Introduction to Perception, Psychophysics, and Signal Detection

Sensation: A biological system used by an organism to gather information about the surroundings through the detection of physical stimuli (e.g., light waves, sound waves, chemical materials).
Perception: The process of regarding, understanding, or interpreting sensory information; the recognition and interpretation of sensory inputs (e.g., recognizing a face, seeing illusions).
The Perceptual Process (7 Steps):
1. Environmental Stimulus: The presence of physical energy in the world.
2. Light is Reflected/Transformed: Stimulation reaches the receptors.
3. Receptor Processes: Sensory receptors (specialized cells like visual pigments) respond to energy.
4. Transduction: Conversion of environmental energy into neural impulses.
5. Neural Processing: Occurs in interconnected circuits (retina, brain lobes like Occipital, Temporal, Parietal, and Frontal).
6. Perception and Recognition: Subjective experience ("I see something") and identification ("It is an oak tree").
7. Action: Motor response (e.g., walking closer).

Bottom-Up Processing: Processing based on incoming stimuli from the environment; also called data-based processing.
Top-Down Processing: Processing based on the perceiver’s previous knowledge, cognitive factors, or expectations; also called knowledge-based processing.
Knowledge: Any information the perceiver brings to a situation, which can influence how ambiguous stimuli are interpreted (e.g., the "B" or "13" perceptual set experiment).

Psychophysics: The science of defining quantitative relationships between physical stimuli and psychological (subjective) events.
Gustav Fechner (1801-1887): Coined the term; sought to measure the link between physical and perceptual worlds.
Ernst Weber (1795-1878): Discovered that the ability to detect differences depends on the magnitude of the stimulus.
Just-Noticeable Difference (JND): The smallest change in a stimulus that can be detected. Also known as the difference threshold.
Weber’s Law: The JND is a constant fraction of the reference stimulus.
- Formula: $\frac{\Delta I}{I} = k$
- Where $\Delta I$ is the JND, $I$ is the intensity, and $k$ is a constant (the Weber fraction).
- Example: If $k = 0.05$ (5%), a 40lb weight needs 2lbs added to notice a difference, but an 80lb weight needs 4lbs.

Fechner’s Law: Derived from Weber's Law using calculus; states that the subjective magnitude of a sensation grows as a proportion of the logarithm of the stimulus intensity.
- Formula: $P = \log(I) + C$ or $P = \log(\frac{I}{I_0})$
- Describes why sound (decibels) is measured on a logarithmic scale.
Stevens’ Power Law: A more general law describing the relationship between stimulus intensity ( $I$ ) and perceived magnitude ( $S$ or $P$ ).
- Formula: $S = aI^b$
- Response Compression: When the exponent b < 1 (e.g., brightness = 0.3, sweetness = 0.8). Doubling intensity less than doubles perception.
- Response Expansion: When the exponent b > 1 (e.g., electric shock = 3.5). Doubling intensity more than doubles perception.
- Linearity: When $b = 1$ (e.g., apparent length).

Magnitude Estimation: Subjects assign numerical values to the perceived intensity of stimuli.
Cross-Modality Matching: Subjects match the intensity of a sensation in one modality (e.g., sound) to another (e.g., light).
Method of Limits: Stimuli are presented in ascending or descending order until detection changes.
Method of Adjustment: Similar to limits, but the subject controls the intensity continuously until the stimulus is barely detectable.
Method of Constant Stimuli: Stimuli of different intensities are presented in a randomized order. Most accurate but time-consuming. Threshold is typically defined as the level detected $50\%$ of the time.
Forced Choice: Two-interval (2IFC) or two-alternative (2AFC) tasks where the subject must choose when or where a stimulus appeared. Advantage: Independent of subjective bias/criterion.

Overview: A theory quantifying the response to a signal in the presence of noise ( $N$ vs. $S+N$ ). It separates actual sensitivity from the observer's decision criteria.
Four Possible Outcomes:
1. Hit: Signal present, respond "Yes."
2. Miss: Signal present, respond "No."
3. False Alarm: Signal absent, respond "Yes."
4. Correct Rejection: Signal absent, respond "No."
Discriminability ( $d'$ ): A measure of sensitivity representing the separation between the noise distribution and signal distribution.
- Formula: $d' = z(\text{hit rate}) - z(\text{false alarm rate})$
- High $d'$ means little overlap/high sensitivity; $d' = 0$ means performance is at chance.
Criterion ( $c$ ): The internal threshold for deciding "Yes" vs. "No."
- Liberal: Low threshold, says "Yes" easily (more hits, but more false alarms).
- Conservative: High threshold, says "No" easily (fewer false alarms, but more misses).
- Influenced by Prior Probability (how likely the signal is) and Payoffs (rewards/punishments).
Receiver Operating Characteristic (ROC) Curve: A graph plotting hit rate vs. false alarm rate. Curves further from the center diagonal indicate higher $d'$ /sensitivity.

Electroencephalogram (EEG): Measures electrical activity via scalp electrodes. High temporal resolution, low spatial resolution.
Magnetoencephalography (MEG): Maps brain activity by recording magnetic fields. Similar to EEG but with better spatial localization.
Positron Emission Tomography (PET): Uses radioactive tracers to track organ/tissue function.
Magnetic Resonance Imaging (MRI): High-resolution structural images of internal anatomy.
Functional MRI (fMRI): Measures brain activity by detecting changes in blood flow using the Blood-Oxygen-Level Dependent (BOLD) signal.
Spatial vs. Temporal Resolution:
- EEG/MEG: Millisecond-level timing (high temporal) but poor location (low spatial).
- fMRI: Accurate location (high spatial) but slow response (low temporal).