Calculation ofsignal detectiontheory measures
CALCULATION OF SIGNAL DETECTION THEORY MEASURES 139 always be exceeded on signal trials This will produce mostly yes responses and a high hit rate However, the cri terion will also be exceeded on most noise trials, resulting in a high proportion ofyes responses on noise trials (i e , a high false-alarmrate) Thus, a liberal criterion biases the
Calculation of signal detection theory measures
Signal detection theory (SDT) is widely accepted by psychologists; the Social Sciences Citation Indexcites over 2,000 references to an influential book by Green and Swets (1966) that describes SDT and its application to psychology Even so, fewer than half of the studies to which SDT is applicable actually make use of the theory (Stanislaw
Sensitivity and Bias - an introduction to Signal Detection
Signal Detection Theory (SDT) offers a framework and method for doing this, and in general for distinguishing between the sensitivity or discriminability (d') of the observer and their response bias or decision criterion (C) in the task
Introduction to Detection Theory
Introduction to Detection Theory (cont ) We wish to make a decision on a signal of interest using noisy measurements Statistical tools enable systematic solutions and optimal design Application areas include: • Communications, • Radar and sonar, • Nondestructive evaluation (NDE) of materials, • Biomedicine, etc
J A MATLAB Radar Range Equation and Probability of Detection
and the signal-to-noise ratio of power is defined as SNR = Al (4) Figure 3 Linear detector *G V Trunk, Detection and Estimation Theory Handbook, notes for Johns Hopkins course 525 728, p 60 +R N McDonough and A D Whalen, Detection of Signals in Noise, 2d edition, Academic Press, 1995, pp 159-166
20 RADAR RANGE EQUATION
the things it impacts, like detection theory, matched filters and the ambiguity function 2 2 BASIC RADAR RANGE EQUATION One form of the basic radar range equation is 2 3 4 4 0 S T T R N n P P G G SNR P R kT BF L (2-1) where SNR is termed the signal-to-noise ratio and has the units of watts/watt, or w/w P S
Chapter 7 Single-SidebandModulation(SSB) andFrequency
signal m(t) is band limited with a cutoff frequency W which is less than the carrier frequency ωc Then the required channel bandwidth for an SSB signal is W ☞ m(t) A ccosω ct × H(ω) a(t) s(t) Figure 1: SSB Modulator Using DSBSC-AM and Filtering 7-2
BBASICS AND THEORYASICS AND THEORY - Minelab
The received signal is usually processed by the electronics to produce at least 2 signals: the strength of one signal is proportional to the R signal strength or magnitude, but is no longer an alternating signal Similarly, the other signal is also not an alternating signal, but rather a signal simply related to X signal strength or magnitude only
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Behavior Research Methods, Instruments,&Computers
1999,3/(I),/37-149
HAROLDSTANISLAW
andNATASHATODOROV
Signaldetectiontheory (SDT)may be applied to anyarea ofpsychology in which two different types ofstimuli must be discriminated. Wedescribe several ofthese areas and the advantagesthatcan be re alizedthroughthe application of SDT.Three of the mostpopulartasks used to study discriminability are then discussed,togetherwith themeasuresthatSDTprescribesfor quantifyingperformancein these tasks. Mathematicalformulae for themeasuresarepresented,as aremethodsfor calculating the measureswith lookup tables,computersoftware specificallydeveloped for SDTapplications,and gen eralpurposecomputersoftware(includingspreadsheetsandstatisticalanalysis software).Signaldetectiontheory (SOT) iswidelyacceptedby
psychologists;theSocialSciencesCitationIndexcites
over 2,000referencesto an influential book by Green andSwets (1966)thatdescribes
SOT and itsapplicationto
psychology.Even so, fewerthan halfofthe studies towhichSOTisapplicableactuallymakeuse
ofthetheory (Stanislaw &Todorov, 1992). One possible reason for this apparent underutilization ofSOT is that relevanttextbooksrarely describe themethodsneeded toimplementthe theory. A typical example isGoldstein's(1996)popularperception textbook, which concludes a nine-page description ofSOT with thestatementthat measuresprescribedby SOT "can becalculated ...by meansofamathematicalprocedure we will not discuss here" (p. 594).The failure
ofmany authors to describe SOT's methods may havebeen acceptable when lengthy,specializedtables wererequiredtoimplementthe theory. Today, however, readily availablecomputersoftware makes an SOT analy sis no moredifficultthan a ttest. Thepresentpaper at tempts todemonstratethis and to render SOT available to a larger audience than currently seems to be the case.We begin with a
briefoverviewofSOT,includinga description ofitsperformancemeasures. We then present the formulae needed to calculate these measures. Next,we describe different methods for calculating SOT measures. Finally, weprovidesamplecalculationsso thatreaders can verify theirunderstandingandimplementationofthe techniques. Weare indebted to James Thomas, Neil Macmillan, John Swets, Doug lasCreelman,ScottMaxwell,MarkFrank,HelenaKadlec,and an anonymousreviewer for providing insightfulcommentson earlier ver sions ofthismanuscript.We alsothankMackGoldsmithfortesting some article should beaddressedto H. Stanislaw,Department ofPsychology, CaliforniaState University, Stanislaus, 801 West Monte Vista Avenue, Turlock, CA 95382 (e-mail:hstanisl@toto.csustan.edu).OVERVIEWOFSIGNAL
DETECTIONTHEORY
Proper applicationofSOT requires an understanding of thetheoryand themeasuresitprescribes.We present an overview ofSOT here; for more extensive discussions, see Green andSwets(1966)orMacmillanandCreelman (1991). Readers who are already familiar with SDT may wish to skip this section.SOT can beapplied whenevertwopossiblestimulus
types must be discriminated. Psychologists first applied the theory in studies ofperception,where subjects discrimi nated between signals(stimuli) andnoise(no stimuli). The signal and noise labels remain, but SOT has since been ap pliedin manyotherareas.Examples(andtheircorre spondingsignal and noisestimuli)includerecognition memory (old and new items), lie detection (lies and truths),personnel selection (desirable and undesirable applicants),jurydecisionmaking(guiltyandinnocentdefendants),
medical diagnosis (diseased and well patients), industrial inspection(unacceptableandacceptableitems), and in formationretrieval (relevant andirrelevantinformation; see also Hutchinson, 1981; Swets, 1973;and the extensive bibliographiescompiled by Swets, 1988b, pp.685-742).