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Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" [1] or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the ...
Stevens' power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus.
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
Qualitative psychological research findings are not arrived at by statistical or other quantitative procedures. Quantitative psychological research findings result from mathematical modeling and statistical estimation or statistical inference. The two types of research differ in the methods employed, rather than the topics they focus on.
Intensity discrimination improves at higher intensities. The first demonstration of the phenomena was presented by Riesz in 1928, in Physical Review. This deviation of the Weber's law is known as the "near miss" of the Weber's law. This term was coined by McGill and Goldberg in their paper of 1968 in Perception & Psychophysics.
The model of hierarchical complexity (MHC) is a formal theory and a mathematical psychology framework for scoring how complex a behavior is. [4] Developed by Michael Lamport Commons and colleagues, [3] it quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized, [5] in terms of information science.
[1] [2] [3] It is also a basic principle that guides modern research in perception. [4] [5] The ideal observer is a theoretical system that performs a specific task in an optimal way. If there is uncertainty in the task, then perfect performance is impossible and the ideal observer will make errors.
A common example is visual acuity testing with an eye chart. The person sees symbols of different sizes (the size is the relevant physical stimulus parameter) and has to decide which symbol it is. Usually, there is one line on the chart where a subject can identify some, but not all, symbols.