Quantitative psychology is a field of scientific study that focuses on the mathematical modeling, research design and methodology, and statistical analysis of psychological 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, 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. 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.

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 (1830s), Fechner's development and use of 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. The work of these individuals and many others dispelled the assertion, by theorists such as Immanuel Kant, that psychology could not become a science because precise experiments on the human mind were impossible.

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. 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 methods are the quantitative tools most used by psychologists. Karl 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 multivariate tests). More recently, popular multivariate techniques were developed—including the hierarchical linear model, structural equation modeling, and independent component analysis.

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. 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. He gave his name to Cohen's kappa and Cohen's d.

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. Coursework in computer science is also useful. Mastery of an object-oriented programming language or learning to write code in R, SAS, or SPSS is useful for the type of data analysis performed in graduate school.^{[citation needed]}

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, are jointly housed across two psychology departments.