Editorial - Journal of Psychology and Cognition (2021) Volume 6, Issue 4

# Editorial note on Mathematical psychology

**Sowmya Vennam**

^{*}Department of Pharmacy, Jawaharlal Nehru Technological University, Hyderabad, Telangana, India

- *Corresponding Author:
- Sowmya Vennam

Veterinary Research Division

Department of Pharmacy

Jawaharlal Nehru Technological University

Hyderabad, Telangana, India

**E-mail:**Sowmya.vennam@gmail.com

Accepted on April 30, 2021

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## Introduction

Mathematical psychology is a branch of psychology that focuses on the mathematical simulation of visual, cognitive, and motor processes, as well as the development of law-like laws that link quantifiable stimuli characteristics to quantifiable conduct.

*What math is used in psychology?*

There are two main branches of statistical methods, descriptive statistics and inferential statistics. Descriptive statistics are used to summarise and describe data.

The analysis of actions through a statistical prism is known as mathematical psychology. Using statistics and mathematical formulas, this science tries to forecast behaviour. In order to do so, scientists must first provide a structure of formulas and laws on which to base their research.

*What does mathematical psychology have to do with real
life?*

Learning, recall, classifications, preference reaction time, decision making, concentration, and problem solving are all topics covered by mathematics-based psychology, according to a Wiley Online Library report. In real life, the ability to forecast how customers will respond to a variety of goods is extremely useful in marketing. People are slower to make decisions when faced with a wide range of alternatives, according to research. This variation in response time can be quantified by researchers to better target ad campaigns. The discipline can also be used to create learning plans and goods. The discipline can also be used to create learning plans and goods. Statistics, a statistical instrument used to solve a social problem, is used to measure intelligence quotient (IQ). Health practitioners will forecast how individuals will respond to health programmes and use the data to develop wellness curriculum that benefits whole populations.

When statistics are used to test psychological experiments, they inform the psychologist whether his data is useful or random. By forecasting habits and recommending software adaptations to overcome the behaviours, the formulas built by behaviour experimentation will help society improve its approach to addressing issues like school dropouts and infectious disease prevention. This is where Mathematical Psychology shines.

*Mathematical psychology of the 21 ^{st} century*

If one took a random study of a mathematical psychologist, she could be loosely classified into four (non-orthogonal) dimensions. First and foremost, we'll need to figure out if her modelling is purely axiomatic or more generally formulated. After that, we might figure out if she prefers deterministic or stochastic simulation. We should then inquire as to whether her method is mainly analytical or computational. Finally, her dissertation may be observational or theoretical in nature. An axiomatic solution is one in which the modeller writes down certain key concepts and then assertions (axioms) on what should be done (at the cost of oversimplification).

The modeller can, for example, define mathematical concepts to describe scenarios in which people are faced with stimulus pairs and their duty is to select the stimulus in the pair with the greater perceived significance. When faced with two tones (the stimulus pair), an axiom may be that people should be able to accurately distinguish the one that is louder with a likelihood greater than or equal to 0.5. As a result of these axioms, mathematical variables and formulas may be linked to psychological principles. The modeller will then draw logical inferences on what people can do under various circumstances based on a series of axioms. Axiomatic theorems are generally deterministic and do not answer problems of inherent randomness. The model generates one and only one outcome when given fixed model parameters and a fixed stimulus. A stochastic model, on the other hand, could yield drastically different effects even if the parameters and stimuli are kept constant. Mostly, models of cognitive processing are stochastic. The stochastic approach is exemplified by sequential sampling models, such as those discussed by Ratcliff and Smith in 2004. Predictions regarding actions are often based on the distribution of dependent variables and how the parameters of those distributions change as experimental procedures change.

Analytical approaches are those in which dependent variables Y can be written as analytical expressions concerning independent variables X, such as Y = g(X) for a function g that does not involve any messy numerical calculations (like taking a limit or integrating). An example of an analytic expression is the general linear model used in regression. Other examples include the expressions for serial and parallel processing method finishing time distributions (e.g., Townsend) also see the section Model Testing, Evaluation, and Comparisons). A nonanalytic expression, on the other hand, does not cause you to write Y = g(X) and make algebraic predictions for Y; instead, you must use a computer to simulate the model or solve for Y. The more complicated the problem at hand, the more likely it is that a computational solution would be required. Form comparative techniques. Bayesian model fitting and models dedicated to especially intractable problems such as text comprehension or language interpretation all necessitate a statistical solution. Finally, many mathematical psychologists are empiricists, which mean they gather evidence to test their theories. A branch of mathematical psychology, on the other hand, seldom or never gather data; their practise is largely theoretical. Where theoretical work proposes a particular scientific method, they either consult with empiricists or reanalyze previously reported research if it is accessible. These mathematical psychologists make theoretical contributions that propose new mathematical representations of various psychological problems, as well as analytical contributions that include modern research techniques. They remind me of theoretical physicists, who had some amazing observations into the essence of things but were famously bad in the lab.