Task 2 Flashcards
Signal detection theory
- Provides general framework to describe & study decisions that are made in uncertain
ambiguous situations - Method for measuring system’s ability to detect patterns/stimuli/signals in info
- Despite background noise
- Starting point of theory: nearly all decision making takes place in presence of some
uncertainty
Signal
- Is the stimulus presented to pp
Noise
everything else besides signal
- Noise is always present
- Noise can sometimes be mistaken for signal
external noise
- Many possible sources of ext. noise
internal noise
-neural responses can be noisy, even if stimulus was exactly the same each trial
Signal and noise distribution
Left probability distribution:
- Represents prob. that given perceptual effect will be caused by noise (N)
Right prob. distribution:
- Represents prob. that given perceptual effect will be caused by signal plus noise (S+N)
-Prob. distribution tell us what the chances are that given loudness of tone is due to (N) or due to (S+N)
Left curve:
- For the noise-alone trials
Right curve:
- For the signal-plus noise trials
Height of each curve -represents how often that level of internal response will occur
- But: there will be some trials with more (or less) internal response
- Because of internal & external noise - The curves overlap:
- Meaning that the internal response for noise-alone trial may exceed internal response for signal-plus noise trial
Hits/ false alarms / correct rejection / misses
Hit: saying yes when stimulus is present
Miss: saying no when stimulus is present
False Alarm: saying yes when stimulus is not present
Correct rejection: saying no when stimulus is not present
liberal vs conservative criterion
Liberal criterion: -Choosing low criterion:
- Respond ‘yes’ to almost everything
- Never miss a signal when present
- Have very high hit rate
- But: also increases nr. of false alarms
Conservative criterion:
-Choosing high criterion:
- Respond ‘no’ to most signals
- Rarely make false alarms
- But will also miss many hits (correct signal w/ yes response)
signal strength
- if signal is increased → pps internal response strength will be stronger
- Shifting the probability density function for signal-plus-noise trials to the right
- Thus: further away from the noise-alone probability density
- When signal is stronger → less overlap btw the 2 curves
- Then: choice making is easier & can pick criterion to get nearly perfect hit rate w/ almost no false alarms
payoffs
We can cause pp to adopt diff. criteria by means of diff. payoffs
- Thus: you can cause pps to change their percentage of hits & FAs w/out changing
intensity of stimulus
d´
-Discriminability of a signal depends on separation & spread of noise.alone & signal-plus-noise curves
-Can be calculated by comparing experimentally determined ROC curve to standard ROC curve
- Or it can be calculated from proportions of hits & FAs
- Calculating d’ enables us to determine pp’s sensitivity by determining only 1 data point on
ROC curve
⇒ Thus: Allows for use of SDprocedures w/ou large nr. of trials - strength of the signal
beta
- Response bias
- Ratio of neural activity produced by signal and noise ar Xc → 𝛽 = 𝑃(𝑋𝐼𝑆)/ P(XIV)
- Ratio of the height of the two curves
- Measure of response bias -> how willing is the participant to say the signal was present
- As Criterion gets larger ß gets larger and participant gets more conservative
- As Criterion gets smaller ß gets closer to 0 and participant is said to be more liberal
- 𝛽 < 1 - liberal values
- 𝛽=1-unbiased
- 𝛽 > 1 - conservative values
- Shifting Xc to right –> beta gets bigger than 1 –> fewer hits and fewer false alarms
optimal beta
- defines where beta should be set and is determined by the ratio of the probability with which noise and signals occur in the environment
- Optimal performance will occur when Xc is placed at the intersection of the two curves, that is when beta is 1 → any other placement would reduce the probability of being correct
sluggish beta
- When beta is not adjusted as much as it should be
making and reading a ROC curve
1) Calculate: peobability that “yes” is above or given score/threshold would be correct for new patient
2) Plot for each potential threshold:
-Rate of hits (true positives) against rate of false alarms (false postive)
3) Check for accuracy:
-Curve bows more to left -> greater accuracy
–> accuracy: defined by amount of area under the curve (AUC)
If accuracy acceptable:
-select threshold for diagnosis (yes/no)
- Threshold should have good rate of true positives (hits) without having
unacceptable rate of false positives (false alarms)
-Each point on curve -> represents threshold
- stricter thresholds at bottom left
- most lenient threshold at top right
