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, and Bayesian statistics. The article also discusses journals in the same field.
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 related activities. Psychometrics is concerned with the objective measurement of latent constructs that cannot be directly observed. Examples of latent constructs include intelligence, introversion, mental disorders, and educational achievement. The levels of individuals on nonobservable latent variables are inferred through mathematical modeling based on what is observed from individuals' responses to items on tests and scales.
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models.
Cronbach's alpha, also known as tau-equivalent reliability or coefficient alpha, is a reliability coefficient and a measure of the internal consistency of tests and measures.
Louis Leon Thurstone was an American 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.
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. There are five major research areas in mathematical psychology: learning and memory, perception and psychophysics, choice and decision-making, language and thinking, and measurement and scaling.
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.
Louis (Eliyahu) Guttman was an American sociologist and Professor of Social and Psychological Assessment at the Hebrew University of Jerusalem, known primarily for his work in social statistics.
Robert Ladd Thorndike was an American psychometrician and educational psychologist who made significant contributions to the analysis of reliability, the interpretation of error, cognitive ability, and the design and analysis of comparative surveys of achievement test performance of students in various countries.
Ledyard R. Tucker was an American mathematician who specialized in statistics and psychometrics. His Ph.D. advisor at the University of Chicago was Louis Leon Thurstone. He was a lecturer in psychology at Princeton University from 1948 to 1960, while simultaneously working at ETS. In 1960, he moved to working full-time in academia when he joined the University of Illinois. The rest of his career was spent as professor of quantitative psychology and educational psychology at UIUC until he retired in 1979. Tucker is best known for his Tucker decomposition and Tucker–Koopman–Linn model. He is credited with the invention of Angoff method.
Willem Jan Heiser is a Dutch social scientist who was Professor of Psychology, Statistical Methods and Data Theory at the Leiden University between 1989 and 2014.
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.
Jeffrey Scott Tanaka was an American psychologist and statistician, known for his work in educational psychology, social psychology and various fields of statistics including structural equation modeling.
The Vectors of Mind is a book published by American psychologist Louis Leon Thurstone in 1935 that summarized Thurstone's methodology for multiple factor analysis.
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.
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.
In statistical models applied to psychometrics, congeneric reliability a single-administration test score reliability coefficient, commonly referred to as composite reliability, construct reliability, and coefficient omega. is a structural equation model (SEM)-based reliability coefficients and is obtained from on a unidimensional model. is the second most commonly used reliability factor after tau-equivalent reliability(; also known as Cronbach's alpha), and is often recommended as its alternative.
Parallel analysis, also known as Horn's parallel analysis, is a statistical method used to determine the number of components to keep in a principal component analysis or factors to keep in an exploratory factor analysis. It is named after psychologist John L. Horn, who created the method, publishing it in the journal Psychometrika in 1965. The method compares the eigenvalues generated from the data matrix to the eigenvalues generated from a Monte-Carlo simulated matrix created from random data of the same size.
Marion Webster Richardson (1896–1965) was an American educational psychologist and psychometrician. He was a founder of the Psychometric Society and a founder and editor of Psychometrika. He was a co-developer of the Kuder–Richardson Formula 20.
Karl John Holzinger was an American educational psychologist known for his work in psychometrics.
