Detection theory and psychophysics

Marill · 1956 · psychophysics · record marill1956-detection-theory-and-psychophysics
tag layer · index · concepts · authors · עברית
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. A 1956 MIT Research Laboratory of Electronics technical report based on a PhD thesis in psychology; no journal venue. Claim type is 'method' because the report's core move is re-founding psychophysical measurement on detection theory plus the two-category forced-choice technique, from which the ideal-detector psychophysical function is derived - but Part I is also an explicit critique of Tanner and Swets, and sections 9 and 11 add a mechanism claim (a wider-than-ideal auditory filter multiplies noise power, accounting for the 13.5 dB deficit, and overlapping versus non-overlapping filters explain the two-component results). Method is recorded as 'behavioural-experiment' (two paid human listeners, 810 runs of 180 forced-choice trials), but a large part of the document is mathematical derivation across ten appendices. The OCR is heavily line-broken and in places column-scrambled, so every quote here was taken from a sentence lying wholly within one extracted line; that ruled out the abstract's own summarising sentences and the 'differed from the ideal detector only to the extent of being, on the average, 13.5 db less sensitive' conclusion, which is split across three lines. 2026-08-14, 2026-08-15 and 2026-08-25 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
How to read this page. The article itself is not reproduced here — this paper is not cleared for redistribution, so what follows is the tag layer alone. The evidence sentences are withheld with the article. The table at the foot lists every tag the record carries; each row names the facet it belongs to, and the whose words column says whether the tag records the paper's own wording or the tagger's sentence about the paper. Every tag links to each other paper in the corpus carrying it. The machine-readable edition of the same thing is the TEI file beside this one, where the tags live in standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.
Other fields define these differently the same word, defined another way in another discipline
value 2 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 9 concept tags on this paper, all 9 are grounded in a quoted sentence. 3 carry the tagger's gloss of what the term means in this paper, which is not something the article can license.
d' detectability detection situation forced-choice method detection theory traditional psychophysical models subject's criterion detectors value A bandpass filter in the auditory system whose passband is about 13.5 db wider than the ideal filter admits proportionally more noise power, so the detector behaves exactly like the ideal detector but requires a correspondingly higher signal-to-noise ratio. When two signal components fall in non-overlapping auditory filters, the two filter outputs are statistically independent, so the two detectors' decisions are independent as well. A decision based on the signs of two independent detector outputs can never beat the better single detector, which is why the 500+1100 cps signal is only as detectable as its more detectable component. ideal detector symmetrical payoff matrix two-category forced-choice method uniform gaussian noise equivalent rectangular bandwidth t-test the t-test technique least squares a least-squares method for fitting the curves proportion of variance explained behavioural-experiment

Legend

relation to other workclaim_relationshow this paper stands to another: agrees, contradicts, extends, qualifies
claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
concept edgeconcept_edgesan asserted relation between two concepts, with the sentence asserting it
conceptconceptsan idea the paper works with, quoted where the paper uses it
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
controlcontrolsan experiment run to eliminate a rival explanation
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
phenomenonphenomenonthe effect or regularity under study
sensesensesa distinct use of a term, quoted where the paper fixes it
transfertransfersa method or concept carried in from another field
unrecordable relationunhoused_relationsa relation the paper asserts that this vocabulary cannot express, with the reason

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at its publisher. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 3 · claim_type 1 · concept_edges 1 · concepts 9 · content_tags 32 · controls 1 · limitations 8 · mechanisms 3 · method 1 · phenomenon 1 · senses 6 · transfers 3 · unhoused_relations 2

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 1 relation here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facettagfieldconf.whose words
claim_typemethod
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
claim_typethe paper's words
phenomenonauditory signal detection in gaussian noise
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
phenomenonthe paper's words
methodbehavioural-experiment
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
methodthe paper's words
mechanismsmechanisms
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
mechanisms[0]the tagger's words
mechanismsmechanisms
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
mechanisms[1]the tagger's words
mechanismsmechanisms
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
mechanisms[2]the tagger's words
limitationsThe theoretical curves were fitted to the data by eye rather than by a least-squares procedure.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: every parameter read off the theoretical curves: THE CURVES WERE FITTED BY EYE
limitations[0]the tagger's words
limitationsThe displacement values are only as accurate as the report's noise spectrum-level measurements, themselves accurate to about 0.8 dB.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: the displacement values: THESE VALUES ARE, OF COURSE, ONLY AS ACCURATE AS OUR NOISE SPECTRUM-LEVEL MEASUREMENTS
limitations[1]the tagger's words
limitationsA planned statistical analysis, for which the number of runs per signal had been deliberately varied, was never completed.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: the statistical analysis the design was built for: THIS ANALYSIS PROVED MORE LENGTHY THAN REWARDING AND WAS ABANDONED - the runs per signal were varied to support a result the paper does not contain
limitations[2]the tagger's words
limitationsThe zero point of the sensitivity scale is set arbitrarily, because the scale itself is stated to be unknown and abstract.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: a d' value as an absolute quantity: the paper states the scale is unknown and abstract and its zero is set arbitrarily
limitations[3]1.0the tagger's words
limitationsFixing the variance at one is described as choosing a unit of measurement, not as an empirical finding.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: the unit-variance assumption as a property of the observer: the paper says it is a choice of measurement unit on an arbitrary scale
limitations[4]1.0the tagger's words
limitationsThe definition of the detection situation is stipulated for this report, with the author noting other formulations are possible.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: the detection situation as a standard construct: the report stipulates one of several possible formulations for its own use
limitations[5]1.0the tagger's words
limitationsOnly some of the weaknesses identified in the existing models are claimed to be removed.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: detection theory as resolving the criticisms of earlier models: the abstract claims only some weaknesses are eliminable
limitations[6]1.0the tagger's words
limitationsThe goodness-of-fit test used is stated to be inapplicable when the data points are not equally spaced.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
what this limits: the fit test on unequally spaced data: the report says makeshift repairs may be needed or the test considered inapplicable
limitations[7]1.0the tagger's words
transfersIntroducing catch-trials turns the psychophysical experiment into a detection situation, so the whole apparatus of detection theory can be applied to psychophysical problems.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
transfers[0]the tagger's words
transfersThe likelihood-ratio distribution functions already computed for signals in uniform gaussian noise are taken over directly to derive the psychophysical function for a human listener.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
transfers[1]the tagger's words
transfersThe sampling theorem is imported so that a band-limited receiver input over an interval can be represented as a finite set of 2TW random variables.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
transfers[2]the tagger's words
controlsevery measurement replicated on each of two subjects, HF and PFL
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
eliminates: an idiosyncrasy of one observer's hearing standing in for a general detection result - two subjects is small, and replicating everything on both is what the paper can say · outcome (stated by the tagger, no quotation): held
controls[0]0.85the tagger's words
conceptsd'
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: d'
concepts[0]the paper's words
conceptsdetectability
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: detectability
concepts[1]the paper's words
conceptsdetection situation
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
concepts[2]the paper's words
conceptsforced-choice method
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
concepts[3]the paper's words
conceptsdetection theory
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
concepts[4]the paper's words
conceptstraditional psychophysical models
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
concepts[5]the paper's words
conceptssubject's criterion
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
concepts[6]0.95the paper's words
conceptsdetectors
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: detectors
concepts[7]0.9the paper's words
conceptsvalue
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: value
concepts[8]0.9the paper's words
unhoused_relationsforced-choice → yes-no
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
PROVED INDISTINGUISHABLE - the FORMAL form / The strongest version of the claim we cannot express: not 'we could not tell them apart' but 'they cannot be told apart', established by argument and holding for a whole class of methods. THE CASE THAT JOINS THE TWO GAPS. 'do not differ at all as far as the fundamental theorem is concerned' is a non-difference SCOPED TO A NAMED RESPECT. We cannot say a relation fails, and we cannot say what a relation is relative to; this one clause needs both. If differs in is built, design against this sentence.
unhoused_relations[0]the tagger's words
unhoused_relationsdetectors → the paper's own definition of detection
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
A METALINGUISTIC SELF-CAUTION, AND THE VOCABULARY HAS NO TYPE FOR A CLAIM ABOUT A WORD. `Quotation withheld` The author uses a term his own definition forbids and says so. The relation is not between two concepts in the paper - it is between A USAGE and THE DEFINITION THAT USAGE VIOLATES. I first wrote `detectors --distinct-from--> value` and the gate refused it for want of a differentiation cue, correctly: those two are not comparable things, and the edge was a bad rendering of a real observation. The observation survives here; the edge does not. Note that the term reaches signal-detection engineering with the caution stripped off. Reached 2026-08-26 by the project.
unhoused_relations[1]0.85the tagger's words
sensesd' - a sensitivity measure on an unknown abstract scale, whose zero point is assigned by convention rather than measured
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[0]1.0the tagger's words
sensesdetectability - the name given to the probability of a correct response, not to a property of the observer alone
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[1]1.0the tagger's words
sensesthreshold - a momentary quantity treated as a random variable, taking a different value on each trial
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[2]1.0the tagger's words
senses`the subject's criterion` - A NAME THAT MAKES A PREDICTION, AND THE PAPER SAYS SO AS IT COINS IT. `the central-tendency term, c, is called "the subject's criterion." This suggests a "psychological" quantity which may, as psychological quantities sometimes do, change its value from psychophysical experiment to experiment.` The name is a parameter of a model; calling it the subject's turns a fitted constant into a property of a person, and the paper flags the consequence rather than the word.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[3]0.95the tagger's words
senses`detectors` - THE AUTHOR USES A WORD HIS OWN DEFINITION FORBIDS, AND LABELS IT AS LOOSE. `Quotation withheld` Detection is defined in this paper through payoff, and a machine has no payoffs. The term survives into signal-detection engineering with the caution stripped off - which is the ordinary fate of a hedged coinage. NO EDGE PROPOSED. The natural endpoints would be `detectors` and `organisms`, and the gate refused `detectors --distinct-from--> value` for want of a differentiation cue - correctly, since those two are not comparable things. The claim is metalinguistic (a word is being used loosely), and the sense layer is where a claim about a word belongs.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[4]0.9the tagger's words
senses`value` - A TECHNICAL TERM PINNED BY AN EVERYDAY ANALOGY INSTEAD OF A DEFINITION. `Quotation withheld` No utility function, no axioms - an appeal to shared usage, in a paper that is otherwise formal to the point of listing its notation. The looseness is deliberate and local.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[5]0.85the tagger's words
claim_relationscontradicts → Tanner and Swets' model and traditional threshold/criterion psychophysical models
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
claim_relations[0]the tagger's words
claim_relationsbuilds-on → Peterson and Birdsall (15)
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
claim_relations[1]the tagger's words
claim_relationsextends → Fletcher's critical-band theory
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
claim_relations[2]the tagger's words
concept_edgesdetection theory —contrasted-with→ traditional psychophysical models
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says weaknesses of the traditional models are eliminable by detection theory; contrasted-with is loose.
concept_edges[0]the tagger's words
content_tagst-test
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: t-test
content_tags.statistics[0]the tagger's words
content_tagsleast squares
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: least squares
content_tags.statistics[1]the tagger's words
content_tagsproportion of variance explained
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.statistics[2]the tagger's words
content_tagsThe subjects were not ideal detectors.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[0]the tagger's words
content_tagsOnce the ideal-detector curve was shifted rightward by a single constant, it fitted the observed psychophysical functions closely, accounting for 99.3 per cent of the variance in the best case and 97.3 per cent in the worst.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[1]the tagger's words
content_tagsApart from a constant loss of about 13.5 db in sensitivity, the subjects' detection behaviour matched the ideal detector's predicted psychophysical function for pure tones.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[2]the tagger's words
content_tagsFor two-component signals at 1060 and 1100 cps, detectability was set by the total energy of the signal, exactly as for the ideal detector, and the energy-summation prediction accounted for 96.5 per cent of the observed variance.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[3]the tagger's words
content_tagsFor the 500+1100 cps signals the energy-summation prediction accounted for only 25 per cent of the variance.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[4]the tagger's words
content_tagsPredicting the 500+1100 cps two-tone detectability from the better single component alone accounted for 93.5 per cent of the variance and a t-test found no difference between that component's detectability and the two-tone detectability.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[5]the tagger's words
content_tagsTwo-component signals at 500 and 540 cps fell between the two extremes, with the energy-summation prediction accounting for 73.6 per cent of the variance.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[6]the tagger's words
content_tagsFor the 1060/1100 and 500/540 pairs, adding the weaker component raised the detectability of the whole signal above that of the stronger component alone, a difference that was highly significant.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[7]the tagger's words
content_tagsThe 13.5 db loss cannot be internal noise adding linearly to external noise, because detection accuracy stays constant whenever the external signal-to-noise ratio is constant, no matter how loud the noise.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[8]the tagger's words
content_tagsAuditory filters near 1100 cps have wider bandwidths than those near 500 cps.
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.findings[9]the tagger's words
content_tagsdetectability
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: detectability
content_tags.definitions[0]the tagger's words
content_tagsideal detector
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.definitions[1]the tagger's words
content_tagssymmetrical payoff matrix
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.definitions[2]the tagger's words
content_tagstwo-category forced-choice method
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.definitions[3]the tagger's words
content_tagsuniform gaussian noise
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.definitions[4]the tagger's words
content_tagsequivalent rectangular bandwidth
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.definitions[5]the tagger's words
content_tagsdetectability
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: detectability
content_tags.variables[2]the tagger's words
content_tags13 db — how much less sensitive the subjects were than the ideal detector, as stated in the abstract
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[0]the tagger's words
content_tags75 per cent at r = 1.4 — accuracy of the ideal detector at a signal-energy to noise-spectrum-level ratio of 1.4
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[1]the tagger's words
content_tags99.3 / 97.3 per cent — variance in the psychophysical data accounted for by the best- and worst-fitting displaced ideal-detector curves
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[2]the tagger's words
content_tags96. 5 per cent — variance in observed two-tone detectability (1060+1100 cps) accounted for by the total-energy prediction
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[3]the tagger's words
content_tags73. 6 per cent — variance accounted for by the total-energy prediction for the 500+540 cps pair
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[4]the tagger's words
content_tags25 per cent — variance accounted for by the total-energy prediction for the 500+1100 cps pair
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[5]the tagger's words
content_tags93.5 per cent — variance accounted for when the 500+1100 cps two-tone detectability is predicted from the more detectable component alone
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[6]the tagger's words
content_tags61 — total number of signals whose detectability was measured
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[7]the tagger's words
content_tags810 — total number of experimental runs made
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[8]the tagger's words
content_tagstwo — subjects, both male MIT students, on whom all measurements were replicated
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[9]the tagger's words
content_tags180 trials / 10 minutes — length of a single run, each trial lasting 3 1/3 seconds
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[10]the tagger's words
content_tags-66 db — measured noise spectrum-level near 500 and 1100 cps, accurate to about 0.8 db
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[11]the tagger's words

Interpretive choices

Tags that could not be placed in the text:

What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.

© 2026 Shir Sivroni · ORCID 0009-0000-2597-2824