Lecture Notes: Signal Detection Theory

Key Concepts

• Signal Detection Theory: Used to measure the ability to differentiate between information-bearing stimuli and random patterns that distract from the information.
• Noise Threshold: The baseline level of noise against which signals are detected.
• Distributions:
  • Noise Distribution: Represents background noise.
  • Signal Distribution: Shifted relative to noise; represents actual signal.
  • D-Prime (d'): The difference between the means of the noise and signal distributions.

Variables

• D-Prime (d'): Indicates the ease of task.
  • Large d': Easy task (e.g., distinguishing a green dot).
  • Small d': Difficult task.
• Stimulus Intensity: How easily a stimulus stands out from the background.

Strategies (Threshold Choices)

• B Strategy: Choose a fixed threshold; decisions made based on this fixed point.
  • Example: Threshold = 2; response is "yes" if value > 2.
• D Strategy: Threshold relative to signal distribution; a function of d'.
  • Example: Threshold = d' - B.
• C Strategy: Represents an ideal observer.
  • Equation: C = B - (d'/2).
  • C Values:
    • C = 0: Ideal observer.
    • C < 1: Liberal strategy (favors saying "yes").
    • C > 1: Conservative strategy (favors saying "no").

Beta Variable

• Beta Strategy: Threshold is the ratio of heights of signal to noise distributions.
  • Equation: log(beta) = d' * C

Strategy Effects

• Ideal Observer (C = 0): Balances false alarms and misses.
• Liberal Observer (C < 1): More likely to say "yes"; fewer misses, more false alarms.
• Conservative Observer (C > 1): More likely to say "no"; fewer false alarms, more misses.

Example Calculations

• If d' = 1, B = 2:
  • D Strategy Calculation: Threshold = 1.
  • C Strategy Calculation: Threshold = 1.5.
  • Beta Calculation: log(beta) = 1 * 1.5 = 1.5.

These concepts help in understanding how individuals can be modeled as observers who use different strategies to detect signals amidst noise, based on varying thresholds and strategies.