TASK 2 - SDT

Question 1

signal detection theory (SDT)

Answer 1

= alternating experimental trials which present a stimulus (S + N) and trials without a stimulus (only noise = N)

• -> theoretical framework for decision-making under uncertainty/near threshold
• used to quantify perceptual sensitivity and decision strategy of subject
• can be applied to any situation with two discrete states of the world (signal or no signal) –> 2 x 2 design
• used as guide to maximise payoffs (decide optimally)

Question 2

signal

Answer 2

= stimulus presented to the subject (S+N curve)

- low-intensity or near threshold

Question 3

noise

Answer 3

= all other stimuli in the environment (N distribution)

a) internal noise: differences in neural processing, perception, individual baseline neural firing
b) external noise: differences in external environment (light source,sounds)

Question 4

SDT

- assumptions

Answer 4

a) internal noise has specific distribution (normal)
b) same noise distribution for N and S+N trials
c) signal and noise add up linearly (no interaction)
d) decision is based on two consecutive processing stages: sensory (sensitivity) –> decision stage (strategy) –> response

Question 5

SDT

- outcomes

Answer 5

• 2 conditions + 2 possible responses –> 4 outcomes
  1. correct rejection = no tone + “no” (correct)
  2. false alarm = no tone + “yes” (mistake)
  3. miss = tone + “no” (mistake)
  4. hit = tone + “yes” (correct)

Question 6

probability distributions

Answer 6

= show frequency of trials against the internal response (X) strength

• N distribution: probability that given perceptual effect will be caused by noise
• -> P(FA)+P(CR)=1
• S+N distribution: probability that a given perceptual effect will be caused by signal (and noise)
• -> P(H)+P(M)=1

Question 7

probability distributions

- internal response (X)

Answer 7

= perceived loudness = what the subject experiences on each trial, personal neural evidence

• -> if internal response strong = decide that signal was present
• on most trials the internal response is intermediate = not 100% sure that signal was present
• S+N distribution always more to the right from N distribution –> when signal is present, internal response always stronger
• -> stronger signal pushes S+N distribution more to the right ( automatically stronger internal response)

Question 8

probability distributions

- decision criteria (Xc)

Answer 8

= if internal response exceeds (personal) decision criteria (Xc), subject decides that the signal was present

• N distribution: left from Xc (say no) = CR; right from Xc (say yes) = FA
• S+N distribution: left from Xc = M; right from XC = H

Question 9

decision criteria

- strategies

Answer 9

• subjects decision whether signal was presented depends on the location of their criterion
  a) liberal criterion: far to the left; FA and H high
  b) conservative criterion: middle; FA fairly low, H fairly high
  c) neutral criterion: far to the right; FA and H low

Question 10

sensitivity

Answer 10

= d’ = measure of sensitivity
= distance between the means of the two distributions normalised to their average std. dev.; 1/(area where two distributions overlap)
- assumptions: normal distribution, independence of sensitivity and bias
–> increasing d’ will lead to less errors (less confusion, more certainty that stimulus presented)

Question 11

d’

- computation

Answer 11

= Z(P(H))-Z(P(FA)) = (mean (S+) - mean (N))/√(0.5*(variance (S+N) ^2 + varaiance (N) ^2)
- need proabilities of FA and H (number of FA or H/ total number of N trials or S+N trials)

Question 12

d’

- interpretation

Answer 12

d’ > 0: high sensitivity (good hearing), able to detect signal, task not too difficult
d’ = 0: just guessing (N and S+N graphs completely overlap)
d’ < 0: high sensitivity but error/cofusion of answers (press yes when no meant)

Question 13

factors influencing d’

- increase intensity of stimulus

Answer 13

= increases d’

• S+N trials generally cause stronger internal response –> graph more to the right
• -> overlap of both graphs smaller: easier to differentiate whether signal was present or not
• affect the means of the graphs (difference between means increases)

Question 14

factors influencing d’

- more sensitive subject

Answer 14

= increase d’

• subject has stronger internal response to stimulus (hears better than ‘normal’ participants; task is too easy) –> graph more to the right
• -> overlap decreases
• affect the means of the graphs (difference between means increases)

Question 15

factors influencing d’

- reduce variability of noise

Answer 15

= increase d’

• graphs become narrower (less influencing factors) –> can only be controlled for if experimenters know the noise)
• affect variation of graphs (graphs do not spread so much)

Question 16

strategy

Answer 16

= B(eta) = measure of strategy
= proportion of heights of two distributions at criterion Xc; decision strategy/response bias of subject
- only change type of errors, not number of errors when changing your B (moving criterion only changes rates of FA and M, but subjects still make mistakes)
–> d’ can change amount of errors made

Question 17

B

- computation

Answer 17

= Y(Z(P(H)))/Y(Z(P(FA))) = P(X I S)/P(X I N)

- need probabilities of FA and H (and their z-scores)

Question 18

B

- interpretation

Answer 18

high B: more conservative decision strategy (do not say yes easily, need strong internal response) –> Xc more to the right (denominator/lower part is smaller = bigger B)
low B: more liberal decision strategy (tend to say yes) –> Xc more to the left

Question 19

factors influencing B

- payoffs

Answer 19

= sum of gains for correct responses and costs for errors

• payoffs can influence subjects’ strategy
• -> e.g. more rewards for CR and less for H –> more conservative (higher B) –> saying “no” will lead to more rewards

Question 20

optimal B

Answer 20

= optimal decision strategy that will maximise payoffs
= gains(CR)+costs(FA)/gains(H)+costs(M)
–> e.g. if costs for M increase –> denominator/lower part larger –> smaller B –> more liberal (don’t want to miss any, so you tend to press yes)
- depends on prior knowledge of probability of signal (if you know prob. of signal is relatively high, wise to have more liberal style (press yes often)
–> (gains(CR)+costs(FA)/gains(H)+costs(M)) x (1-P(S)/P(S))

Question 21

sluggish B

Answer 21

= in real life people tend to be less conservative or less liberal than suggested by optimal B

• -> I guess we are just to dumb to actually maximise our payoffs?
• finding optimal B is more difficult in real life: difficult to quantify payoffs

Question 22

ROC curves

Answer 22

= receiver operating characteristic = plot of the percentage of H vs. percentage of FA; illustrates perceivers responses for a range of strategies
- each ROC corresponds to different perceiver or signal intensity (related to d’)

Question 23

ROC curves

- plotting

Answer 23

1. locate very conservative criterion: few H + few FA
2. locate a little more neutral criterion: a bit more H + FA
3. repeat; change strategy/criterion, becoming more and more liberal –> fit curve to data

Question 24

ROC curves

- shape

Answer 24

• curvature corresponds to d’

- -> d’ > 0 (more curved); d’ = 0 (linear); d’ < 0 (reversed curve)

Question 25

ROC curves

- alternative

Answer 25

• z-scores: constant units of distance along each axis represent constant numbers of standard scores of the normal distribution
• for a given point, d’ is equal to Z(H) – Z(FA): reflecting the number of standardized scores that the point lies to the upper left of the chance diagonal