or "measurement vs. inference" prime, this may be a special case of it rather than a prime in its own right. Sharp keep/cut question: is *magnitude-vs-significance* a distinct reusable structure, or is it simply `effect_size` with the frequentist packaging removed?

**At incorporation.** Re-run similarity against `effect_size` first (confirm the candidate is a genus that covers it, not a paraphrase) and against any measurement / estimation / uncertainty prime already in the corpus. If it survives, draw a subsumption edge `effect_size` → `magnitude_vs_significance` and sibling edges from the candidate to the epidemiology/meta-analysis/economics instances as they are drafted; flag a missing-edge if a broader estimation-under-noise genus already exists. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
