Signal Detection Theory

Question 1

Signal Detection Theory

Answer 1

A theory relating choice behavior to a psychological decision space. An observer’s choices are determined by the distances between distributions in the space due to different stimuli (sensitivities) and by the manner in which the space is partitioned to generate the possible responses (response biases).

Question 2

Yes-no experiment

Answer 2

One-interval design: Participants are presented with a single stimulus and
have to classify it in one of two classes.

Performance on a task can be decomposed in the extent to which responses
mimic the stimuli (sensitivity), and the extent to which observers prefer to
use one response more than the other (bias).

Depending on the task, it can be useful to be biased to one or the other
response

Question 3

Sensitivity

Answer 3

What is a good measure of sensitivity

• it needs to be a fuction of H and F
• Perfect sensitivity implies H=1 and F=0
• Zero sensitivity H=F

Question 4

Measure of Sensitivity

Answer 4

Sensitivity = H-F
Sensitivity= 1/2(H-F)+1/2

Measure based on signal detection theory
sensitivity = d’= z(H) − z(F)
Perfect accuracy implies infinite d’

Question 5

Visulaization of H vs F is also called Receiver operating characteristic ROC

Answer 5

An Roc curve connects points with an equal sensitivity and a different bias

Two important characteristics:

(1) H = 1 can only be achieved for F = 1 (same for 0)
(2) steepness of the slope decreases as bias to say “yes” increases

ROC curves can also be expressed in z-coordinates (zROC curves)

Question 6

Signal detection model

Answer 6

• The two distributions together comprise the decision space.
• The observer cna asses the familiarity of the stimulus, but does not know from which distribution it came
• What is a good strategy to make a decision?
• Establishing a criterion somewhere in decision space. When familiarity is
  above this criterion, observers will say “yes”, when below observers will say
  “no”
• Four possible response alternatives are possible given that stimuli can be generated by two different distributions
  -This decision space defines an ROC, and moving the criterion will generate different points on a particular ROC curve
• d’ can be conceptualized as the distance between distributions. This only
  holds for equal-variance Gaussian SDT
• All different response types (hits, false alarms, …) as taking areas under the
  curve relative to the criterion.

Question 7

Response bias

Answer 7

• d’ does not depend on response bias, so a good measure of response bias is
  also independent of sensitivity.
• Bias should depend on H and F, but now increasing when both increase

– Criterion c = -1/2(z(h)+z(f))
– Relative criterion c’= c/d’
– Likelihood ratio under SDT assumption
ln(β) = cd’

Question 8

Which measure should be prefferd

Answer 8

Three standards
1 empirical support
2 increase H or F increase
3 independent of sensitivity

Criterion location c satisfies (2) and (3). (1) has yielded ambiguous evidence
(3) has been disputed as well, however. Experiments have shown that c
covaries with d’.

Question 9

The empirical ROC: What if the slope of the zROC curve is not equal to 1

Answer 9

Detectability as quantified by d’is no longer constant (i.e., it varies with criterion location)

What kind of underlying distribution can cause this type of ROC? When the
slope is smaller than 1, moving one z-unit on the F axis of the zROC implies
moving less than one z-unit on the H axis.

Question 10

The empirical ROC

Answer 10

offers a straightforward alternative nonparametric way of estimating sensitivity: area under the ROC

Question 11

Type II sensitivity

Answer 11

• SDT assumptions of equal variance are problematic for type 2 d’
• Area under development!