Signal detection theory
Theory
--> percentage of htis and false alarms depend on criterion
--> persons sensitivity can be shown by roc curve
Terms
Signal + Noise
Probability Distribution
--> depends on subjective perceived loudness of subjects
--> sound intensity is always the same, just subjective experience changes
Criterion (Xc)
--> if perceived effect (signal) > than criterion (to the right of it) = "Yes I perceived
--> if perceived effect (signal < than cirterion (to the left of it) = "No i did not perceive"
receiver operator characteristic (ROC)
--> used to make sure the signal is perceived the same by everyone / everyone equally sensitive to signal
--> persons sensitivity to signal is shown by ROC curve shape
Responders
conservative
---> only says detection if very sure
--> lots of misses
--> many correct rejections
liberal
--> says detection even if unsure
--> lots of hits (cause low threshold for saying yes)
--> lots false positives / alarms
response criterion
--> difference between these two responses (one - the other)
.
Psychophysical vs signal detection
--> example of sound detection
Psychophysics
--> multiple sounds at different loudness levels presented to find threshhold
--> assumes threshold constant, which its not as shown by ROC curves where its manipulated through payoff manipulation #
signal detection
--> only one hard to hear tone
--> sometimes presented, sometimes not
Outcomes
Hit
--> saying yes if stimulus present
--> probability = Hit / total signals presented
#
Miss
--> saying no when stimulus actually present
correct rejection
--> correctly saying no, when no stimulus there
Created by adjusting participants criterion through payoffs/rewards!!
--> adjusted 3 ways
--> level of signal = kept same
--> if not adjusted, differences in test results migh tjsut be because different criterions or differences in focus of attention or ear adjustements! (see above under loudness)
high reward for hit rate
high reward for correct rejection
equal reward for all (hit, miss, false alarm, correct rejection)
Important if all points fall on the curve they each have same sensitivity to the tone !!
Signal = stimulus
-->for example: a tone
--> Presented as Signal + Noise (S+N)
Noise = all other stimulie
--> might be perceived as signal
--> Presented as just Noise (N)
Noise = always present
--> in some trials a signal is simply added :3 !!
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click to edit
Perceived loudness
--> left = only noise
--> middle where overlap = equal
---------> difficult zone
--> right = high probability of Signal (+noise)
Liberal
--> position far in Noise Curve
-----> high hit
-----> high false alarm
Conservative
--> positioned far in S+N curve
--> small hit rate (cause only little of S+N curve on right of criterion)
--> almost no false alarms (as no N curve on right of criterion)
--> high correct rejections
Neutral
--> positioned exactly in middle of overlap of N vs S+N
--> Hit and false alarm = equal (but on low side)
Distance (d`) between a persons peaks (of N and S+N) indicate sensitivity of person to stimulus and is reflected on ROC curve !!
Sensitivity example
Low sensitivity
High sensitivity
Loudness
= subjective hearing of the actual sound
—> shifts with attention for example or changes in autidtory system, even though intensity = always same!! #
Sound intensity
= physical loudness of tone
D' = Zscore of Probability of hit - Zscore of probability Fasle positive
- -----> d' > 0 <-- good sensitivity
- -----> d' = 0 <-- N and S+N courves cpmpletely overlap, ppl just guessing
- -----> d' < 0 <-- good sensitivity but got instructions the wrong way round lol[
Increased by:
- making signal stronger
- signal curve moves further to the right)
- person more sensitive to signal
- reducing variability in noise
- overlap reduces and both distributions become more peaked :3 !!) eg. see course manual
BETA (wickens ereader)
--> Height / value of the probability distributions of the Noise and Noise + Signal distribution at the CRITERION :3 !!
--> information about strategy choosen
--> depends on Criterion #
Conservative = Bigger beta for (S+N)
--> smaller for Noise (cause criterion moved far into S+N curve , so N curve is probably just the small end of the curve of the N curve, so the height is low)
Liberal = small beta for (S+N)
--> bigger beta for Noise (cause criterion far to the left in noise curve, so the height of noise curve is high, while only the slope of (S+N) curve touches it, thus lower hight for it :3 !!
Evidence (wickens ereader)
--> whatever the person perceives, perceived value of the signal / stimulus / how strongy tehy perceive ti
--> depends on many things like attention, changes in auditory system #
sensitivity = true positive = hits
specificity = true negative = correct rejection
false positives = false alarms
false negative = miss
ratio of probabilities of noise and signal plus noise at the criterion ... but check again cause better in different words :3 !!
--> hight of criterion for S+N vs height of criterion for just N (noise)
Ratio between the heights = Beta
y(zscore of probability of hit) / y (zscore of probability of false alarm)
---> actually calculation ratio of hit/false alarm :D!! (thing statistics about ratios/odds :)!!
= same as
y(zscore of signal + noise) / y(zscore of probability noise)
Optimum BETA = (correct rejections + false alarms / hits + miss) * (1- probability of signal / probability of signal :3 !! )
SO can also be like this (correct rejections + false alarms / hits + miss) * (1- probability of hit / probability of hit :3 !! )
or like this: (correct rejections + false alarms / hits + miss) * (Noise / probability of signal :3 !!)
--> 1-Signal ; is same as 1- probability of hit ; is same as probability of false alarms ; is same as N; (N = Noise )
sluggish beta = ppl don't adjust their beta as would make most sense (game theory)
criticism:
--> the curves are never the same cause variation / spread si different
D' = seperation (actual d'calculation) /spread