L3:
Outline the learning objectives of cog psych lecture 3: perception/ psychophysics
- Use common psychophysical terms (the psychophysical function, just noticeable difference, weber fraction, psychometric function)
- Apply signal detection theory to relevant examples (SDT; false alarms, hits, misses, correct rejections, sensitivity and bias, criterion)
- Calculate and interpret d’ and bias
- Interpret ROC curves
- Understand the relation between SDT and qualities of statistical tests (power, alpha)
L3:
LO1: What is the psychophysical/ psychometric function?
This is where you have the stimulus magnitude (e.g. the heaviness of a weight, as physical intensity) as compared to magnitude estimate (how heavy it feels, a psychological intensity).
The line is curved, so, for example, looking at weight, the heavier an object becomes, the more weight needs to be added to notice a difference.
L3:
LO1: What is the just noticeable difference?
The just noticeable difference is the amount something must be changed in order for a difference to be noticeable or detectable at least half the time.
L3:
LO1: What is the Weber Law/ Fraction?
Weber’s Law states that the just noticeable difference (JND) is a constant proportion of the stimulus intensity.
Rephrased:
The law states that the change in a stimulus that will be just noticeable is a constant ratio of the original stimulus.
So... for taste, this is 1/5 for brightness, this is 1/60 for pitch, this is 1/333 etc etc
L3:
What is psychometrics?
It’s how you measure the psychological quality
(Relevant when you want to assess, measure, count or quantify something psychological)
This serves to make ensure reliability, consistency and accuracy of data, results etc
Methods mainly developed for use in the field perception but it is also used elsewhere e.g. discriminating frequency of sound tones or how high someone measures on anxiety questionnaire
L3:
What is the perceptual threshold?
This is the difference is psychological intensity (estimated magnitude) at which absence or presence can be noticed/ perceived.
Interested in people judging the presence or absence of something, whats the physical change on the x axis that will change their response on the y axis from “no, there’s no difference” to “yes, there is a difference”
L3:
Psychometric Functions
A graph of responses - “psychometric function is an inferential model applied in detection and discrimination tasks. It models the relationship between a given feature of a physical stimulus, e.g. velocity, duration, brightness, weight etc., and forced-choice responses of a human test subject”
People’s responses are probabilistic, not completely certain, sometimes people spot quietest sound and miss the loudest sound. On a graph we see a smooth change between something they probably won’t hear and something they probably will.
L3:
Sensitivity and Bias
Perceivers’ sensitivity can be distinguished from their bias.
Sensitivity is your ability, bias is your prejudice to respond in a certain way or not e.g. bias toward responding yes.
Bias depends on instructions, personality, pay-offs etc
*Bias is separate from ability to distinguish differences
L3:
Perceptual thresholds in more detail
Recap: This is the difference is psychological intensity (estimated magnitude) at which absence or presence can be noticed/ perceived.
Perceptual thresholds can differ…
More sensitive:
- When stimulus quiet, can’t hear, when really loud say they can, still switch between but switch is sharper, more reliable results, very sharp curve
- For a stimulus just on the threshold they are still 50%, the same as the person who is less sensitive, their bias hasn’t changed
Less sensitive:
- Someone who is less sensitive, response curve is flatter, quiet stuff say they can’t hear, really loud stuff say they can hear, but person is still a bit sensitive, less sharp discrimination
Different bias, same sensitivity:
- Someone who has same sensitivity (ability to discriminate) but they are much more cautious, line on graph shifted to the right, less likely to say yes unless they are very confident - can be bias in favour of responding or against
L3:
LO2: Signal detection theory
Relevant to any domain where you, a detector, want to make a judgement about a signal
- 4 fundamental categories of response (stimulus: present/absent, judgement; hit/ miss)
- Get them by combining your response (yes/no, loud/quiet, present/absent) with the state of the world
- Origins of SDT in radar, you have to look and say are there planes or not
- Fundamental for how good you are at a task, you want to get hits and correct rejections, want to minimise false alarms and misses
L3:
LO2: Signal detection theory –> underlying mechanism
- Idea is that inside yourself there is signal noise (just like there’s electrical noise in a radar machine) in the own intensity of your perceptions
- Stimulus may be exactly the same quality of tone every time, but inside neural signals there is noise, sometimes you get strong response, other times week response (to the same noise)
- (graph 1) (Target present) Strength of internal response varies with noise, shape of noise is normal distribution
- May be a beep, part of brain that says you heard a beep, but how strongly it responds varies
- (graph 2) (Target absent) Even when there is no physical stimulus there is an internal signal reporting the strength
- distribution of internal response, when target is present can be weaker or stronger, when stimulus is weak internal response is weak as it should be, when internal response is at its strongest that’s what generates the false alarm, the internal response is at its weakest that’s what generates miss, the physical stimulus is there but the corresponding internal response is not
- (graph 3) Don’t get to see this distribution, you think you heard something, have to judge whether you did or not, use criterion (internal threshold) if it’s above say yes, if below you say no, if your two internal distributions (target present and target absent) overlap , then this makes a false alarm response. Some trials will be so weak, is below criterion, make a miss
This is the underlying mechanism that helps us understand SDT, logic behind how we are going to understand why sensitivity and bias is different and how experimentally we can disambiguate these two things
- (graph 4) When we have an easy judgement to make the internal signals are further apart, there is still noise, it never goes away, but if you are an accurate perceiver or trying to tell the difference between stimulus, easy judgement/loud stimulus is going to trigger an internal signal well above your criterion
L3:
LO2: Signal detection theory –> Hard judgement
- In a hard/difficult judgement the two distributions overlap broadly, if the stimulus is really weak or there is lots of noise, doesn’t matter where you put criterion you will always make error, nearly 50-50 mix of false alarms and misses
- Blue line, internal response when there’s no signal e.g. walking a dark road and having an internal response to noise that wasn’t there
- If you don’t want any false alarms you move the criterion to the right so that the blue distribution is to the left but when you do this you will make more misses because it is a harder judgement and harder to detect whether or not the target is present
- Don’t get to make perfect decisions because there’s noise in the system, have to make trade-off for fewer false alarms for some misses or more misses and fewer false alarms
- impossible to imagine that we could be perfectly noiseless signal detectors
- Skewed distributions – different proportions of false alarms
- Criterion is the threshold against which you judge the internal signal, say yes you saw or no you didn’t by saying is it above or below the criterion (threshold)
L3:
LO2: Signal detection theory
Sensitivity and Bias (SDT definitions)
- Sensitivity: Separation of underlying present/absent distributions
- Bias: Where you put the criterion
- Criterion - NOT THE STIMULUS it’s the threshold against which you judge the internal signal, from which you decide whether or not you heard something
L3:
LO2: Signal detection theory and police lineups
Eyewitness Identification: American Judicature Society
- Simultaneous presentation: 6 pack line-ups (6 photos), got witness to crime, someone you think might have committed crime, show witness line up of 5 people who aren’t the target, they are absent of having been seen before, have one person who is target, ask witness to identify who committed crime
- Can have 6 random people who didn’t commit the crime OR 5 and 1, same fundamentals of SDT but seeing if witness can really identify a criminal rather than a noise
Sequential Presentation:
- Same 6 photos, target is either present or absent from photos, witness goes through, decides if they can identify person who committed crime
L3:
LO2: Signal detection theory and police lineups
Which method is better?
- If you show photos one at a time people are less likely to misidentify criminal (Lindsay & Wells (1985) –> lower false alarm rate with sequential presentation
- 2006 International Association of Chiefs of Police recommends sequential presentation
- Of 15000 US police departments 5000 switched to sequential presentation
- -> ALL WRONG
- Easy to generate fewer false alarms you just tell people to be more cautious, doesn’t show people are better or worse at identifying criminals, change of procedure is not enough to support that sequential presentation is better, evidence is actually that they are about the same or maybe sequential is slightly better
If you want to say one is better you need to consider false alarms and hits together, does procedure increase sensitivity or change bias?
L3:
LO3: d’ explanation
What is d’?
d’ = d prime, a statistic you can calculate that gives you measure of sensitivity (combines hit and false alarms)
- Separation between the 2 distributions, how sensitive receiver is or how hard task is
- When d’ is big, distributions far apart, rarely make mistake, when d’ is small distributions are close together, make a lot of mistakes
- If you’re asking whether a task is easier or harder, need to consider both hits and false alarms simultaneously - d’ is not subject to changing criterion/ threshold
- Calculating d’ gives you method for doing this
d’ = Z(hits) – Z(FAs)
- Z is a function, converts a number into another number, in: a proportion between 0 and 1, out: a number between -infinity and +infinity (DONT NEED TO KNOW HOW OR WHY)
Examples:
- the Z of 0.1 = -1.28
- Z (0.5) = 0
- Z (0.9) = +1.28
L3:
LO3: d’ Worked examples
***Scenario 1: ‘simultaneous presentation case’
If the hit rate is 0.68%, false alarm rate is 0.35%
Z (0.68) = 0.47
Z (0.35) = -0.39
What is d’?
d’ = Z(hits) – Z(FAs)
d’ = 0.86
…because 0.47 - -0.39 is 0.47 + 0.39 = 0.86
d’ is bigger, rarely make mistake but still make few
right 2/3rd of a time, wrong 1/3rd
***Scenario 2: ‘sequential presentation case’ Hits = 50% False alarms = 0.17% Z (0.50) = 0.00 Z (0.17) = -0.81
What is d’?
d’ = 0.81
right 50% time, wrong 17%
First Scenario is better, d’ is bigger. Would conduct this for two conditions (e.g. (simultaneous and sequential presentation) and compare d’ in order to identify how sensitive receiver is. This is what people do when there are different conditions with different proportions of hits and false alarms, are you getting better or is sensitivity staying the same and just your criterion is changing
L3:
LO4: ROC Curves: (Receiver Operator Characteristics)
- Graph of where you are in the hit vs false positive space
- number of false positives on x axis
- number of hits on y
move along curve if you change criterion (threshold), more likely to make hits but also false alarms - Point A, not many hits, not many false alarms
- Point C, lots of hits, lots of false alarms
- No better at task, you’re not more sensitive you’ve just changed your bias
- d’ is distance you are from having a straight line, you ideally want a really wide angle curve (bigger d’) where you don’t make many false alarms but you can get lots of hits
SEE IMAGE
> MUST KNOW
- Different curves = different levels of sensitivity
- Difference between different points for the same bias
L3:
LO5: Relation between SDT and qualities of statistical tests (power, alpha)
Trade offs in psychology, see image
