Under what terms is a relationship between mathematics and psychology possible?

In this brief guide we are going to answer the question: ‘’Does psychology need math?’’ We will analyze the relationship between psychology and mathematics, and we will detail the numerical tools that allow us to understand the psychological elements.

## Does psychology need math?

Yes, psychology needs mathematics. As a science, psychology must demonstrate its theories according to the scientific method, which is based on statistical analysis.

Mathematics occupies a prominent place in the school curriculum of all countries. The role of mathematics in society is subtle and sometimes difficult to perceive, it even remains totally hidden in the gadgets, tools and utensils of daily use.

The skills to **calculate **and organize information (related to the power of technology and the improvement of economic and social organization), as well as the **geometric **understanding of space-time (this is the physical world and its models), are two aspects that show the cultural and scientific role of the discipline.

## What ‘s statistic?

Statistics is a set of methods used to collect, summarize, classify, analyze and interpret the behavior of data with respect to a characteristic, subject of study or research. Statistics is considered as a collection of numerical facts expressed in a summative way, and that have been compiled from other numerical data.

## Statistic in psychology

Statistics is today an instrument deeply used by researchers from very diverse scientific areas. In particular, its need and importance have been growing in recent years within the Behavioral Sciences and, more specifically, within Psychology.

To be convinced of this, it’s enough to read the contemporary publications on Experimental Psychology, Learning Psychology, Social Psychology, Psychophysics, etc. Even clinical psychology itself demands a no small mastery of statistical techniques.

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

When an investigation is carried out, the methods of statistics 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 extracting and summarizing useful information from the observations that are made, the psychologist must base their decisions on limited data and these are easier to make with the help of statistics, it gives greater clarity and precision to the psychological research.

## How are mathematics and psychology related?

But, before we dive into mathematical psychology, let’s do a brief review of mathematics in the history of psychology.

The first contributions of mathematics to psychology date back to the nineteenth century with the scientists Fechner and Weber, founding physiologists of the so-called psychophysics, which consisted in establishing regular relationships between physical and psychic aspects.

Later, the philosopher Wilhem Wundt, founding father of what we know as modern psychology, established the first experimental laboratory in Leipzig in 1879, where the explanation of psychic phenomena was started based on a set of primitive elements that were assembled into more complex concepts, however, mathematics served only as an adjunct to theoretical models.

**Mathematics and psychology relationship**

There is certainly a relationship between psychology and mathematics. However, we must understand that the order in which we position both sciences gives us a different result. That is, on the one hand, we can find studies in which psychology is used as a means for teaching-learning mathematics (eg didactics).

On the other hand, we also find studies that analyze the use and importance of mathematics in psychology as a means to carry out research of a mental nature and obtain ‘measurable’ results (eg psychometry).

Psychology, as an experimental science, with significantly great factual knowledge, requires communication through the conceptual language of mathematics. There are three great fields to approach mathematics in psychology.

The first, **statistics**, refers directly to the set of methods, norms, rules, laws and principles intended to observe, group, describe and quantify a certain amount of data collected in order to analyze the behavior of one or more groups.

The second, **psychometrics**, responsible for the development of psychological tests in order to measure aspects such as intelligence, aptitude, interest and personality of certain individuals.

Psychometrics establishes the procedures for estimating the relevance, validity, reliability and margin of error in the data used, and establishes methods for the selection and use of stipulated instruments; allows the construction, application and analysis of objective tests, as well as the methods for the interpretation of the data; establishes measurement objects and relevant measurement items.

The third, **psychophysics**, seeks to determine the physical mechanisms and processes of the various sensory and / or perceptual systems. It comprises a relatively broad field of procedures, methods, instruments, and both theoretical and empirical contributions.

**Psychometrics**

Psychometrics is understood as the discipline that is responsible for the quantitative measurement of mental processes and capacities.

In this way, a numerical value can be assigned to specific characteristics and events, allowing comparison and contrast with other people or with specific criteria that can be used to establish and test theories and hypotheses about the functioning of the mind.

Thanks to psychometrics it’s possible to quantify the psychic, having largely allowed the development of psychology as a science.

As the mind is something not directly observable, it’s necessary to use elements that can indicate the aspect to be treated, using observable indicators such as behavior or the registration of physiological activity.

Broadly speaking, we can say that psychometrics uses statistical calculation and analysis of results in order to be able to acquire information regarding a certain construct (which speaks about some psychological aspect) through a measurement element that it has previously created.

**What is psychometry about?**

As we have seen, psychometry is the branch of psychology that is responsible for measuring specific aspects of the mind.

According to Scientific Research, this implies, establishing a theory that can link mental characteristics with measurable elements, on the other, the creation of measurement scales, and finally, the elaboration of mechanisms and instruments that allow such measurement.

- Theory
- Scales
- Measurement tools

**Some relevant concepts**

As a discipline that allows the measurement of the unobservable, psychometrics must take into account various concepts in order to ensure that such measurement is correct and representative. Some of the most relevant concepts are the following.

**1. Correlation**

The concept of correlation refers to the existence of some type of link between two variables, which causes changes in one of them to make variations in the second, although this does not ensure that the relationship is cause-consequence.

**2. Variance and standard deviation**

The variance is the level at which the scores of a test or of the same variable can be dispersed. The standard deviation refers to how much the scores are typically expected to spread out relative to the average.

**3. Reliability**

Reliability refers to the level at which an item or element used in the measurement of a characteristic does not produce errors, obtaining consistent results in different measurements of the same characteristic in the same subject and context.

**Psychophysics**

Psychophysics is understood to be the branch of psychology whose main object of study is the relationship between external stimulation, its qualities and a subject’s perception of said stimulation.

This is one of the first types of study to be carried out in a scientific way, in which psychological aspects such as sensation were analyzed.

The measurement of psychophysical aspects required highly precise instruments and the elaboration of different techniques that would allow the obtaining of valid and reliable data, being in fact psychophysics the direct precursor of psychometry.

In psychophysics, models began to be developed in which a numerical value was assigned to the characteristics of stimuli and their perception, being a pioneer in the quantitative investigation of mental phenomena.

In other words, it measures the behavioral response to physical stimulus. Psychophysics was born at the beginning dedicated to the study of visual perception, but later it will be expanded in such a way that it ended up being extended to the study of the relationship between the physiological and the psychic.

Psychophysics has used different methods to measure sensation. Among them we find the description by the subject of what is perceived, its recognition, detection, perception of the magnitude or the search for the stimulus.

## Why is statistics important to the psychologist?

The psychologist, therefore, must know these techniques with some seriousness. It’s not enough that you know how to apply a few formulas in a more or less mechanical way. It’s necessary that you know the basis and the deduction thereof, as well as the conditions required by each statistical technique for their use to be valid.

Only then can you apply the most appropriate in each specific case. In turn, they will be able to carry out their specific task as a psychologist, offering an adequate psychological interpretation of the numerical results obtained in their investigations.

However, we must remember that people cannot be limited to numbers; The wealth of research in Contemporary Psychology lies precisely in not losing individuality. This means that it’s important to complement the statistics with the qualitative approach.

## Final words

Statistics has always played an important role in Psychology practically since its inception and, above all, since the experimental method emerged.

However, the truth is that it has not always been applied correctly and many psychologists still don’t understand its importance when stating that psychic phenomena cannot be measured, much less reduced to simple numbers.

In reality, psychic phenomena can be measured without losing the richness that individuality brings. In fact, at present, in order to be able to publish in prestigious scientific journals, it’s not enough to have a good experimental design, it’s also important that the study is supported by a serious statistical analysis.

For this reason, most of the faculties of Psychology teach the subject of Statistics Applied to Social Sciences.

If statistics didn’t exist in psychology, we could not know if the results we are observing are valid and reliable. A correct methodology and mathematical study gives us the security that the data we have obtained in our research; which will be useful when we want to apply them to real situations.

Psychology is a science, and for this reason you have to use an abstract system that allows you to work as far as possible from opinion and subjectivity. This system is the **scientific method**, and one of its key aspects is the use of statistics as a tool.

For this reason, it’s very important that psychologists are trained in it and understand in depth at least its concepts.

## FAQS: Does psychology need math?

**What level of math is required for psychology?**

Psychology students need to pass a couple of math and calculus courses. Emphasizing statistical methods.

**Do psychologists use math?**

Yes, psychologists use formulas, statistics, and other mathematical tools to predict certain behaviors or tasks.

**What major does not require math?**

There’s no major that does NOT have ANY math. However, majors in Social Sciences, like sociology, anthropology, psychology don’t need a lot of math.

**Is there a lot of math in psychology?**

Many students enter psychology thinking that they will not find math. However, mathematics, especially statistics, is important in psychology study plans.

Similarly, it’s not that you will see classes like Calculus III, but you will need to pass at least a couple of Mathematics and several Statistics classes.

**Do you need pure maths to study psychology?**

Not for long, you’ll take a couple of Calculus classes, but nothing too extreme. For the rest, you will find pure Statistics.

In this brief guide we answered the question: ‘’Does psychology need math?’’ We analyzed the relationship between psychology and mathematics, and we detailed the numerical tools that allow us to understand the psychological elements.

If you have any questions or comments please let us know!

## References

McCall, R. B., & Kagan, J. (1975). *Fundamental statistics for psychology* (No. BF39. M3 1970.). New York: Harcourt Brace Jovanovich.

Statistics Class When Studying Psychology? Retrieved October 13, 2020, from Verywell Mind website: https://www.verywellmind.com/why-are-statistics-necessary-in-psychology-2795146#:~:text=Math%20classes%2C%20and%20statistics%20in,your%20psychology%20program’s%20core%20requirements.

Rust, J., & Golombok, S. (2014). *Modern psychometrics: The science of psychological assessment*. Routledge.