Psychometrics in the context of Measurement

Human intelligence is the intellectual capability of humans, which is marked by complex cognitive feats and high levels of motivation and self-awareness. Using their intelligence, humans are able to learn, form concepts, understand, and apply logic and reason. Human intelligence is also thought to encompass their capacities to recognize patterns, plan, innovate, solve problems, make decisions, retain information, and use language to communicate.

There are conflicting ideas about how intelligence should be conceptualized and measured. In psychometrics, human intelligence is commonly assessed by intelligence quotient (IQ) tests, although the validity of these tests is disputed. Several subcategories of intelligence, such as emotional intelligence and social intelligence, have been proposed, and there remains significant debate as to whether these represent distinct forms of intelligence.

Validity is the main extent to which a concept, conclusion, or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence (e.g. face validity, construct validity, etc.) described in greater detail below.

In psychometrics, validity has a particular application known as test validity: "the degree to which evidence and theory support the interpretations of test scores" ("as entailed by proposed uses of tests").

In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:

For example, measurements of people's height and weight are often extremely reliable.

In psychology and psychometrics, the big five personality trait model or five-factor model (FFM)—sometimes called by the acronym OCEAN or CANOE—is a scientific model for measuring and describing human personality traits. The framework groups variation in personality into five separate factors, all measured on a continuous scale:

• openness (O) measures creativity, curiosity, and willingness to entertain new ideas.
• conscientiousness (C) measures self-control, diligence, and attention to detail.
• extraversion (E) measures boldness, energy, and social interactivity.
• agreeableness (A) measures kindness, helpfulness, and willingness to cooperate.
• neuroticism (N) measures depression, irritability, and moodiness.

The five-factor model was developed using empirical research into the language people used to describe themselves, which found patterns and relationships between the words people use to describe themselves. For example, because someone described as "hard-working" is more likely to be described as "prepared" and less likely to be described as "messy", all three traits are grouped under conscientiousness. Using dimensionality reduction techniques, psychologists showed that most (though not all) of the variance in human personality can be explained using only these five factors.

Educational measurement refers to the use of educational assessments and the analysis of data such as scores obtained from educational assessments to infer the abilities and proficiencies of students. The approaches overlap with those in psychometrics.Educational measurement is the assigning of numerals to traits such as achievement, interest, attitudes, aptitudes, intelligence and performance.

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 tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments". By contrast, item response theory treats the difficulty of each item (the item characteristic curves, or ICCs) as information to be incorporated in scaling items.

It is based on the application of related mathematical models to testing data. Because it is often 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).

The concepts of fluid intelligence (g_f) and crystallized intelligence (g_c) were introduced in 1943 by the psychologist Raymond Cattell. According to Cattell's psychometrically-based theory, general intelligence (g) is subdivided into g_f and g_c. Fluid intelligence is the ability to solve novel reasoning problems. It is correlated with a number of important skills such as comprehension, problem-solving, and learning. Crystallized intelligence, on the other hand, involves the ability to deduce secondary relational abstractions by applying previously learned primary relational abstractions.

Cognitive tests are assessments of the cognitive capabilities of humans and other animals. Tests administered to humans include various forms of IQ tests; those administered to animals include the mirror test (a test of visual self-awareness) and the T maze test (which tests learning ability). Such testing is used in psychology and psychometrics, as well as other fields studying human and animal intelligence.

Modern cognitive tests originated through the work of James McKeen Cattell who coined the term "mental tests". They followed Francis Galton's development of physical and physiological tests. For example, Galton measured strength of grip and height and weight. He established an "Anthropometric Laboratory" in the 1880s where patrons paid to have physical and physiological attributes measured. Galton's measurements had an enormous influence on psychology. Cattell continued the measurement approach with simple measurements of perception. Cattell's tests were eventually abandoned in favor of the battery test approach developed by Alfred Binet.

Psychological testing refers to the administration of psychological tests. Psychological tests are administered or scored by trained evaluators. A person's responses are evaluated according to carefully prescribed guidelines. Scores are thought to reflect individual or group differences in the theoretical construct the test purports to measure. The science behind psychological testing is psychometrics.

Aaron Temkin Beck (July 18, 1921 – November 1, 2021) was an American psychiatrist who was a professor in the department of psychiatry at the University of Pennsylvania. He is regarded as the father of cognitive therapy and cognitive behavioral therapy (CBT). His pioneering methods are widely used in the treatment of clinical depression and various anxiety disorders. Beck also developed self-report measures for depression and anxiety, notably the Beck Depression Inventory (BDI), which became one of the most widely used instruments for measuring the severity of depression. In 1994 he and his daughter, psychologist Judith S. Beck, founded the nonprofit Beck Institute for Cognitive Behavior Therapy, which provides CBT treatment and training, as well as research. Beck served as President Emeritus of the organization up until his death.

Beck was noted for his writings on psychotherapy, psychopathology, suicide, and psychometrics. He published more than 600 professional journal articles, and authored or co-authored 25 books. He was named one of the "Americans in history who shaped the face of American psychiatry", and one of the "five most influential psychotherapists of all time" by The American Psychologist in July 1989.

A Likert scale (/ˈlɪkərt/ LIK-ərt,) is a psychometric scale named after its inventor, American social psychologist Rensis Likert, which is commonly used in research questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term (or more fully the Likert-type scale) is often used interchangeably with rating scale, although there are other types of rating scales.

Likert distinguished between a scale proper, which emerges from collective responses to a set of items (usually eight or more), and the format in which responses are scored along a range. Technically speaking, a Likert scale refers only to the former. The difference between these two concepts has to do with the distinction Likert made between the underlying phenomenon being investigated and the means of capturing variation that points to the underlying phenomenon.

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 (in practice often constituted by task performance). 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.

Although psychology, as an independent subject of science, is a more recent discipline than physics, the application of mathematics to psychology has been done in the hope of emulating the success of this approach in the physical sciences, which dates back to at least the seventeenth century. Mathematics in psychology is used extensively roughly in two areas: one is the mathematical modeling of psychological theories and experimental phenomena, which leads to mathematical psychology; the other is the statistical approach of quantitative measurement practices in psychology, which leads to psychometrics.

A latent variable model is a statistical model that relates a set of observable variables (also called manifest variables or indicators) to a set of latent variables. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. Common use cases for latent variable models include applications in psychometrics (e.g., summarizing responses to a set of survey questions with a factor analysis model positing a smaller number of psychological attributes, such as the trait extraversion, that are presumed to cause the survey question responses), and natural language processing (e.g., a topic model summarizing a corpus of texts with a number of "topics").

It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable (local independence).

Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in chemistry, biochemistry, medicine, biology and chemical engineering. In this way, it mirrors other interdisciplinary fields, such as psychometrics and econometrics.

The Minnesota Multiphasic Personality Inventory (MMPI) is a standardized psychometric test of adult personality and psychopathology. A version for adolescents also exists, the MMPI-A, and was first published in 1992. Psychologists use various versions of the MMPI to help develop treatment plans, assist with differential diagnosis, help answer legal questions (forensic psychology), screen job candidates during the personnel selection process, or as part of a therapeutic assessment procedure.

The original MMPI was developed by Starke R. Hathaway and J. C. McKinley, faculty of the University of Minnesota, and first published by the University of Minnesota Press in 1943. It was replaced by an updated version, the MMPI-2, in 1989 (Butcher, Dahlstrom, Graham, Tellegen, and Kaemmer). An alternative version of the test, the MMPI-2 Restructured Form (MMPI-2-RF), published in 2008, retains some aspects of the traditional MMPI assessment strategy, but adopts a different theoretical approach to personality test development. The newest version (MMPI-3) was released in 2020.

A criterion-referenced test is a style of test that uses test scores to generate a statement about the behavior that can be expected of a person with that score. Most tests and quizzes that are written by school teachers can be considered criterion-referenced tests. In this case, the objective is simply to see whether the student has learned the material. Criterion-referenced assessment can be contrasted with norm-referenced assessment and ipsative assessment.

Criterion-referenced testing was a major focus of psychometric research in the 1970s.