Quantitative psychology

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Quantitative psychology is a field of scientific study that focuses on the mathematical modeling, research design and methodology, and statistical analysis of human or animal psychological processes. It includes tests and other devices for measuring human abilities. [1] Quantitative psychologists develop and analyze a wide variety of research methods, including those of psychometrics, a field concerned with the theory and technique of psychological measurement. [2]

Statistics Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, displaying, analysis, interpretation and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.

Psychometrics is a field of study concerned with the theory and technique of psychological measurement. As defined by the US National Council on Measurement in Education (NCME), psychometrics refers to psychological measurement. Generally, it refers to the field in psychology and education that is devoted to testing, measurement, assessment, and related activities.


Psychologists have long contributed to statistical and mathematical analysis, and quantitative psychology is now a specialty recognized by the American Psychological Association. Doctoral degrees are awarded in this field in a number of universities in Europe and North America, and quantitative psychologists have been in high demand in industry, government, and academia. Their training in both social science and quantitative methodology provides a unique skill set for solving both applied and theoretical problems in a variety of areas.

American Psychological Association scientific and professional organization

The American Psychological Association (APA) is the largest scientific and professional organization of psychologists in the United States, with over 118,000 members including scientists, educators, clinicians, consultants, and students. The APA has an annual budget of around $115m. There are 54 divisions of the APA—interest groups covering different subspecialties of psychology or topical areas.

Social science The academic disciplines concerned with society and the relationships between individuals in society

Social science is a category of academic disciplines concerned with society and the relationships among individuals within a society. The disciplines include, but are not limited to: anthropology, archaeology, communication studies, economics, history, musicology, human geography, jurisprudence, linguistics, political science, psychology, public health, and sociology. The term is also sometimes used to refer specifically to the field of sociology, the original "science of society", established in the 19th century. For a more detailed list of sub-disciplines within the social sciences see: Outline of social science.


Francis Galton's correlation diagram, 1875. Galton's correlation diagram 1875.jpg
Francis Galton's correlation diagram, 1875.

Quantitative psychology has its roots in early experimental psychology 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 (1930s), Fechner's development and use of the psychophysical methods (1850-1860), and Helmholtz's research on vision and audition beginning after 1850. Wilhelm Wundt 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. [3] The work of these and many others helped put to rest the assertion, by theorists such as Immanuel Kant, that psychology could not become a science because precise experiments on the human mind were impossible.

Experimental psychology refers to work done by those who apply experimental methods to psychological study and the processes that underlie it. Experimental psychologists employ human participants and animal subjects to study a great many topics, including sensation & perception, memory, cognition, learning, motivation, emotion; developmental processes, social psychology, and the neural substrates of all of these.

Gustav Fechner German philosopher, physicist and experimental psychologist

Gustav Theodor Fechner was a German philosopher, physicist and experimental psychologist. An early pioneer in experimental psychology and founder of psychophysics, he inspired many 20th-century scientists and philosophers. He is also credited with demonstrating the non-linear relationship between psychological sensation and the physical intensity of a stimulus via the formula: , which became known as the Weber–Fechner law.

Hermann von Helmholtz physicist and physiologist

Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions in several scientific fields. The largest German association of research institutions, the Helmholtz Association, is named after him.

Intelligence testing

Intelligence testing has long been an important branch of quantitative psychology. The nineteenth-century English statistician Francis Galton, 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 reflexes, muscle strength, and head size are correlated with intelligence. [4] [5] 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".

Francis Galton English polymath: geographer, statistician, pioneer in eugenics (1822–1911)

Sir Francis Galton, FRS was an English Victorian era statistician, polymath, sociologist, psychologist, anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, and psychometrician. He was knighted in 1909.

A reflex, or reflex action, is an involuntary and nearly instantaneous movement in response to a stimulus. A reflex is made possible by neural pathways called reflex arcs which can act on an impulse before that impulse reaches the brain. The reflex is then an automatic response to a stimulus that does not receive or need conscious thought.

Muscle contractile soft tissue of mammals

Muscle is a soft tissue found in most animals. Muscle cells contain protein filaments of actin and myosin that slide past one another, producing a contraction that changes both the length and the shape of the cell. Muscles function to produce force and motion. They are primarily responsible for maintaining and changing posture, locomotion, as well as movement of internal organs, such as the contraction of the heart and the movement of food through the digestive system via peristalsis.

Statistical techniques

IQ scores represented by a normal distribution. IQ curve.svg
IQ scores represented by a normal distribution.

Statistical methods are the quantitative tools most used by psychologists. Pearson introduced the correlation coefficient and the chi-squared test. 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 the multivariate tests). Popular techniques (such as Hierarchical Linear Model, Arnold, 1992, Structural Equation Modeling, Byrne, 1996 and Independent Component Analysis, Hyvarinën, Karhunen and Oja, 2001) are relatively recent. [6]

In 1946, psychologist Stanley Smith Stevens organized levels of measurement into four scales: Nominal, Ordinal, Ratio, and Interval in a paper that is still often cited. [7] Jacob Cohen, a New York University professor of psychology, analyzed quantitative methods involving statistical power and effect size, which helped to lay foundations for current statistical meta-analysis and the methods of estimation statistics. [8] He gave his name to Cohen's kappa and Cohen's d.

Stanley Smith Stevens 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 authored a milestone textbook, the 1400+ page Handbook of Experimental Psychology (1951). He was also one of the founding organizers of the Psychonomic Society. In 1946 he introduced a theory of levels of measurement widely used by scientists but criticized by statisticians.

Jacob Cohen was an American psychologist and statistician best known for his work on statistical power and effect size, which helped to lay foundations for current statistical meta-analysis and the methods of estimation statistics. He gave his name to such measures as Cohen's kappa, Cohen's d, and Cohen's h.

New York University private research university in New York, NY, United States

New York University (NYU) is a private research university based in New York City. Founded in 1831, NYU's historical campus is in Greenwich Village, Lower Manhattan. NYU also has degree-granting campuses in Abu Dhabi and Shanghai, and academic centers in Accra, Berlin, Buenos Aires, Florence, London, Los Angeles, Madrid, Paris, Prague, Sydney, Tel Aviv, and Washington, D.C.

In 1990, an influential paper titled "Graduate Training in Statistics, Methodology, and Measurement in Psychology" was published in the American Psychologist journal. This article discussed the need for increased and up-to-date training in quantitative methods for psychology graduate programs in the United States. [9]

Education and training


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 (including multivariate calculus) and a course in linear algebra. Quantitative coursework in other fields such as economics 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 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. [10] Coursework in computer science is also useful. Mastery of an object-oriented programming language or learning to write code in SPSS or R is useful for the type of data analysis performed in graduate school.


Peabody College (pictured) at Vanderbilt University houses their Quantitative Methods program. Peabodyvu.JPG
Peabody College (pictured) at Vanderbilt University houses their Quantitative Methods program.

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 or in their psychology department. Programs that focus especially in educational research and psychometrics are often part of education or educational psychology 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 or the "Quantitative Methods" degree at the University of Pennsylvania. However, some universities may have separate programs in their two colleges. For example, the University of Washington 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's Ph.D in Psychological Sciences is jointly housed across its two psychology departments.

Universities with a mathematical focus include McGill University's "Quantitative Psychology and Modeling" program and Purdue University's "Mathematical and Computational Cognitive Science" degrees. Students with an interest in modeling biological or functional data may go into related fields such as biostatistics or computational neuroscience.

Doctoral programs typical 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 in Psychology, Master of Science in Statistics or Applied statistics, or both.

Additionally, several universities offer minor concentrations in quantitative methods, such as New York University.

Companies that produce standardized tests such as College Board, Educational Testing Service, and American College Testing are some of the biggest private sector employers of quantitative psychologists. These companies also often provide internships to students in graduate school.

Shortage of qualified applicants

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. [11] 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 Asian countries, especially South Korea and China. [12] In response to the lack of qualified applicants, the APA Council of Representatives authorized a special task force in 2006. [13] The task force was chaired by Leona S. Aiken from Arizona State University.

Research areas

Example of a social network diagram. Social Red.jpg
Example of a social network diagram.

Quantitative psychologists generally have a main area of interest. [14] Notable research areas in psychometrics include item response theory and computer adaptive testing, which focus on education and intelligence testing. Other research areas include modeling psychological processes through time series analysis, such as in fMRI data collection, and structural equation modeling, social network analysis, human decision science, and statistical genetics.

Two common types of psychometric tests are: aptitude tests, which are supposed to measure raw intellectual ability, and personality tests that aim to assess your character, temperament, and how you deal with problems.

Item response theory is based on the application of related mathematical models to testing data. Because it is generally regarded as superior to classical test theory, it is the preferred method for developing scales in the United States, especially when optimal decisions are demanded, as in so-called high-stakes tests, e.g., 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 American Psychological Association (Evaluation, Measurement and Statistics), the Society of Multivariate Experimental Psychology, and the European Society for Methodology. Associated disciplines include statistics, mathematics, educational measurement, educational statistics, sociology, and political science. Several scholarly journals reflect the efforts of scientists in these areas, notably Psychometrika , Multivariate Behavioral Research, Structural Equation Modeling and Psychological Methods.

Notable people

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

See also

Related Research Articles

Psychological statistics is application of formulas, theorems, numbers and laws to psychology. Statistical Methods for psychology include development and application statistical theory and methods for modeling psychological data. These methods include psychometrics, Factor analysis, Experimental Designs, Multivariate Behavioral Research. The article also discusses journals in the same field Wilcox, R. (2012).

In natural and social sciences, and sometimes in other fields, quantitative research is the systematic empirical investigation of observable phenomena via statistical, mathematical, or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships.

Louis Leon Thurstone was a U.S. pioneer in the fields of psychometrics and psychophysics. He conceived the approach to measurement known as the law of comparative judgment, and is well known for his contributions to factor analysis. A Review of General Psychology survey, published in 2002, ranked Thurstone as the 88th most cited psychologist of the 20th century, tied with John Garcia, James J. Gibson, David Rumelhart, Margaret Floy Washburn, and Robert S. Woodworth.

Raymond Cattell British-American psychologist

Raymond Bernard Cattell was a British and American psychologist, known for his psychometric research into intrapersonal psychological structure. His work also explored the basic dimensions of personality and temperament, the range of cognitive abilities, the dynamic dimensions of motivation and emotion, the clinical dimensions of abnormal personality, patterns of group syntality and social behavior, applications of personality research to psychotherapy and learning theory, predictors of creativity and achievement, and many multivariate research methods including the refinement of factor analytic methods for exploring and measuring these domains. Cattell authored, co-authored, or edited almost 60 scholarly books, more than 500 research articles, and over 30 standardized psychometric tests, questionnaires, and rating scales. According to a widely cited ranking, Cattell was the 16th most eminent, 7th most cited in the scientific journal literature, and among the most productive, but controversial psychologists of the 20th century.

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. The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. Quantifiable behavior is in practice often constituted by task performance.

Norman Cliff is an American psychologist. He received his Ph.D. from Princeton in psychometrics in 1957. After research positions in the US Public Health Service and at Educational Testing Service he joined the University of Southern California in 1962. He has had a number of research interests, including quantification of cognitive processes, scaling and measurement theory, computer-interactive psychological measurement, multivariate statistics, and ordinal methods. One of his major contributions to psychometrics was the method for rotation of canonical components. Asserting that much of psychological data have only ordinal justification, Cliff also published various papers and a book on ordinal methods for research. On the one hand this included extensions to the established ordinal methods for correlating data. However, on the other hand, Cliff also suggested that there are viable and robust ordinal alternatives to mean comparisons. He introduced a measure of proportional difference between two sets of data often referred to as Cliff's delta. He has been president of the Psychometric Society and of the Society for Multivariate Experimental Psychology. Now an Emeritus Professor, he lives in New Mexico.

Lee Joseph Cronbach was an American educational psychologist who made contributions to psychological testing and measurement. At the University of Illinois, Urbana, Cronbach produced many of his works: the "Alpha" paper, as well as an essay titled The Two Disciplines of Scientific Psychology, in the American Psychologist magazine in 1957, where he discussed his thoughts on the increasing divergence between the fields of experimental psychology and correlational psychology.

Frank L. Schmidt is a retired American psychology professor known for his work in personnel selection and employment testing. Schmidt is a researcher in the area of industrial and organizational psychology with the most number of publications in the two major journals in the 1980s. In the 1990s he was the 4th most published researcher in Journal of Applied Psychology (JAP) and Personnel Psychology (PP), the two principal publications in the field of industrial-organizational psychology. He is also winner of the first Dunnette Prize, the most prestigious lifetime achievement award given by the Society for Industrial and Organizational Psychology "to honor living individuals whose work has significantly expanded knowledge of the causal significance of individual differences through advanced research, development, and/or application".

Michael Friendly American psychologist

Michael Louis Friendly is an American psychologist, Professor of Psychology at York University in Ontario, Canada, and director of its Statistical Consulting Service, especially known for his contributions to graphical methods for categorical and multivariate data, and on the history of data and information visualisation.

Karl Gustav Jöreskog is a Swedish statistician. Jöreskog is a Professor Emeritus at Uppsala University, and a co-author of the LISREL statistical program. He is also a member of the Royal Swedish Academy of Sciences. Jöreskog received his bachelor's, master's, and doctoral degrees in Uppsala University. He is also a former student of Herman Wold. He was a statistician at Educational Testing Service (ETS) and a visiting professor at Princeton University.

Jan de Leeuw is a Dutch statistician and psychometrician. He is Distinguished Professor Emeritus of Statistics and Founding Chair of the Department of Statistics, University of California, Los Angeles. In addition, he is the founding editor and former editor-in-chief of the Journal of Statistical Software, as well as the former editor-in-chief of the Journal of Multivariate Analysis and the "Journal of Educational and Behavioral Statistics".

Gideon J. Mellenbergh Dutch psychologist

Gideon Jan (Don) Mellenbergh is a Dutch psychologist, and Emeritus Professor of Psychological methods at the University of Amsterdam, known for his contribution in the field of psychometrics, and Social Research Methodology.

Jacqueline Meulman Dutch psychologist

Jacqueline Meulman is a Dutch statistician and Professor of Applied Statistics at the Mathematical Institute - Leiden University.

Dorothy Christina Adkins was an American psychologist. Adkins is best known for her work in psychometrics and education testing, particularly in achievement testing. She was the first female president of the Psychometric Society and served in several roles in the American Psychological Association.

Ben James Winer was an American research psychologist and academic. He served as a psychology professor at Purdue University and was president of the Psychometric Society. He has been listed as one of the most highly cited psychologists in the United States, having authored a well-known textbook on statistical analysis.

Bruno D. Zumbo is an applied mathematician working primarily in the psychological, social and health sciences. He is currently Professor and Distinguished University Scholar, and Paragon UBC Professor of Psychometrics & Measurement at University of British Columbia. He is known for his contributions in the fields of statistics, psychometrics, validity theory, and studies of the mathematical basis of classical test theory and measurement error models.

Li Cai is a statistician and quantitative psychologist. He is a professor of Advanced Quantitative Methodology at the UCLA Graduate School of Education and Information Studies with a joint appointment in the quantitative area of the UCLA Department of Psychology. He is also Director of the National Center for Research on Evaluation, Standards, and Student Testing, Managing Partner at Vector Psychometric Group.

Patrick James Curran is an American statistician and professor of quantitative psychology at the University of North Carolina, where he is also a faculty member at the Center for Developmental Science.

Daniel John Bauer is an American statistician, professor, and director of the quantitative psychology program at the University of North Carolina, where he is also on the faculty at the Center for Developmental Science. He is known for rigorous methodological work on latent variable models and is a proponent of integrative data analysis, a meta-analytic technique that pools raw data across multiple independent studies.


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  8. Cohen's entry in Encyclopedia of Statistics in Behavioral Science
  9. Aiken, Leona S.; West, Stephen G. (June 1990). "Graduate Training in Statistics, Methodology, and Measurement in Psychology: A Survey of PhD Programs in North America" (PDF). American Psychologist. 45 (6): 721–734. doi:10.1037/0003-066x.45.6.721. Archived from the original (PDF) on 2015-01-19. Retrieved 19 January 2015.
  10. "Undergraduate Minor in Social and Behavioral Sciences Methodology". University of Kansas. Retrieved 13 December 2014.
  11. Report of the Task Force for Increasing the Number of Quantitative Psychologists, page 1. American Psychological Association. Retrieved February 15, 2012
  12. "Report of the Task Force for Increasing the Number of Quantitative Psychologists" (PDF). American Psychological Association. Retrieved 13 December 2014.
  13. "Quantitative Psychology". American Psychological Association. Retrieved 19 January 2015.
  14. Mitchell J. Prinstein (31 August 2012). The Portable Mentor: Expert Guide to a Successful Career in Psychology. Springer Science & Business Media. p. 24. ISBN   978-1-4614-3993-6.

Further reading