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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 variable that cannot be directly observed. Examples of latent constructs include intelligence, introversion, Mental disorder, and educational achievement. (2025). 9780321056771, Allyn and Bacon. ISBN 9780321056771 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.
Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications, such as degrees or certifications, and most are psychologists with advanced graduate training in psychometrics and measurement theory. In addition to traditional academic institutions, practitioners also work for organizations, such as Pearson and the Educational Testing Service. Some psychometric researchers focus on the construction and validation of assessment instruments, including Survey sampling, Scale invariance, and open- or close-ended Questionnaire. Others focus on research relating to measurement theory (e.g., item response theory, intraclass correlation) or specialize as learning and development professionals.
Galton wrote a book entitled Hereditary Genius which was first published in 1869. The book described different characteristics that people possess and how those characteristics make some more "fit" than others. Today these differences, such as sensory and motor functioning (reaction time, visual acuity, and physical strength), are important domains of scientific psychology. Much of the early theoretical and applied work in psychometrics was undertaken in an attempt to measure intelligence. Galton often referred to as "the father of psychometrics," devised and included mental tests among his anthropometric measures. James McKeen Cattell, a pioneer in the field of psychometrics, went on to extend Galton's work. Cattell coined the term mental test, and is responsible for research and knowledge that ultimately led to the development of modern tests. (2012). 9781133492016, Cengage Learning. ISBN 9781133492016
E.H. Weber built upon Herbart's work and tried to prove the existence of a psychological threshold, saying that a minimum stimulus was necessary to activate a sensory system. After Weber, Gustav Fechner expanded upon the knowledge he gleaned from Herbart and Weber, to devise the law that the strength of a sensation grows as the logarithm of the stimulus intensity. A follower of Weber and Fechner, Wilhelm Wundt is credited with founding the science of psychology. It is Wundt's influence that paved the way for others to develop psychological testing.
More recently, psychometric theory has been applied in the measurement of , attitudes and , and academic achievement. These latent constructs cannot truly be measured, and much of the research and science in this discipline has been developed in an attempt to measure these constructs as close to the true score as possible.
Figures who made significant contributions to psychometrics include Karl Pearson, Henry F. Kaiser, Carl Brigham, L. L. Thurstone, E. L. Thorndike, Georg Rasch, Eugene Galanter, Johnson O'Connor, Frederic M. Lord, Ledyard R Tucker, Louis Guttman, and Jane Loevinger.
Indeed, Stevens's definition of measurement was put forward in response to the British Ferguson Committee, whose chair, A. Ferguson, was a physicist. The committee was appointed in 1932 by the British Association for the Advancement of Science to investigate the possibility of quantitatively estimating sensory events. Although its chair and other members were physicists, the committee also included several psychologists. The committee's report highlighted the importance of the definition of measurement. While Stevens's response was to propose a new definition, which has had considerable influence in the field, this was by no means the only response to the report. Another, notably different, response was to accept the classical definition, as reflected in the following statement:
These divergent responses are reflected in alternative approaches to measurement. For example, methods based on covariance matrices are typically employed on the premise that numbers, such as raw scores derived from assessments, are measurements. Such approaches implicitly entail Stevens's definition of measurement, which requires only that numbers are assigned according to some rule. The main research task, then, is generally considered to be the discovery of associations between scores, and of factors posited to underlie such associations.
On the other hand, when measurement models such as the Rasch model are employed, numbers are not assigned based on a rule. Instead, in keeping with Reese's statement above, specific criteria for measurement are stated, and the goal is to construct procedures or operations that provide data that meet the relevant criteria. Measurements are estimated based on the models, and tests are conducted to ascertain whether the relevant criteria have been met.
Another major focus in psychometrics has been on . There has been a range of theoretical approaches to conceptualizing and measuring personality, though there is no widely agreed upon theory. Some of the better-known instruments include the Minnesota Multiphasic Personality Inventory, the Five-Factor Model (or "Big 5") and tools such as Personality and Preference Inventory and the Myers–Briggs Type Indicator. Attitudes have also been studied extensively using psychometric approaches. (2025). 9780028683867, Gale. ISBN 9780028683867 An alternative method involves the application of unfolding measurement models, the most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993).
Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: factor analysis,Thompson, B.R. (2004). Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications. American Psychological Association. a method of determining the underlying dimensions of data. One of the main challenges faced by users of factor analysis is a lack of consensus on appropriate procedures for determining the number of latent factors. A usual procedure is to stop factoring when eigenvalues drop below one because the original sphere shrinks. The lack of the cutting points concerns other multivariate methods, also.
Multidimensional scalingDavison, M.L. (1992). Multidimensional Scaling. Krieger. is a method for finding a simple representation for data with a large number of latent dimensions. Cluster analysis is an approach to finding objects that are like each other. Factor analysis, multidimensional scaling, and cluster analysis are all multivariate descriptive methods used to distill from large amounts of data simpler structures.
More recently, structural equation modelingKaplan, D. (2008). Structural Equation Modeling: Foundations and Extensions, 2nd ed. Sage. and path analysis represent more sophisticated approaches to working with large covariance matrices. These methods allow statistically sophisticated models to be fitted to data and tested to determine if they are adequate fits. Because at a granular level psychometric research is concerned with the extent and nature of multidimensionality in each of the items of interest, a relatively new procedure known as bi-factor analysis can be helpful. Bi-factor analysis can decompose "an item's systematic variance in terms of, ideally, two sources, a general factor and one source of additional systematic variance."
Both reliability and validity can be assessed statistically. Consistency over repeated measures of the same test can be assessed with the Pearson correlation coefficient, and is often called test-retest reliability. Similarly, the equivalence of different versions of the same measure can be indexed by a Pearson correlation, and is called equivalent forms reliability or a similar term.
Internal consistency, which addresses the homogeneity of a single test form, may be assessed by correlating performance on two halves of a test, which is termed split-half reliability; the value of this Pearson product-moment correlation coefficient for two half-tests is adjusted with the Spearman–Brown prediction formula to correspond to the correlation between two full-length tests. Perhaps the most commonly used index of reliability is Cronbach's α, which is equivalent to the mean of all possible split-half coefficients. Other approaches include the intra-class correlation, which is the ratio of variance of measurements of a given target to the variance of all targets.
There are a number of different forms of validity. Criterion-related validity refers to the extent to which a test or scale predicts a sample of behavior, i.e., the criterion, that is "external to the measuring instrument itself."Nunnally, J.C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill. That external sample of behavior can be many things including another test; college grade point average as when the high school SAT is used to predict performance in college; and even behavior that occurred in the past, for example, when a test of current psychological symptoms is used to predict the occurrence of past victimization (which would accurately represent postdiction). When the criterion measure is collected at the same time as the measure being validated the goal is to establish concurrent validity; when the criterion is collected later the goal is to establish predictive validity. A measure has construct validity if it is related to measures of other constructs as required by theory. Content validity is a demonstration that the items of a test do an adequate job of covering the domain being measured. In a personnel selection example, test content is based on a defined statement or set of statements of knowledge, skill, ability, or other characteristics obtained from a job analysis.
Item response theory models the relationship between and responses to test items. Among other advantages, IRT provides a basis for obtaining an estimate of the location of a test-taker on a given latent trait as well as the standard error of measurement of that location. For example, a university student's knowledge of history can be deduced from his or her score on a university test and then be compared reliably with a high school student's knowledge deduced from a less difficult test. Scores derived by classical test theory do not have this characteristic, and assessment of actual ability (rather than ability relative to other test-takers) must be assessed by comparing scores to those of a "norm group" randomly selected from the population. In fact, all measures derived from classical test theory are dependent on the sample tested, while, in principle, those derived from item response theory are not.
Each publication presents and elaborates a set of standards for use in a variety of educational settings. The standards provide guidelines for designing, implementing, assessing, and improving the identified form of evaluation.[ Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under the accuracy topic. For example, the student accuracy standards help ensure that student evaluations will provide sound, accurate, and credible information about student learning and performance.
Two types of tools used to measure personality traits are Objective test and Projective test. Examples of such tests are the: Big Five Inventory (BFI), Minnesota Multiphasic Personality Inventory (MMPI-2), Rorschach test, Neurotic Personality Questionnaire KON-2006, or Eysenck Personality Questionnaire. Some of these tests are helpful because they have adequate reliability and Test validity, two factors that make tests consistent and accurate reflections of the underlying construct. The Myers–Briggs Type Indicator (MBTI), however, has questionable validity and has been the subject of much criticism. Psychometric specialist Robert Hogan wrote of the measure: "Most personality psychologists regard the MBTI as little more than an elaborate Chinese fortune cookie."
Lee Cronbach noted in American Psychologist (1957) that, "correlational psychology, though fully as old as experimentation, was slower to mature. It qualifies equally as a discipline, however, because it asks a distinctive type of question and has technical methods of examining whether the question has been properly put and the data properly interpreted." He would go on to say, "The correlation method, for its part, can study what man has not learned to control or can never hope to control ... A true federation of the disciplines is required. Kept independent, they can give only wrong answers or no answers at all regarding certain important problems."
The evaluation of abilities, traits and learning evolution of machines has been mostly unrelated to the case of humans and non-human animals, with specific approaches in the area of artificial intelligence. A more integrated approach, under the name of universal psychometrics, has also been proposed.
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