Detection theory and psychophysics — TEI-tagged view

Cross-disciplinary analysis

content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text

phenomenon	auditory signal detection in gaussian noise— “The aim of these experiments is to determine the extent to which and the manner in which subjects differ from the "ideal detector" of detection theory.”
claim-type	method— “There do seem, however, to be certain advantages in our formulation.”
method — evidence	— “The two-category symmetrical forced-choice technique was used throughout.”
transfer	from detection theory (statistical decision theory developed for radio/radar receivers): Introducing catch-trials turns the psychophysical experiment into a detection situation, so the whole apparatus of detection theory can be applied to psychophysical problems.— “is relatively new, perhaps, is the realization that introducing them brings the psychophysical experiment under the rubric of detection, thereby rendering psychophysical”	`transfers[0]`
transfer	from radar/receiver detection engineering (Peterson and Birdsall): The 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.— “Fortunately, Peterson and Birdsall (15) have calculated these functions for a wide variety of signals presented in uniform gaussian noise.”	`transfers[1]`
transfer	from communication theory / signal processing: The 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.— “The Sampling Theorem. We shall need one form of the so-called sampling theorem”	`transfers[2]`
mechanism	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.— “Our data could then be generated by a detector consisting of a filter like the ideal filter except for having a passband approximately 13. 5 db wider.”	`mechanisms[0]`
mechanism	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.— “the same input containing gaussian noise is applied to both filters, the outputs of the two”	`mechanisms[1]`
mechanism	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.— “only assume that 500 cps and 1100 cps fall within the passbands of nonoverlapping filters.”	`mechanisms[2]`
contradicts	Tanner and Swets' model and traditional threshold/criterion psychophysical models— “Part I: Traditional psychophysical models and Tanner and Swets' model are critically examined.”	`claim_relations[0]`
builds-on	Peterson and Birdsall (15)— “The material for this section is drawn from Peterson and Birdsall (15).”	`claim_relations[1]`
extends	Fletcher's critical-band theory— “The auditory theory of the present section is, of course, essentially Fletcher's critical-band theory (3, 4).”	`claim_relations[2]`
sense	d' - a sensitivity measure on an unknown abstract scale, whose zero point is assigned by convention rather than measured— “Since we measure d' on an unknown abstract scale, it is reasonable to let this lower value arbitrarily be zero.”	`senses[0]`
sense	detectability - the name given to the probability of a correct response, not to a property of the observer alone— “the probability of a correct response, is called the detectability.”	`senses[1]`
sense	threshold - a momentary quantity treated as a random variable, taking a different value on each trial— “In this approach we argue that the quantity c is a random variable (which, in our notation, must be represented by C - with the exception of the random variable ', all random variables will be designated by underlined capital letters). On a given trial, C assumes a certain value”	`senses[2]`
sense	`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.— “In the criterion approach, 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.”	`senses[3]`
sense	`detectors` - THE AUTHOR USES A WORD HIS OWN DEFINITION FORBIDS, AND LABELS IT AS LOOSE. `On occasion we shall refer to certain mechanical devices as "detectors." This is a loose way of speaking, since, presumably, the occurrence of events can be said to have value only to organisms.` 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.— “On occasion we shall refer to certain mechanical devices as "detectors." This is a loose way of speaking, since, presumably, the occurrence of events can be said to have value only to organisms.”	`senses[4]`
sense	`value` - A TECHNICAL TERM PINNED BY AN EVERYDAY ANALOGY INSTEAD OF A DEFINITION. `The term "value" is used in the sense in which it is said that gold has greater value than silver.` 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.— “The term "value" is used in the sense in which it is said that gold has greater value than silver.”	`senses[5]`
control	every measurement replicated on each of two subjects, HF and PFL — held — rules out 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— “All measurements were replicated on each of two subject (HF and PFL).”	`controls[0]`
audit	detection theory —contrasted-with→ traditional psychophysical models — 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.— “Traditional psychophysical models and Tanner and Swets' model are critically examined. Some of the weaknesses of these models are found to be eliminable by a more sophisticated analysis in terms of detection theory.”	`concept_edges[0]`
outcome (stated by the tagger, no quotation)	control — held	`controls[0]`
for which use	limitation — every parameter read off the theoretical curves: THE CURVES WERE FITTED BY EYE— “(The curves were fitted by eye.”	`limitations[0]`
for which use	limitation — the displacement values: THESE VALUES ARE, OF COURSE, ONLY AS ACCURATE AS OUR NOISE SPECTRUM-LEVEL MEASUREMENTS— “These values are, of course, only as accurate as our noise spectrumlevel measurements.”	`limitations[1]`
for which use	limitation — 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— “This analysis proved more lengthy than rewarding and was abandoned.”	`limitations[2]`
for which use	limitation — a d' value as an absolute quantity: the paper states the scale is unknown and abstract and its zero is set arbitrarily— “Since we measure d' on an unknown abstract scale, it is reasonable to let this lower value arbitrarily be zero.”	`limitations[3]`
for which use	limitation — the unit-variance assumption as a property of the observer: the paper says it is a choice of measurement unit on an arbitrary scale— “Picking the value unity is of no particular significance, since the scale on which H is measured is still arbitrary: letting Var(H) = 1 amounts to picking a unit of measurement on this scale.”	`limitations[4]`
for which use	limitation — the detection situation as a standard construct: the report stipulates one of several possible formulations for its own use— “Many different formulations are possible. In this report we shall use the concept exclusively in accordance with the following definition.”	`limitations[5]`
for which use	limitation — detection theory as resolving the criticisms of earlier models: the abstract claims only some weaknesses are eliminable— “Traditional psychophysical models and Tanner and Swets' model are critically examined. Some of the weaknesses of these models are found to be eliminable by a more sophisticated analysis in terms of detection theory.”	`limitations[6]`
for which use	limitation — the fit test on unequally spaced data: the report says makeshift repairs may be needed or the test considered inapplicable— “The data-points may not be equally spaced along the abscissa. In this case appropriate makeshift repairs may suggest themselves, or the test may be considered inapplicable.”	`limitations[7]`
replication	untested
no type for this	forced-choice → yes-no — 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.— “Let us call the two densities fS:S and fS In this formulation the forced-choice and yes-no situations do not differ at all as far as the fundamental theorem is concerned.”	`unhoused_relations[0]`
no type for this	detectors → the paper's own definition of detection — A METALINGUISTIC SELF-CAUTION, AND THE VOCABULARY HAS NO TYPE FOR A CLAIM ABOUT A WORD. `On occasion we shall refer to certain mechanical devices as "detectors." This is a loose way of speaking, since, presumably, the occurrence of events can be said to have value only to organisms.` 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.— “On occasion we shall refer to certain mechanical devices as "detectors." This is a loose way of speaking, since, presumably, the occurrence of events can be said to have value only to organisms.”	`unhoused_relations[1]`
limitation	The theoretical curves were fitted to the data by eye rather than by a least-squares procedure.— “(The curves were fitted by eye.”	`limitations[0]`
limitation	The displacement values are only as accurate as the report's noise spectrum-level measurements, themselves accurate to about 0.8 dB.— “These values are, of course, only as accurate as our noise spectrumlevel measurements.”	`limitations[1]`
limitation	A planned statistical analysis, for which the number of runs per signal had been deliberately varied, was never completed.— “This analysis proved more lengthy than rewarding and was abandoned.”	`limitations[2]`
limitation	The zero point of the sensitivity scale is set arbitrarily, because the scale itself is stated to be unknown and abstract.— “Since we measure d' on an unknown abstract scale, it is reasonable to let this lower value arbitrarily be zero.”	`limitations[3]`
limitation	Fixing the variance at one is described as choosing a unit of measurement, not as an empirical finding.— “Picking the value unity is of no particular significance, since the scale on which H is measured is still arbitrary: letting Var(H) = 1 amounts to picking a unit of measurement on this scale.”	`limitations[4]`
limitation	The definition of the detection situation is stipulated for this report, with the author noting other formulations are possible.— “Many different formulations are possible. In this report we shall use the concept exclusively in accordance with the following definition.”	`limitations[5]`
limitation	Only some of the weaknesses identified in the existing models are claimed to be removed.— “Traditional psychophysical models and Tanner and Swets' model are critically examined. Some of the weaknesses of these models are found to be eliminable by a more sophisticated analysis in terms of detection theory.”	`limitations[6]`
limitation	The goodness-of-fit test used is stated to be inapplicable when the data points are not equally spaced.— “The data-points may not be equally spaced along the abscissa. In this case appropriate makeshift repairs may suggest themselves, or the test may be considered inapplicable.”	`limitations[7]`

Content tags

content-observations: finding · quantity · variable · definition · key-term — grounded in the full text

finding	The subjects were not ideal detectors.— “As the first item of comparison we notice, and this comes as no surprise, that our subjects were not ideal detectors.”	`content_tags.findings[0]`
finding	Once 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.— “the best-fitting curve (PFL:500 cps) accounts for 99.3 per cent of the variance in the graph; the worst-fitting curve (HF:1100 cps) accounts for 97.3 per cent”	`content_tags.findings[1]`
finding	Apart 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.— “our subjects differed from the ideal detector only to the extent of being, on the average, 13. 5 db less sensitive at the frequencies tested”	`content_tags.findings[2]`
finding	For 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.— “a very close agreement between the predicted and observed detectability; the predictions account for 96. 5 per cent of the variance”	`content_tags.findings[3]`
finding	For the 500+1100 cps signals the energy-summation prediction accounted for only 25 per cent of the variance.— “In Table 4 the agreement between predicted and observed detectability is practically nil; the variance accounted for is only 25 per cent.”	`content_tags.findings[4]`
finding	Predicting 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.— “If we do this, our predictions account for 93.5 per cent of the variance; a t-test fails to reveal any difference between the observed detectability and that of the more detectable component.”	`content_tags.findings[5]`
finding	Two-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.— “In Table 3 the agreement is still appreciable, but less than in Table 2; here the predictions account for 73. 6 per cent of the variance in column 6.”	`content_tags.findings[6]`
finding	For 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.— “Similar t-tests reveal that the difference in detectability between the two-component signal and the more detectable of the two components is highly significant in both Tables 2 and 3, indicating that in these cases the presence of the less detectable component increases the detectability of the total signal”	`content_tags.findings[7]`
finding	The 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.— “We know, therefore, that if we repeated our experiment with a noise of higher level, we should arrive again at a figure close to 13. 5 db. This refutes the hypothesis of linearly additive internal noise”	`content_tags.findings[8]`
finding	Auditory filters near 1100 cps have wider bandwidths than those near 500 cps.— “auditory filters in the neighborhood of 1100 cps have wider bandwidths than those in the neighborhood of 500 cps.”	`content_tags.findings[9]`
quantity	13 db — how much less sensitive the subjects were than the ideal detector, as stated in the abstract— “It is found that, except for being approximately 13 db less”	`content_tags.quantities[0]`
quantity	75 per cent at r = 1.4 — accuracy of the ideal detector at a signal-energy to noise-spectrum-level ratio of 1.4— “The ideal detector operates with 75 per cent accuracy when r = 1. 4.”	`content_tags.quantities[1]`
quantity	99.3 / 97.3 per cent — variance in the psychophysical data accounted for by the best- and worst-fitting displaced ideal-detector curves— “(PFL:500 cps) accounts for 99.3 per cent of the variance in the graph; the worst-fitting curve (HF:1100 cps) accounts for 97.3”	`content_tags.quantities[2]`
quantity	96. 5 per cent — variance in observed two-tone detectability (1060+1100 cps) accounted for by the total-energy prediction— “between the predicted and observed detectability; the predictions account for 96. 5 per”	`content_tags.quantities[3]`
quantity	73. 6 per cent — variance accounted for by the total-energy prediction for the 500+540 cps pair— “less than in Table 2; here the predictions account for 73. 6 per cent of the variance in column 6.”	`content_tags.quantities[4]`
quantity	25 per cent — variance accounted for by the total-energy prediction for the 500+1100 cps pair— “In Table 4 the agreement between predicted and observed detectability is practically nil; the variance accounted for is only 25 per cent.”	`content_tags.quantities[5]`
quantity	93.5 per cent — variance accounted for when the 500+1100 cps two-tone detectability is predicted from the more detectable component alone— “If we do this, our predictions account for 93.5 per cent of the variance; a t-test fails to reveal any difference between the observed detectability and that of the more detectable component.”	`content_tags.quantities[6]`
quantity	61 — total number of signals whose detectability was measured— “and fifteen complex signals were used. All in all, then, the detectability of each of 61”	`content_tags.quantities[7]`
quantity	810 — total number of experimental runs made— “In all, 810 runs were made.”	`content_tags.quantities[8]`
quantity	two — subjects, both male MIT students, on whom all measurements were replicated— “Subjects. All measurements were replicated on each of two subject (HF and PFL).”	`content_tags.quantities[9]`
quantity	180 trials / 10 minutes — length of a single run, each trial lasting 3 1/3 seconds— “The duration of a trial was 3 1/3 seconds, a run of 180 trials thereby lasting 10”	`content_tags.quantities[10]`
quantity	-66 db — measured noise spectrum-level near 500 and 1100 cps, accurate to about 0.8 db— “the noise spectrum-level was found to be (to approximately 0.8 db) -66 db in the neighborhood of 500 cps and 1100 cps.”	`content_tags.quantities[11]`
variable	detectability (dependent)— “The experiments consisted in the measurement of the detectability of auditory signals in the presence of noise.”	`content_tags.variables[2]`
definition	detectability— “response, is called the detectability.”	`content_tags.definitions[0]`
definition	ideal detector— “A detector behaving in accordance with the decision procedure will be called "an ideal detector".”	`content_tags.definitions[1]`
definition	symmetrical payoff matrix— “A payoff matrix for which Eq. 4. 1 holds will be called symmetrical.”	`content_tags.definitions[2]`
definition	two-category forced-choice method— “In the two-category forced-choice method there are on each trial two observationintervals, during one and only one of which the signal occurs”	`content_tags.definitions[3]`
definition	uniform gaussian noise— “3 to * By a uniform gaussian noise we mean a time-function whose distribution of instantaneous amplitudes is gaussian (normal) and whose power-spectrum is uniform over a given range and zero outside that range.”	`content_tags.definitions[4]`
definition	equivalent rectangular bandwidth— “The equivalent rectangular bandwidth of a bandpass filter F 1 whose gain-versus-frequency characteristic exhibits a maximum at frequency fo shall be the difference in cycles per second between the upper and lower cutoff frequencies of a bandpass filter F2”	`content_tags.definitions[5]`

Concepts

terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.

concept	d'— “Since we measure d' on an unknown abstract scale”	`concepts[0]`
concept	detectability— “the probability of a correct response, is called the detectability.”	`concepts[1]`
concept	detection situation— “In order to understand this, let us examine in a general way what we mean by a detection situation. Many different formulations are possible. In this report we shall use the concept exclusively in accordance with the following definition.”	`concepts[2]`
concept	forced-choice method— “the two-category forced-choice technique is found to be particularly advantageous on theoretical grounds”	`concepts[3]`
concept	detection theory— “Some of the weaknesses of these models are found to be eliminable by a more sophisticated analysis in terms of detection theory.”	`concepts[4]`
concept	traditional psychophysical models— “Traditional psychophysical models and Tanner and Swets' model are critically examined.”	`concepts[5]`
concept	subject's criterion — not defined in this paper's own words; the name given to the model's central-tendency term c - and the paper immediately warns that naming a parameter psychologically invites the expectation that it will vary between experiments— “In the criterion approach, 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.”	`concepts[6]`
concept	detectors — not defined in this paper's own words; used of mechanical devices, and disowned in the same breath: on the paper's own account only organisms can detect, because detection is defined through VALUE— “On occasion we shall refer to certain mechanical devices as "detectors." This is a loose way of speaking, since, presumably, the occurrence of events can be said to have value only to organisms.”	`concepts[7]`
concept	value — not defined in this paper's own words; fixed by ANALOGY rather than by definition - the ordinary sense in which gold is worth more than silver, not a technical utility— “The term "value" is used in the sense in which it is said that gold has greater value than silver.”	`concepts[8]`

Statistics — cross-field join keys

field-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.

t-test	as written: the t-test technique— “*No difference in detectability between 500 cps and 540 cps nor between 1060 cps and 1100 cps could be found by the t-test technique.”	`content_tags.statistics[0]`
least squares	as written: a least-squares method for fitting the curves— “a least-squares method for fitting the curves been applied, the percentage of variance”	`content_tags.statistics[1]`
proportion of variance explained	as written: accounts for 99.3 per cent of the variance— “(PFL:500 cps) accounts for 99.3 per cent of the variance in the graph; the worst-fitting”	`content_tags.statistics[2]`

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Detection theory and psychophysics — TEI-tagged view

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