SIGNAL DETECTION THEORY

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SIGNAL DETECTION THEORY

• A situation is described in terms of two states
  of the world
• a signal is present ("Signal")
• a signal is absent ("Noise")
• You have two possible responses
• the signal is present ("Yes")
• the signal is absent ("No")

Signal Noise
Response Yes Hit P(H) False Alarm P(FA)
Response No Miss P(M) Correct Rejection P(CR)
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• The theory assumes that what you are doing is
• First, you collect sensory evidence concerning
  the presence or absence of the signal.
• Next, you decide whether this evidence
  constitutes a signal. This means that you must
  have some criterion C that you use as a "cutoff"
  if the evidence is less than C, you decide "No"
  if the evidence exceeds C, you decide "Yes".

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Measures of Performance in SDT

• 1. Response bias (b)
• We can describe performance in terms of response
  bias you may be prone to say "yes" (which is
  "risky") or you may be prone to say "no" (which
  is "conservative").
• Response bias the ratio of the heights of the two
  curves at the cutoff point and is measured by the
  quantity
• P(X/S)
• ß
• P(X/N)
• where X "evidence variable
• S signal
• N noise
• Note your book has a simplified equation
  for representing ?. You may refer to whichever
  best helps you understand the concept of response
  bias.

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• Studies of human performance show that humans do
  change ß in response to changes in probabilities
  and payoffs -- but not as much as they should!
• This phenomenon is called sluggish beta.
• Note the terms risky and conservativerefer
  only to a persons propensity to say yes
  (signal) or no (noise).
• Examples
• radiologists reading x-rays for signs of tumors
• radar operators on a battle ship looking for
  incoming enemy aircraft
• scanning a parking lot for a parking space

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• The cutoff (C) for determining the presence of a
  signal vs the response bias parameter (ß).
• Not the same but correlated.
• Risky strategy ß ? and C ?
• More conservative both C and ß ?
• Setting ß
• Strategy can be affected by relative costs and
  values assigned to outcomes.
• Examples
• radiologists reading x-rays for signs of tumors
• radar operators on a battle ship looking for
  incoming enemy aircraft

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Measures of Performance in SDT

• 2. Sensitivity (d)
• Signal detection theory distinguishes response
  bias from sensitivity
• a function of the keenness or sensitivity of the
  human's detection mechanisms and the relative
  strength of the signal in noise.
• For example, a person may be "risky" (i.e., prone
  to say "Yes, I detect a signal") but may have bad
  eyesight (or be looking at a very fuzzy screen)
  and thus may often miss signals because of this
  low sensitivity.
• Table 4.5 on page 84 of your textbook gives some
  possible values of d corresponding to observed
  P(H) and P(FA). This value may also be
  calculated from the probabilities of a hit and a
  false alarm.

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Receiver Operating Characteristic (ROC) curve

• Plots the probability of a hit against the
  probability of a false alarm.
• Each curve represents the same sensitivity at
  different levels of response bias.

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Your Turn .

• An experiment was performed to determine how
  students who participated in a distance learning
  course responded to a signal from the instructor
  indicating that they had been called on to
  respond to a question. The results for two of the
  students using a particular type of signal and
  with varying feedback (i.e., rewards for
  responding) are given in the table below. Plot
  the results for both students on the same ROC
  curve. Who is more sensitive? Identify risky
  and conservative behavior. Comment on the
  results.

  Feedback P(fa) P(hit)
  Negative 0.1 0.3
Student 1 Neutral 0.33 0.55
  Positive 0.65 0.78
  Negative 0.05 0.33
Student 2 Neutral 0.35 0.68
  Positive 0.7 0.86