Detection theory and psychophysics

Detection theory and psychophysics Marill

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Detection theory and psychophysics 1956 marill1956-detection-theory-and-psychophysics marill1956-detection-theory-and-psychophysics.txt, the project's staged copy 60621f6ee5af993eef4eaf16bc7b28d649dde324 open-access psychophysics

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them method Quotation withheld because this record is not cleared for redistribution. auditory signal detection in gaussian noise Quotation withheld because this record is not cleared for redistribution. behavioural-experiment behavioural-experiment Quotation withheld because this record is not cleared for redistribution. mechanisms 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. Quotation withheld because this record is not cleared for redistribution. mechanisms 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. Quotation withheld because this record is not cleared for redistribution. mechanisms 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. Quotation withheld because this record is not cleared for redistribution. The theoretical curves were fitted to the data by eye rather than by a least-squares procedure. what this limits: every parameter read off the theoretical curves: THE CURVES WERE FITTED BY EYE Quotation withheld because this record is not cleared for redistribution. The displacement values are only as accurate as the report's noise spectrum-level measurements, themselves accurate to about 0.8 dB. what this limits: the displacement values: THESE VALUES ARE, OF COURSE, ONLY AS ACCURATE AS OUR NOISE SPECTRUM-LEVEL MEASUREMENTS Quotation withheld because this record is not cleared for redistribution. A planned statistical analysis, for which the number of runs per signal had been deliberately varied, was never completed. 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 Quotation withheld because this record is not cleared for redistribution. The zero point of the sensitivity scale is set arbitrarily, because the scale itself is stated to be unknown and abstract. 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 Quotation withheld because this record is not cleared for redistribution. Fixing the variance at one is described as choosing a unit of measurement, not as an empirical finding. 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 Quotation withheld because this record is not cleared for redistribution. The definition of the detection situation is stipulated for this report, with the author noting other formulations are possible. what this limits: the detection situation as a standard construct: the report stipulates one of several possible formulations for its own use Quotation withheld because this record is not cleared for redistribution. Only some of the weaknesses identified in the existing models are claimed to be removed. what this limits: detection theory as resolving the criticisms of earlier models: the abstract claims only some weaknesses are eliminable Quotation withheld because this record is not cleared for redistribution. The goodness-of-fit test used is stated to be inapplicable when the data points are not equally spaced. what this limits: the fit test on unequally spaced data: the report says makeshift repairs may be needed or the test considered inapplicable Quotation withheld because this record is not cleared for redistribution. Introducing 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 because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. every measurement replicated on each of two subjects, HF and PFL 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 Quotation withheld because this record is not cleared for redistribution. d' d' Quotation withheld because this record is not cleared for redistribution. detectability detectability Quotation withheld because this record is not cleared for redistribution. detection situation detection situation Quotation withheld because this record is not cleared for redistribution. forced-choice method forced-choice method Quotation withheld because this record is not cleared for redistribution. detection theory detection theory Quotation withheld because this record is not cleared for redistribution. traditional psychophysical models traditional psychophysical models Quotation withheld because this record is not cleared for redistribution. subject's criterion subject's criterion Quotation withheld because this record is not cleared for redistribution. detectors detectors Quotation withheld because this record is not cleared for redistribution. value value Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. detectors → the paper's own definition of detection 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. Quotation withheld because this record is not cleared for redistribution. d' - a sensitivity measure on an unknown abstract scale, whose zero point is assigned by convention rather than measured Quotation withheld because this record is not cleared for redistribution. detectability - the name given to the probability of a correct response, not to a property of the observer alone Quotation withheld because this record is not cleared for redistribution. threshold - a momentary quantity treated as a random variable, taking a different value on each trial Quotation withheld because this record is not cleared for redistribution. `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 because this record is not cleared for redistribution. `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 because this record is not cleared for redistribution. `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 because this record is not cleared for redistribution. contradicts → Tanner and Swets' model and traditional threshold/criterion psychophysical models Quotation withheld because this record is not cleared for redistribution. builds-on → Peterson and Birdsall (15) Quotation withheld because this record is not cleared for redistribution. extends → Fletcher's critical-band theory Quotation withheld because this record is not cleared for redistribution. detection theory —contrasted-with→ traditional psychophysical models detection theory traditional psychophysical models 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. Quotation withheld because this record is not cleared for redistribution. t-test t-test Quotation withheld because this record is not cleared for redistribution. least squares least squares Quotation withheld because this record is not cleared for redistribution. proportion of variance explained proportion of variance explained Quotation withheld because this record is not cleared for redistribution. The subjects were not ideal detectors. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. For the 500+1100 cps signals the energy-summation prediction accounted for only 25 per cent of the variance. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. Auditory filters near 1100 cps have wider bandwidths than those near 500 cps. Quotation withheld because this record is not cleared for redistribution. detectability detectability Quotation withheld because this record is not cleared for redistribution. ideal detector ideal detector Quotation withheld because this record is not cleared for redistribution. symmetrical payoff matrix symmetrical payoff matrix Quotation withheld because this record is not cleared for redistribution. two-category forced-choice method two-category forced-choice method Quotation withheld because this record is not cleared for redistribution. uniform gaussian noise uniform gaussian noise Quotation withheld because this record is not cleared for redistribution. equivalent rectangular bandwidth equivalent rectangular bandwidth Quotation withheld because this record is not cleared for redistribution. detectability detectability Quotation withheld because this record is not cleared for redistribution. 13 db — how much less sensitive the subjects were than the ideal detector, as stated in the abstract Quotation withheld because this record is not cleared for redistribution. 75 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 because this record is not cleared for redistribution. 99.3 / 97.3 per cent — variance in the psychophysical data accounted for by the best- and worst-fitting displaced ideal-detector curves Quotation withheld because this record is not cleared for redistribution. 96. 5 per cent — variance in observed two-tone detectability (1060+1100 cps) accounted for by the total-energy prediction Quotation withheld because this record is not cleared for redistribution. 73. 6 per cent — variance accounted for by the total-energy prediction for the 500+540 cps pair Quotation withheld because this record is not cleared for redistribution. 25 per cent — variance accounted for by the total-energy prediction for the 500+1100 cps pair Quotation withheld because this record is not cleared for redistribution. 93.5 per cent — variance accounted for when the 500+1100 cps two-tone detectability is predicted from the more detectable component alone Quotation withheld because this record is not cleared for redistribution. 61 — total number of signals whose detectability was measured Quotation withheld because this record is not cleared for redistribution. 810 — total number of experimental runs made Quotation withheld because this record is not cleared for redistribution. two — subjects, both male MIT students, on whom all measurements were replicated Quotation withheld because this record is not cleared for redistribution. 180 trials / 10 minutes — length of a single run, each trial lasting 3 1/3 seconds Quotation withheld because this record is not cleared for redistribution. -66 db — measured noise spectrum-level near 500 and 1100 cps, accurate to about 0.8 db Quotation withheld because this record is not cleared for redistribution.

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