Quantitative psychology is a field of scientific study that focuses on the

mathematical modeling A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

research design Research design refers to the overall strategy utilized to answer research questions. A research design typically outlines the theories and models underlying a project; the research question(s) of a project; a strategy for gathering data and info ...

and

methodology In its most common sense, methodology is the study of research methods. However, the term can also refer to the methods themselves or to the philosophical discussion of associated background assumptions. A method is a structured procedure for bri ...

, and

statistical analysis Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of ...

psychological Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...

processes. It includes tests and other devices for measuring cognitive abilities. Quantitative psychologists develop and analyze a wide variety of research methods, including those of

psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and rela ...

, a field concerned with the theory and technique of psychological measurement. Psychologists have long contributed to statistical and mathematical analysis, and quantitative psychology is now a specialty recognized by the

American Psychological Association The American Psychological Association (APA) is the main professional organization of psychologists in the United States, and the largest psychological association in the world. It has over 170,000 members, including scientists, educators, clin ...

. Doctoral degrees are awarded in this field in a number of universities in

Europe Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east ...

and

North America North America is a continent in the Northern Hemisphere, Northern and Western Hemisphere, Western hemispheres. North America is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South Ameri ...

, and quantitative psychologists have been in high demand in industry, government, and academia. Their training in both

social science Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...

and quantitative methodology provides a unique skill set for solving both applied and theoretical problems in a variety of areas.

History

Quantitative psychology has its roots in early

experimental psychology Experimental psychology is the work done by those who apply Experiment, experimental methods to psychological study and the underlying processes. Experimental psychologists employ Research participant, human participants and Animal testing, anim ...

when, in the nineteenth century, the scientific method was first systematically applied to psychological phenomena. Notable contributions included E. H. Weber's studies of tactile sensitivity (1830s), Fechner's development and use of psychophysical methods (1850–1860), and Helmholtz's research on vision and audition beginning after 1850.

Wilhelm Wundt Wilhelm Maximilian Wundt (; ; 16 August 1832 – 31 August 1920) was a German physiologist, philosopher, and professor, one of the fathers of modern psychology. Wundt, who distinguished psychology as a science from philosophy and biology, was t ...

is often called the "founder of experimental psychology", because he called himself a psychologist and opened a psychological laboratory in 1879 where many researchers came to study. The work of these individuals and many others dispelled the assertion, by theorists such as

Immanuel Kant Immanuel Kant (born Emanuel Kant; 22 April 1724 – 12 February 1804) was a German Philosophy, philosopher and one of the central Age of Enlightenment, Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works ...

, that psychology could not become a science because precise experiments on the human mind were impossible.

Intelligence testing

Intelligence testing has long been an important branch of quantitative psychology. The nineteenth-century English statistician

Francis Galton Sir Francis Galton (; 16 February 1822 – 17 January 1911) was an English polymath and the originator of eugenics during the Victorian era; his ideas later became the basis of behavioural genetics. Galton produced over 340 papers and b ...

, a pioneer in psychometrics, was the first to create a standardized test of intelligence, and he was among the first to apply statistical methods to the study of human differences and their inheritance. He came to believe that intelligence is largely determined by heredity, and he also hypothesized that other measures such as the speed of

reflex In biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a stimulus. Reflexes are found with varying levels of complexity in organisms with a nervous system. A reflex occurs ...

es,

muscle Muscle is a soft tissue, one of the four basic types of animal tissue. There are three types of muscle tissue in vertebrates: skeletal muscle, cardiac muscle, and smooth muscle. Muscle tissue gives skeletal muscles the ability to muscle contra ...

strength, and head size are correlated with intelligence. He established the world's first mental testing center in 1882; in the following year, he published his observations and theories in "Inquiries into Human Faculty and Its Development".

Statistical techniques

Statistical methods are the quantitative tools most used by psychologists.

Karl Pearson Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English biostatistician and mathematician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university ...

introduced the correlation coefficient and the

chi-squared test A chi-squared test (also chi-square or test) is a Statistical hypothesis testing, statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine w ...

. The 1900–1920 period saw the t-test (Student, 1908), the ANOVA (Fisher, 1925) and a non-parametric correlation coefficient (Spearman, 1904). A large number of tests were developed in the latter half of the 20th century (e.g., all multivariate tests). More recently, popular multivariate techniques were developed—including the hierarchical linear model,

structural equation modeling Structural equation modeling (SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly in the social and behavioral science fields, but it is also used in epidemiology, business, ...

, and

independent component analysis In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and ...

. In 1946, psychologist

Stanley Smith Stevens Stanley Smith Stevens (November 4, 1906 – January 18, 1973) was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory, studying psychoacoustics, and he is credited with the introduction of Stevens's power law. Stevens aut ...

organized

levels of measurement Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to dependent and independent variables, variables. Psychologist Stanley Smith Stevens developed the best-known class ...

into four scales, Nominal, Ordinal, Ratio, and Interval, in a paper that is still often cited. Jacob Cohen, a

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

professor of psychology, analyzed quantitative methods involving statistical power and effect size, which helped to lay foundations for current statistical

meta-analysis Meta-analysis is a method of synthesis of quantitative data from multiple independent studies addressing a common research question. An important part of this method involves computing a combined effect size across all of the studies. As such, th ...

and the methods of estimation statistics. He gave his name to Cohen's kappa and Cohen's d.

Education and training

Undergraduate

Training for quantitative psychology can begin informally at the undergraduate level. Many graduate schools recommend that students have some coursework in psychology and complete the full college sequence of

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

(including

multivariate calculus Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables ('' mult ...

) and a course in

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

. Quantitative coursework in other fields such as

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

and research methods and statistics courses for psychology majors are also helpful. Historically, however, students without all these courses have been accepted if other aspects of their application show promise. Some schools also offer formal minors in areas related to quantitative psychology. For example, the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States. Two branch campuses are in the Kansas City metropolitan area on the Kansas side: the university's medical school and hospital ...

offers a minor in "Social and Behavioral Sciences Methodology" that provides advanced training in research methodology, applied data analysis, and practical research experience relevant to quantitative psychology. Coursework in computer science is also useful. Mastery of an

object-oriented programming language Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and impleme ...

or learning to write code in R, SAS, or

SPSS SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Versi ...

is useful for the type of data analysis performed in graduate school.

Graduate

Quantitative psychologists may possess a doctoral degree or a master's degree. Due to its interdisciplinary nature and depending on the research focus of the university, these programs may be housed in a school's

college of education In the United States and Canada, a school of education (or college of education; ed school) is a division within a university that is devoted to scholarship in the field of education, which is an interdisciplinary branch of the social sciences e ...

or in their psychology department. Programs that focus especially in

educational research Educational research refers to the systematic collection and analysis of evidence and data related to the field of education. Research may involve a variety of methods and various aspects of education including student learning, interaction, tea ...

and psychometrics are often part of education or

educational psychology Educational psychology is the branch of psychology concerned with the scientific study of human learning. The study of learning processes, from both cognitive psychology, cognitive and behavioral psychology, behavioral perspectives, allows researc ...

departments. These programs may therefore have different names mentioning "research methods" or "quantitative methods", such as the "Research and Evaluation Methodology" Ph.D. from the

University of Florida The University of Florida (Florida or UF) is a public university, public land-grant university, land-grant research university in Gainesville, Florida, United States. It is a senior member of the State University System of Florida and a preem ...

or the "Quantitative Methods" degree at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

. However, some universities may have separate programs in their two colleges. For example, the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

has a "Quantitative psychology" degree in their psychology department and a separate "Measurement & Statistics" Ph.D. in their college of education. Others, such as

Vanderbilt University Vanderbilt University (informally Vandy or VU) is a private university, private research university in Nashville, Tennessee, United States. Founded in 1873, it was named in honor of shipping and railroad magnate Cornelius Vanderbilt, who provide ...

's Ph.D. in Psychological Sciences, are jointly housed across two psychology departments. Universities with a mathematical focus include

McGill University McGill University (French: Université McGill) is an English-language public research university in Montreal, Quebec, Canada. Founded in 1821 by royal charter,Frost, Stanley Brice. ''McGill University, Vol. I. For the Advancement of Learning, ...

's "Quantitative Psychology and Modeling" program and

Purdue University Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...

's "Mathematical and Computational Psychology" degrees. Students with an interest in modeling biological or functional data may go into related fields such as

biostatistics Biostatistics (also known as biometry) is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experimen ...

computational neuroscience Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand th ...

. Doctoral programs typically accept students with only bachelor's degrees, although some schools may require a master's degree before applying. After the first two years of studies, graduate students typically earn a

Master of Arts A Master of Arts ( or ''Artium Magister''; abbreviated MA or AM) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Those admitted to the degree have ...

in Psychology,

Master of Science A Master of Science (; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medici ...

in Statistics or Applied Statistics, or both. For example, most students in the

University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...

's "Quantitative and Psychometric Methods" Ph.D. program are also Master of Science students in the School of Statistics. Additionally, several universities offer minor concentrations in quantitative methods, such as

. Companies that produce

standardized tests A standardized test is a Test (assessment), test that is administered and scored in a consistent or standard manner. Standardized tests are designed in such a way that the questions and interpretations are consistent and are administered and scored ...

such as

College Board The College Board, styled as CollegeBoard, is an American not-for-profit organization that was formed in December 1899 as the College Entrance Examination Board (CEEB) to expand access to higher education. While the College Board is not an asso ...

Educational Testing Service Educational Testing Service (ETS), founded in 1947, is the world's largest private educational testing and assessment organization. It is headquartered in Lawrence Township, Mercer County, New Jersey, Lawrence Township, New Jersey, but has a P ...

, and American College Testing are some of the largest private sector employers of quantitative psychologists. These companies also often provide internships to students in graduate school.

Shortage of qualified applicants

In 1990, an influential paper titled "Graduate Training in Statistics, Methodology, and Measurement in Psychology" was published in the ''

American Psychologist ''American Psychologist'' is a peer-reviewed academic journal published by the American Psychological Association. The journal publishes articles of broad interest to psychologists, including empirical reports and scholarly reviews covering science ...

'' journal. This article discussed the need for increased and up-to-date training in quantitative methods for psychology graduate programs in the United States. In August 2005, the American Psychological Association expressed the need for more quantitative psychologists in the industry—for every PhD awarded in the subject, there were about 2.5 quantitative psychologist position openings. Due to a lack of applicants in the field, the APA created a Task Force to study the state of quantitative psychology and predict its future. Domestic U.S. applicants are especially lacking. The majority of international applicants come from

Asia Asia ( , ) is the largest continent in the world by both land area and population. It covers an area of more than 44 million square kilometres, about 30% of Earth's total land area and 8% of Earth's total surface area. The continent, which ...

n countries, especially

South Korea South Korea, officially the Republic of Korea (ROK), is a country in East Asia. It constitutes the southern half of the Korea, Korean Peninsula and borders North Korea along the Korean Demilitarized Zone, with the Yellow Sea to the west and t ...

and

China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...

. In response to the lack of qualified applicants, the APA Council of Representatives authorized a special task force in 2006. The task force was chaired by Leona S. Aiken from

Arizona State University Arizona State University (Arizona State or ASU) is a public university, public research university in Tempe, Arizona, United States. Founded in 1885 as Territorial Normal School by the 13th Arizona Territorial Legislature, the university is o ...

Research areas

Quantitative psychologists generally have a main area of interest. Notable research areas in psychometrics include

item response theory In psychometrics, item response theory (IRT, also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of Test (student assessment), tests, questionnaires, and sim ...

and computer adaptive testing, which focus on education and intelligence testing. Other research areas include

social network analysis Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) ...

, human decision science,

statistical genetics Statistical genetics is a scientific field concerned with the development and application of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical ge ...

, and modeling psychological processes through

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. ...

analysis, such as in

fMRI Functional magnetic resonance imaging or functional MRI (fMRI) measures brain activity by detecting changes associated with blood flow. This technique relies on the fact that cerebral blood flow and neuronal activation are coupled. When an area o ...

data collection. Two common types of psychometric tests are aptitude tests, which are supposed to measure raw intellectual suitability for a purpose, and personality tests, which aim to assess tendencies toward certain thoughts, feelings, or behaviors. Item response theory (IRT) is based on the application of related

mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

s to testing data. Because it is generally regarded as superior to

classical test theory Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological Test (assessment), testing such as the difficulty of items or the ability of test-takers. It is a theory of testing based on the idea that ...

, it is the preferred method for developing scales in the United States. IRT is especially preferred when optimal decisions are demanded in so-called high-stakes tests, such as the Graduate Record Examination (GRE) and Graduate Management Admission Test (GMAT).

Professional organizations

Quantitative psychology is served by several scientific organizations. These include the Psychometric Society, Division 5 of the

(Quantitative and Qualitative Methods), the Society of Multivariate Experimental Psychology, and the European Society for Methodology. Associated disciplines include statistics,

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, educational measurement, educational statistics, sociology, and political science. Several scholarly journals reflect the efforts of scientists in these areas, notably '' Psychometrika'', '' Psychological Methods'', '' Multivariate Behavioral Research'', ''

Journal of Mathematical Psychology The ''Journal of Mathematical Psychology'' is a peer-reviewed scientific journal established in 1964. It covers all areas of mathematical and theoretical psychology, including sensation and perception, psychophysics, learning and memory, problem s ...

'', and ''

Structural Equation Modeling (journal) ''Structural Equation Modeling'' is a peer-reviewed Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of ...

''.

Notable people

The following is a select list of quantitative psychologists or people who have contributed to the field:

References

External links

APA Division 5: Quantitative and Qualitative Methods

The Psychometric Society

The Society of Multivariate Experimental Psychology

The European Society for Methodology

Society for Mathematical Psychology
Quantitative psychology Applied statistics Psychometrics Quantitative analysis of behavior Quantitative research