lecture 2 - SDT

Question 1

what kind of data does SDT use

Answer 1

• choice data to model how choices are being made
• binary outcomes: yes/no questions

Question 2

modeling in SDT

Answer 2

• uses hit- and false alarm rates to model an underlying sensitivity and decision criterion

Question 3

biases

Answer 3

1. conservative
2. liberal

• response biases (proportion of answering yes/no) tells us something about these underlying biases (liberal/conservative)

Question 4

conservative criterion

Answer 4

• positive shift in c
• more likely to say no signal was seen
• leads to more misses

Question 5

liberal criterion

Answer 5

• negative shift in c
• more likely to say a signal was detected
• leads to more false alarms

Question 6

accuracy

Answer 6

• accuracy in SDT is not just about seeing a signal, but is influenced by personal biases
• the observer’s criterion can affect their accuracy
• accuracy is therefore distinct from sensitivity

Question 7

internal response distribution

Answer 7

• there are two internal probability distributions representing an underlying explicit concept: noise or signal
• the variances of these distributions are assumed to be the same

Question 8

x-axis of the internal response distribution

Answer 8

• represents the strength of the internal response
• low values are likely under the noise distribution
• the higher the internal response value, the more likely it is that a signal is perceived

Question 9

equal-variance SDT model

Answer 9

• implies that in this model, the variance of the noise and signal distributions is assumed to be the same
• the distributions are gaussians because they arise from the combination of very many independent noise processes. it is not reasonable to assume that these noise processes change due to our signal being present or not

Question 10

decision criterion (c): definition

Answer 10

• threshold that determines whether a particular internal response will be classified as a ‘signal’ or ‘noise’
• if the internal response is larger than the criterion: respond yes
• if the internal response is smaller than the criterion: respond no

Question 11

decision criterion (c): formula

Answer 11

c = - (Z(Phit) + Z(Pfa))/2

Question 12

decision criterion and sensitivity

Answer 12

• the criterion determines answers independently of sensitivity and incoming information
• it represents bias

Question 13

liberal vs conservative criterion:

hit rates and false alarm rates +
optimal value

Answer 13

• the criterion affects the HR/FAR balance, but not the sensitivity.
• a liberal criterion increases hit rates and false alarm rates
• a conservative criterion reduces false alarm rates but also reduces hit rates
• the optimal placement of the criterion therefore depends on the contexts and the costs of each type of error

Question 14

unbiased detector

Answer 14

• would place the criterion right in between the two distributions of signal and noise
• a bias represents a displacement c, which can be positive (conservative) or negative (liberal)

Question 15

what does the criterion affect

Answer 15

the criterion affects HR&FAR/accuracy, not sensitivity.

Question 16

sensitivity (d’): definition

Answer 16

• quantifies the difference between signal and noise distributions (how much overlap)
• measure of how well an observer can distinguish between signal and noise

Question 17

what are errors

Answer 17

• false alarms and misses
• caused by overlap in the distribution
• the more overlap, the more errors

Question 18

sensitivity (d’): formula

Answer 18

• d’ = Z(Phit) - Z(Pfa)
• d’ = 1.5 implies that the means of the distributions are 1.5 standard deviations away from each other

= d’ = 0 indicates no difference between the distributions

Question 19

interpretation of high d’ vs low d’

Answer 19

• high d’: indicates high sensitivity/precision, less overlap in the distributions, and better discrimination ability
• low d’: indicates low sensitivity/precision, more overlap in the distributions, and poor discrimination ability

Question 20

the influence of variance on d’

Answer 20

• d’ is influenced by the amount of overlap between distributions, not by the shape of the distributions alone
• this means that if the variances differ, but the overlap is equal, d’ will be the same.

Question 21

Receiver Operating Characteristic (ROC) curve

Answer 21

• visualizes the trade-off between hit rates and false alarm rates at different criterion settings, while keeping sensitivity d’ constant
• since the sensitivity d’ remains the same along each individual curve, it shows that that the inherent ability to distinguish between signal and noise does not change when the criterion is shifted
• this shows that behavioral outcomes can vary due to criterion shifts, even if the observer’s actual ability to discriminate between signal and noise is constant

Question 22

changing the criterion along a ROC curve

Answer 22

• shows how changing the criterion affects the hit and false alarm rates
• moving to the right on the curve corresponds to a more liberal criterion, leading to higher hit and false alarm rates
• moving to the left on the curve corresponds to a more conservative criterion, leading to lower hit and false alarm rates

Question 23

d’ = 0 implication

Answer 23

• the hit rate equals the false alarm rate: for every criterion, the amount of the Gaussian that falls over the criterion is the same for noise and signal trials
• the signal and noise distributions completely overlap
• corresponds to no sensitivity

Question 24

accuracy

Answer 24

• sensitivity is separate from accuracy
• sensitivity measures how well an observer can distinguish between signal and noise, while accuracy refers to the percentage of correct responses
• the observer’s criterion can affect their accuracy. therefore, our criterion can get in the way of getting the optimal result.
• only when criterion is 0 (unbiased), is your percentage correct optimal

Question 25

What is the problem with representing sensitivity by accuracy

Answer 25

• accuracy alone conflates changes in bias/criterion and sensitivity.
• accuracy alone cannot differentiate between changes in senstivity and bias
• it does not provide direct evidence of improved sensitivity unless d’ is explicitly measured

Question 26

What happens with the hit rate and the false alarm rate when d’ is increased?

Answer 26

• HR increases because more of the signal distribution falls above the criterion
• FAR decreases because less of the noise distribution falls above the criterion

Question 27

What happens to the difference between the hit rate and the false alarm rate when d’ increases?

Answer 27

• the difference increases between hit rate and false alarm rate grows because the overlap between the distributions decreases
• this makes it easier to distinguish signal from noise

Question 28

P_fa

Answer 28

• mathematically, the false alarm rate P_fa is the proportion of the noise distribution that lies above the criterion

Question 29

positive shift in c: impact on Z(P_{hit}​) and Z(P_{FA}​)

Answer 29

• shifts the criterion closer to the signal distribution

1. decreases P_{hit}: fewer hits occur because the threshold is harder to surpass
2. decreases P_{FA}: fewer false alarms occur because the noise rarely surpasses the higher threshold

• as a result of these proportions decreasing, both z-scores are decreased as well.

Question 30

negative shift in c: impact on Z(P_{hit}​) and Z(P_{FA}​)

Answer 30

• shifts the criterion closer to the noise distribution

1. increases P_{hit}: more hits occur because the threshold is easier to surpass
2. increases P_{FA}: more false alarms occur because the noise easily surpasses the low threshold

• as a result of these proportions increasing, both z-scores are increased as well.

Question 31

How does𝑍(𝑃_{ℎ𝑖𝑡})relate to𝑍(𝑃_{𝐹𝐴}), when c = 0

Answer 31

one is (1-the other)