Sensitivity index¶
A signal-detection statistic measuring separation between signal and noise distributions in standard-deviation units, commonly denoted d-prime.
Core Idea¶
The common formula assumes equal-variance Gaussian distributions, hit and false-alarm extremes need correction and discriminability must be separated from decision bias. Observed hit and false-alarm rates are transformed to normal quantiles and subtracted, or distribution means are normalized by common spread, estimating sensory separation independent of criterion. 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 signal detection theory. It is the domain-specific identity fixed by the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit.
Scope of Application¶
Sensitivity index belongs to signal detection theory and is useful where the analyst can specify the typed signal detection theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit. The scope is broad within that domain but bounded by the need for the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
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 Sensitivity index. Sensitivity index 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: the typed signal detection theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of signal detection theory because they reuse the typed signal detection theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Observed hit and false-alarm rates are transformed to normal quantiles and subtracted, or distribution means are normalized by common spread, estimating sensory separation independent of criterion., and type the carrier, state every parameter and convention in the definition, test that the signal and noise conditions, response rule, hit and false-alarm rates, distributional and equal-variance assumptions, z-transform formula or mean-separation formula, sign and scale, extreme-rate correction, sampling uncertainty and distinction from criterion sensitivity and percent correct are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Sensitivity index Domain-specific
Parents (1) — more general patterns this builds on
-
Sensitivity index is a kind of Measurement Prime
The proposed strict upward parent is
prime:measurement.
Hierarchy path (1) — routes to 1 parentless root
- Sensitivity index → Measurement
Neighborhood in Abstraction Space¶
Sensitivity index sits in a crowded region of the domain-specific corpus (38th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Signal Processing & Spectral Estimation (23 abstractions)
Nearest neighbors
- Detection limit — 0.90
- Sampling (signal processing) — 0.90
- Estimation of signal parameters via rotational invariance techniques — 0.90
- Signal averaging — 0.90
- Constant-Q transform — 0.89
Computed from structural-signature embeddings · 2026-09-08