In this brief guide we are going to answer the question ‘’’What kind of math is used in psychology?’’ we will explain how psychology uses mathematics and its importance.

## What kind of math is used in psychology?

Statistics is the kind of math used in psychology. Psychology as a branch of knowledge allows us to inquire about the behavior of humans, while mathematics is a language for understanding the universe.

For example, mathematics mainly supports psychology in the creation and revision of psychometric tests, in the same way, individual cognitive processes make individuals vary the procedures to reach a mathematical calculation although the result is the same, in general, mathematics arises as a necessity of man, and men based on their psychological processes and interpretation of environmental phenomena created a mathematical language.

Among other relationships that exist, psychometry is a branch of psychology whose purpose is to measure the psychological aspects of a person, such as mental abilities, knowledge, and personality traits, among others.

Psychophysics is another branch of knowledge that addresses how physical relationships interact with human behavior, and thus several constructs where mathematics is immersed in psychology can be observed.

## Psychology and statistics

Statistics is today an instrument widely used in the different branches of psychology such as experimental psychology, learning psychology, educational psychology, clinical psychology, etc.

The basic training in statistics of “every” psychologist must be oriented to be able to statistically analyze the data he/she obtains, and to be able to properly understand the statistical methodology of the published works in any area of psychology.

Statistics is a science with mathematical bases that deals with the collection, analysis and interpretation of data that allow us to understand more clearly a given phenomenon in the field of psychology as well as in other branches of formal and empirical sciences.

When an investigation is carried out, statistical methods allow us to know the causality, and to obtain a conclusion about the effect that some changes in the independent variables have on the dependent variables.

The different experimental models require measuring, manipulating and re-measuring to know if the manipulation of one or more factors within the experimental model has undergone modifications.

Statistics is important in psychology because it allows to extract and summarize useful information from the observations that are made, the psychologist must base his decisions on limited data and these are easier to make with the help of statistics, it gives greater clarity and precision to thinking and psychological research.

## Research and methodology in psychology

The method used in psychology is the hypothetical method: through a hypothesis, experiments are carried out and conclusions are drawn, then the process is replicated if necessary. If 100% of the results support the hypothesis, they are General Results, if the majority are correct, they are Partial Results, if the results are true, they are only called Existential Results, which cannot be worked with.

In conducting a psychological experiment the following steps are necessary:

Statistical planning of the research: Locate the sources of information, and choose the material. To pose a study problem.

Designing the experiment. The model is validated by comparing it with what happens in reality. Statistical methods known as hypothesis testing or significance testing are used.

Descriptive statistics are produced.

Statistical inference. A consensus is reached about what the observations say about the world we observe.

The validated model is used to make decisions or predict future events. A final report is produced with the results of the study.

## Mathematical psychology

Psychology is a discipline that investigates human behavior and treats pathologies related to people’s mental processes.

There are different types of psychology, among them mathematical psychology. This focuses on implementing formulas and models related to mathematics to understand and assess human behavior.

Mathematical psychology aims to measure certain aspects related to the psychological processes that affect people. For example, the relationships that exist between stimulus and response.

The first approaches between psychology and mathematics originated in the 17th century. Prestigious scientists such as Galileo Galilei and Kepler were interested in studying and investigating whether thoughts were governed by certain laws.

## What is the purpose of mathematical psychology?

These are the most important functions of mathematical psychology:

The use of mathematical psychology is important since it serves to measure certain processes, skills or aspects related to the mind of the human being.

Psychometric tests, statistics, and stimulus sampling, among other resources, have been created to measure the psychological processes of people.

The information that emerges as a result of the mathematical application is very useful to measure important parameters such as memory, learning, social skills, among other aspects.

The measurements that are carried out thanks to mathematics serve to test hypotheses.

## Example of mathematical psychology

Mathematics plays an important role in psychology. It studies and investigates human behavior, pathologies related to psychological aspects and the most effective treatments for them.

Within the investigations that are carried out, hypotheses are put forward that have to be proven. Mathematics makes its presence felt and claims its importance when it comes to testing these hypotheses and the relevant measurements on the processes of the mind.

In order to carry out the study of a given behavior in the human being, one can resort to the generation of statistics. For example, these serve to know the approximate recovery time of a patient or to elaborate experiments related to the human mind.

Therefore, far from being two opposite and different disciplines, we must bear in mind that they complement each other and serve to deepen the study of the psychological processes of the human being.

## Differences between mathematical psychology and psychometrics

It is important not to confuse mathematical psychology with psychometrics. Psychometry refers to the statistical studies of quantitative measurements made in psychology studies.

On the other hand, mathematical psychology, as we have already seen, refers to the use of mathematical models that attempt to predict psychological phenomena such as cognitive processes.

In addition, psychometry is especially concerned with explaining or classifying individual or population differences, while mathematical psychology, for its part, tries to generate models that can offer an explanation for the behavior of any average individual, i.e., that predict psychological behavior under given conditions.

Similarly, psychometry tries to find out the relationship between different variables of the population analyzed statistically. In contrast, mathematical psychology focuses on the creation of mathematical models into which all experimentally recorded psychological phenomena can be fitted.

This is why, although mathematical psychology has a certain relationship with psychometry in some aspects, this link is more powerful with other branches of this science such as cognitive psychology and experimental psychology.

It is also related to other branches such as econometrics or computational neuroscience, since it has in common with them the use of statistical optimization.

This question is generated by the premise that our brain, evolutionarily, must be configured to be able to face the different problems it encounters in an optimized way that increases the probabilities of overcoming them satisfactorily and with the minimum possible use of resources.

Returning to cognitive psychology, some of its most important studies, such as those related to the dichotomy between limited or unlimited processing capacity, or also the different types of processing (parallel or serial, for example), are very present issues for the studies of mathematical psychology.

## Conclusion

For obvious reasons, if you want to dedicate yourself to research in psychology (or simply research that is published beyond popularization), methodology and statistics are essential so that you can really assess the weight of the conclusions obtained in the research you have in hand.

You will be able to assess to what extent the procedure used by the researchers is the most appropriate or how reliable are the results they have finally obtained.

## References

Rasch, G. (1960). Studies in mathematical psychology: I. Probabilistic models for some intelligence and attainment tests.

Townsend, J.T. (2008). Mathematical psychology: Prospects for the 21st century: A guest editorial. Journal of mathematical psychology. Elsevier.

Busemeyer, J.R., Wang, Z., Townsend, J.T., Eidels, A. (2015). The Oxford handbook of computational and mathematical psychology. Oxford University Press.