S&P ch1 Psychophysics and Signal Detection Theory

Perception: Identification that sensory stimuli are present. Example: "Something is on the tree."
Recognition: Categorization and identification of the stimulus. Example: "Oh, it’s a moth."
Action: Physical movement or adjustment in response to the perception to gather more information. Example: "I will walk closer so I can see it better."

Psychophysics: The study specifically investigating the relationship between physical stimuli (the outer world) and psychological responses (the inner world).
* Just Noticeable Difference (JND): The minimum change in a stimulus that can be detected.
* Absolute Threshold: The minimum intensity of a stimulus required for detection.
Physiological Approach: Investigates the relationship between physical stimuli and internal physiological processes.
Psychophysiology: Investigates the relationship between physiological processes and psychological responses.
Neuroimaging Tools:
* PET scans: Used to reveal the functional organization of the brain.
* fMRI scans: Used to reveal functional brain organization through changes in blood flow.

Historical Context - Cartesian Dualism: Traditional views (Descartes) separated the Body (governed by laws of physics) from the Mind (governed by religion).
The Mission of Psychophysics: To create a "science of the mind" by mapping the dimensions of the physical world onto the dimensions of the mental world.
One-to-Many Mapping: Early researchers discovered that the relationship between a physical stimulus and the resultant subjective response is not a simple one-to-one ratio but a complex one-to-many mapping.

Ernst Weber (1795–1878): Developed Weber’s Law regarding the Just Noticeable Difference (JND).
* Weber’s Law formula: $JND = k \times I$
Gustav Theodor Fechner (1801–1887): Often cited as the Father of Psychophysics.
    * Fechner Day: Celebrated on October 22, 1850.
    * Fechner’s Law formula: $S = k \times \log(\frac{I}{I_0})$
    * Developed classical methods and scaling techniques.
S. S. Stevens (1906–1973): Introduced magnitude estimation.
* Stevens’ Power Law formula: $S = k \times I^n$
* Response Compression: Occurs when n < 1. * Response Expansion: Occurs when n > 1.
Green & Swets: Facilitated primary contributions to the development of Signal Detection Theory (SDT).

Diagnosis of Individual Abilities: Clinical assessments, such as determining if an individual's hearing falls within normal ranges.
Comparison of Group Abilities: Population-based studies, such as investigating whether users of portable music devices (iPods) experience a loss in auditory sensitivity.
Training and Optimization: Improving the diagnostic accuracy of professionals, such as X-ray technicians, through perceptual training.

The Goal: To plot the psychophysical function, measuring the relationship between the intensity of a physical stimulus and the amount of psychological experience.
Method of Limits (Staircase): Stimuli are presented in ascending or descending order of intensity.
Method of Adjustment: The observer manually adjusts the stimulus intensity until they can just barely perceive it.
Method of Constant Stimuli:
    * Stimuli of varying intensities are presented in a random order.
    * Absolute Threshold Example: Identifying the stimulus intensity that results in "yes" responses $50\%$ of the time.
    * Difference Threshold Example: Measuring the ability to distinguish between two stimulus levels.

Limitations of Classical Methods: Classical psychophysics is confounded by two different processes:
* Sensitivity ( $d'$ ): The actual ability to detect stimulus energy.
* Response Bias ( $\beta$ ): Non-sensory factors including attention, motivation, expectations, and conscientiousness.
SDT Outcome Matrix:
    * Hit: Signal present, observer responds "yes."
    * Miss: Signal present, observer responds "no" (Type II Error).
    * False Alarm: Signal absent (noise only), observer responds "yes" (Type I Error).
    * Correct Rejection: Signal absent (noise only), observer responds "no."
Underlying Theory: SDT assumes two distributions are present in the sensory system: Noise ( $n$ ) and Signal + Noise ( $s+n$ ).
* Sensitivity ( $d'$ ): Measured in z-score units; it represents how far apart the means of the noise and signal+noise distributions are.
* Observer Criterion ( $\beta$ ): The internal threshold set by the observer to decide between a "yes" or "no" response.

Lawful Changes: For any fixed sensitivity ( $d'$ ), the criterion can shift based on consequences.
Punishing False Alarms: If False Alarms are penalized, they may decline (e.g., to $2.5\%$ ), but Hits will also decline (e.g., to $50\%$ ).
Rewarding Hits: If Hits are incentivized, they may increase (e.g., to $99.5\%$ ), but False Alarms will also increase (e.g., to $92\%$ ).
Statistical Example: An observer who detects a stimulus on $84\%$ of signal+noise trials ( $-1z$ ) and "detects" it on $50\%$ of noise-only trials reveals the relative positions of the distributions and the criterion.

Definition: A plot showing the hit rate (true positives) against the false alarm rate (false positives).
Sensitivity Visualization:
    * $d' = 0$ : Hit rate equals False Alarm rate ( $50\%$ / $50\%$ ), representing performance below threshold/random guessing.
    * $d' = 1$ : Low stimulus intensity (e.g., Hit rate $0.70$ , FA rate $0.30$ ).
    * $d' = 2$ : Moderate stimulus intensity (e.g., Hit rate $0.85$ , FA rate $0.15$ ).
    * $d' = 3$ : High stimulus intensity (e.g., Hit rate $0.95$ , FA rate $0.05$ ).
Modern Application (Mammography): Comparing standard methods of mammogram assessment versus enhanced methods. ROC plots show variance in opinion among radiologists; for instance, a study of $140$ Australian radiologists used heat-maps to show where different practitioners identified potential lesions compared to actual cancerous lesions.