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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.
Structural equation modeling (SEM) is a diverse set of methods used by scientists doing both observational and experimental research. SEM is used mostly in the social and behavioral sciences but it is also used in epidemiology, business, and other fields. A definition of SEM is difficult without reference to technical language, but a good starting place is the name itself.
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.
In statistics, latent variables are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such latent variable models are used in many disciplines, including political science, demography, engineering, medicine, ecology, physics, machine learning/artificial intelligence, bioinformatics, chemometrics, natural language processing, management, psychology and the social sciences.
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.
Multilevel models are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models, although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available.
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as OpenMx, lavaan, AMOS, Mplus, LISREL, or EQS among others may be used to estimate growth trajectories.
In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable. Rather than a direct causal relationship between the independent variable and the dependent variable, which is often false, a mediation model proposes that the independent variable influences the mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables.
In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis, most commonly used in social science research. It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct. As such, the objective of confirmatory factor analysis is to test whether the data fit a hypothesized measurement model. This hypothesized model is based on theory and/or previous analytic research. CFA was first developed by Jöreskog (1969) and has built upon and replaced older methods of analyzing construct validity such as the MTMM Matrix as described in Campbell & Fiske (1959).
Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods. For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed.
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 at 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.
In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale and serves to identify a set of latent constructs underlying a battery of measured variables. It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables. Measured variables are any one of several attributes of people that may be observed and measured. Examples of measured variables could be the physical height, weight, and pulse rate of a human being. Usually, researchers would have a large number of measured variables, which are assumed to be related to a smaller number of "unobserved" factors. Researchers must carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.
In statistics, the Sobel test is a method of testing the significance of a mediation effect. The test is based on the work of Michael E. Sobel, and is an application of the delta method. In mediation, the relationship between the independent variable and the dependent variable is hypothesized to be an indirect effect that exists due to the influence of a third variable. As a result when the mediator is included in a regression analysis model with the independent variable, the effect of the independent variable is reduced and the effect of the mediator remains significant. The Sobel test is basically a specialized t test that provides a method to determine whether the reduction in the effect of the independent variable, after including the mediator in the model, is a significant reduction and therefore whether the mediation effect is statistically significant.
One application of multilevel modeling (MLM) is the analysis of repeated measures data. Multilevel modeling for repeated measures data is most often discussed in the context of modeling change over time ; however, it may also be used for repeated measures data in which time is not a factor.
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.
Patrick James Curran is an American psychologist and statistician. He is a professor of quantitative psychology at the University of North Carolina, where he is also a faculty member at the Center for Developmental Science.
John J. McArdle is Professor of Psychology and Gerontology at the University of Southern California (USC), where he is also director of the Unified Studies of Cognition (CogUSC) Lab. He is known for his work on quantitative research methodology and on the changes in cognitive function and personality that occur as individuals age.
In statistics, confirmatory composite analysis (CCA) is a sub-type of structural equation modeling (SEM). Although, historically, CCA emerged from a re-orientation and re-start of partial least squares path modeling (PLS-PM), it has become an independent approach and the two should not be confused. In many ways it is similar to, but also quite distinct from confirmatory factor analysis (CFA). It shares with CFA the process of model specification, model identification, model estimation, and model assessment. However, in contrast to CFA which always assumes the existence of latent variables, in CCA all variables can be observable, with their interrelationships expressed in terms of composites, i.e., linear compounds of subsets of the variables. The composites are treated as the fundamental objects and path diagrams can be used to illustrate their relationships. This makes CCA particularly useful for disciplines examining theoretical concepts that are designed to attain certain goals, so-called artifacts, and their interplay with theoretical concepts of behavioral sciences.
References
- ↑ Integrative Data Analysis and Big Data, National Cancer Institute
- ↑ University teaching awards
- ↑ Conference presentations
- ↑ Google Scholar profile
