Psychometrics

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Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. [1] 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. [2] 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. [2]

Contents

Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess a specific qualification 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 the Educational Testing Service and Psychological Corporation. Some psychometric researchers focus on the construction and validation of assessment instruments including surveys, scales, and open- or close-ended questionnaires. Others focus on research relating to measurement theory (e.g., item response theory; intraclass correlation) or specialize as learning and development professionals.

Historical foundation

Psychological testing has come from two streams of thought: the first, from Darwin, Galton, and Cattell on the measurement of individual differences, and the second, from Herbart, Weber, Fechner, and Wundt and their psychophysical measurements of a similar construct. The second set of individuals and their research is what has led to the development of experimental psychology and standardized testing. [3]

Victorian stream

Charles Darwin was the inspiration behind Sir Francis Galton, a scientist who advanced the development of psychometrics. In 1859, Darwin published his book On the Origin of Species . Darwin described the role of natural selection in the emergence, over time, of different populations of species of plants and animals. The book showed how individual members of a species differ among themselves and how they possess characteristics that are more or less adaptive to their environment. Those with more adaptive characteristics are more likely to survive to procreate and give rise to another generation. Those with less adaptive characteristics are less likely. These ideas stimulated Galton's interest in the study of human beings and how they differ one from another and, more importantly, how to measure those differences.

Galton wrote a book entitled Hereditary Genius. 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. [4]

German stream

The origin of psychometrics also has connections to the related field of psychophysics. Around the same time that Darwin, Galton, and Cattell were making their discoveries, Herbart was also interested in "unlocking the mysteries of human consciousness" through the scientific method. [4] Herbart was responsible for creating mathematical models of the mind, which were influential in educational practices in years to come.

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, G.T. 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. [4]

20th century

In 1936 the psychometrician L. L. Thurstone, founder and first president of the Psychometric Society, developed and applied a theoretical approach to measurement referred to as the law of comparative judgment, an approach that has close connections to the psychophysical theory of Ernst Heinrich Weber and Gustav Fechner. In addition, Spearman and Thurstone both made important contributions to the theory and application of factor analysis, a statistical method developed and used extensively in psychometrics. [5] In the late 1950s, Leopold Szondi made an historical and epistemological assessment of the impact of statistical thinking onto psychology during previous few decades: "in the last decades, the specifically psychological thinking has been almost completely suppressed and removed, and replaced by a statistical thinking. Precisely here we see the cancer of testology and testomania of today." [6]

More recently, psychometric theory has been applied in the measurement of personality, attitudes, and beliefs, 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.

Definition of measurement in the social sciences

The definition of measurement in the social sciences has a long history. A current widespread definition, proposed by Stanley Smith Stevens, is that measurement is "the assignment of numerals to objects or events according to some rule." This definition was introduced in a 1946 Science article in which Stevens proposed four levels of measurement. [7] Although widely adopted, this definition differs in important respects from the more classical definition of measurement adopted in the physical sciences, namely that scientific measurement entails "the estimation or discovery of the ratio of some magnitude of a quantitative attribute to a unit of the same attribute" (p. 358) [8]

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:

Measurement in psychology and physics are in no sense different. Physicists can measure when they can find the operations by which they may meet the necessary criteria; psychologists have but to do the same. They need not worry about the mysterious differences between the meaning of measurement in the two sciences (Reese, 1943, p. 49). [9]

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. [10]

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.[ citation needed ]

Instruments and procedures

The first psychometric instruments were designed to measure intelligence. [11] One historical approach involved the Stanford–Binet IQ test, developed originally by Alfred Binet and Theodore Simon.

Another major focus in psychometrics has been on personality testing. There have 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.[ citation needed ] An alternative method involves the application of unfolding measurement models, the most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993). [12]

Theoretical approaches

Psychometricians have developed a number of different measurement theories. These include classical test theory (CTT) and item response theory (IRT). [13] [14] An approach which seems mathematically to be similar to IRT but also quite distinctive, in terms of its origins and features, is represented by the Rasch model for measurement. The development of the Rasch model, and the broader class of models to which it belongs, was explicitly founded on requirements of measurement in the physical sciences. [15]

Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: factor analysis, [16] 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. [17] 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.[ citation needed ]

Multidimensional scaling [18] 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 modeling [19] 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 [20] [21] [22] 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." [23]

Key concepts

Key concepts in classical test theory are reliability and validity. A reliable measure is one that measures a construct consistently across time, individuals, and situations. A valid measure is one that measures what it is intended to measure. Reliability is necessary, but not sufficient, for validity.

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. [24] 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. [24]

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. [24] 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." [25] 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 latent traits 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.

Standards of quality

The considerations of validity and reliability typically are viewed as essential elements for determining the quality of any test. However, professional and practitioner associations frequently have placed these concerns within broader contexts when developing standards and making overall judgments about the quality of any test as a whole within a given context. A consideration of concern in many applied research settings is whether or not the metric of a given psychological inventory is meaningful or arbitrary. [26]

Testing standards

In 2014, the American Educational Research Association (AERA), American Psychological Association (APA), and National Council on Measurement in Education (NCME) published a revision of the Standards for Educational and Psychological Testing , [27] which describes standards for test development, evaluation, and use. The Standards cover essential topics in testing including validity, reliability/errors of measurement, and fairness in testing. The book also establishes standards related to testing operations including test design and development, scores, scales, norms, score linking, cut scores, test administration, scoring, reporting, score interpretation, test documentation, and rights and responsibilities of test takers and test users. Finally, the Standards cover topics related to testing applications, including psychological testing and assessment, workplace testing and credentialing, educational testing and assessment, and testing in program evaluation and public policy.

Evaluation standards

In the field of evaluation, and in particular educational evaluation, the Joint Committee on Standards for Educational Evaluation [28] has published three sets of standards for evaluations. The Personnel Evaluation Standards [29] was published in 1988, The Program Evaluation Standards (2nd edition) [30] was published in 1994, and The Student Evaluation Standards [31] was published in 2003.

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. [32] 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.

Controversy and criticism

Because psychometrics is based on latent psychological processes measured through correlations, there has been controversy about some psychometric measures. [33] [ page needed ] Critics, including practitioners in the physical sciences, have argued that such definition and quantification is difficult, and that such measurements are often misused by laymen, such as with personality tests used in employment procedures. The Standards for Educational and Psychological Measurement gives the following statement on test validity: "validity refers to the degree to which evidence and theory support the interpretations of test scores entailed by proposed uses of tests". [34] Simply put, a test is not valid unless it is used and interpreted in the way it is intended. [35]

Two types of tools used to measure personality traits are objective tests and projective measures. Examples of such tests are the: Big Five Inventory (BFI), Minnesota Multiphasic Personality Inventory (MMPI-2), Rorschach Inkblot test, Neurotic Personality Questionnaire KON-2006, [36] or Eysenck's Personality Questionnaire (EPQ-R). Some of these tests are helpful because they have adequate reliability and 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." [37]

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." [38]

Non-human: animals and machines

Psychometrics addresses human abilities, attitudes, traits, and educational evolution. Notably, the study of behavior, mental processes, and abilities of non-human animals is usually addressed by comparative psychology, or with a continuum between non-human animals and the rest of animals by evolutionary psychology. Nonetheless, there are some advocators for a more gradual transition between the approach taken for humans and the approach taken for (non-human) animals. [39] [40] [41] [42]

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. [43]

See also

Related Research Articles

Psychological statistics

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 Multivariate Behavioral Research. The article also discusses journals in the same field.

Psychological testing

Psychological testing is the administration of psychological tests. Psychological tests are administered 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 construct the test purports to measure. The science behind psychological testing is psychometrics.

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:

"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 and 1.00, are usually used to indicate the amount of error in the scores."

In the social sciences, scaling is the process of measuring or ordering entities with respect to quantitative attributes or traits. For example, a scaling technique might involve estimating individuals' levels of extraversion, or the perceived quality of products. Certain methods of scaling permit estimation of magnitudes on a continuum, while other methods provide only for relative ordering of the entities.

Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological testing such as the difficulty of items or the ability of test-takers. It is a theory of testing based on the idea that a person's observed or obtained score on a test is the sum of a true score and an error score. Generally speaking, the aim of classical test theory is to understand and improve the reliability of psychological tests.

In psychometrics, item response theory (IRT) 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" (p. 197). By contrast, item response theory treats the difficulty of each item as information to be incorporated in scaling items.

Louis Leon Thurstone was a U.S. 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.

Personality test Method of assessing human personality constructs

A personality test is a method of assessing human personality constructs. Most personality assessment instruments are in fact introspective self-report questionnaire measures or reports from life records (L-data) such as rating scales. Attempts to construct actual performance tests of personality have been very limited even though Raymond Cattell with his colleague Frank Warburton compiled a list of over 2000 separate objective tests that could be used in constructing objective personality tests. One exception however, was the Objective-Analytic Test Battery, a performance test designed to quantitatively measure 10 factor-analytically discerned personality trait dimensions. A major problem with both L-data and Q-data methods is that because of item transparency, rating scales and self-report questionnaires are highly susceptible to motivational and response distortion ranging all the way from lack of adequate self-insight to downright dissimulation depending on the reason/motivation for the assessment being undertaken.

In psychology and sociology, the Thurstone scale was the first formal technique to measure an attitude. It was developed by Louis Leon Thurstone in 1928, as a means of measuring attitudes towards religion. It is made up of statements about a particular issue, and each statement has a numerical value indicating how favorable or unfavorable it is judged to be. People check each of the statements to which they agree, and a mean score is computed, indicating their attitude.

Construct validity is the accumulation of evidence to support the interpretation of what a measure reflects. Modern validity theory defines construct validity as the overarching concern of validity research, subsuming all other types of validity evidence such as content validity and criterion validity.

The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession, agriculture, and market research because of their general applicability.

The law of comparative judgment was conceived by L. L. Thurstone. In modern-day terminology, it is more aptly described as a model that is used to obtain measurements from any process of pairwise comparison. Examples of such processes are the comparison of perceived intensity of physical stimuli, such as the weights of objects, and comparisons of the extremity of an attitude expressed within statements, such as statements about capital punishment. The measurements represent how we perceive things, rather than being measurements of actual physical properties. This kind of measurement is the focus of psychometrics and psychophysics.

Quantitative psychology

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.

Lee Joseph Cronbach was an American educational psychologist who made contributions to psychological testing and measurement. At the University of Illinois, Urbana, Cronbach produced many of his works: the "Alpha" paper, as well as an essay titled The Two Disciplines of Scientific Psychology, in the American Psychologist magazine in 1957, where he discussed his thoughts on the increasing divergence between the fields of experimental psychology and correlational psychology.

Nambury S. Raju was an American psychology professor known for his work in psychometrics, meta-analysis, and utility theory. He was a Fellow of the Society of Industrial Organizational Psychology.

<i>Measuring the Mind</i>

Measuring the Mind: Conceptual Issues in Contemporary Psychometrics is a book by Dutch academic Denny Borsboom, Assistant Professor of Psychological Methods at the University of Amsterdam, at time of publication. The book discusses the extent to which psychology can measure mental attributes such as intelligence and examines the philosophical issues that arise from such attempts.

Psychometric software is software that is used for psychometric analysis of data from tests, questionnaires, or inventories reflecting latent psychoeducational variables. While some psychometric analyses can be performed with standard statistical software like SPSS, most analyses require specialized tools.

Klaus Kubinger

Klaus D. Kubinger, is a psychologist as well as a statistician, professor for psychological assessment at the University of Vienna, Faculty of Psychology. His main research work focuses on fundamental research of assessment processes and on application and advancement of Item response theory models. He is also known as a textbook author of psychological assessment on the one hand and on statistics on the other hand.

Bruno D. Zumbo is an applied mathematician working at the intersection of the mathematical sciences and the behavioral, social and health sciences. He is currently Professor and Distinguished University Scholar, the Tier 1 Canada Research Chair in Psychometrics and Measurement, and the Paragon UBC Professor of Psychometrics & Measurement at University of British Columbia.

Automatic Item Generation (AIG), or Automated Item Generation, is a process linking psychometrics with computer programming. It uses a computer algorithm to automatically create test items that are the basic building blocks of a psychological test. The method was first described by John R. Bormuth in the 1960s but was not developed until recently. AIG uses a two-step process: first, a test specialist creates a template called an item model; then, a computer algorithm is developed to generate test items. So, instead of a test specialist writing each individual item, computer algorithms generate families of items from a smaller set of parent item models.

References

  1. National Council on Measurement in Education http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorP Archived 2017-07-22 at the Wayback Machine
  2. 1 2 Tabachnick, B.G.; Fidell, L.S. (2001). Using Multivariate Analysis. Boston: Allyn and Bacon. ISBN   978-0-321-05677-1.[ page needed ]
  3. Kaplan, R.M., & Saccuzzo, D.P. (2010). Psychological Testing: Principles, Applications, and Issues. (8th ed.). Belmont, CA: Wadsworth, Cengage Learning.
  4. 1 2 3 Kaplan, R.M., & Saccuzzo, D.P. (2010). Psychological testing: Principles, applications, and issues (8th ed.). Belmont, CA: Wadsworth, Cengage Learning.
  5. Nunnally, J., & Berstein, I. H. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill.
  6. Leopold Szondi (1960) Das zweite Buch: Lehrbuch der Experimentellen Triebdiagnostik. Huber, Bern und Stuttgart, 2nd edition. Ch.27, From the Spanish translation, B)II Las condiciones estadisticas, p.396. Quotation:
    el pensamiento psicologico especifico, en las ultima decadas, fue suprimido y eliminado casi totalmente, siendo sustituido por un pensamiento estadistico. Precisamente aqui vemos el cáncer de la testología y testomania de hoy.
  7. Stevens, S. S. (7 June 1946). "On the Theory of Scales of Measurement". Science . 103 (2684): 677–680. Bibcode:1946Sci...103..677S. doi:10.1126/science.103.2684.677. PMID   17750512. S2CID   4667599.
  8. Michell, Joel (August 1997). "Quantitative science and the definition of measurement in psychology". British Journal of Psychology. 88 (3): 355–383. doi:10.1111/j.2044-8295.1997.tb02641.x.
  9. Reese, T.W. (1943). The application of the theory of physical measurement to the measurement of psychological magnitudes, with three experimental examples. Psychological Monographs, 55, 1–89. doi : 10.1037/h0061367
  10. http://www.assessmentpsychology.com/psychometrics.htm
  11. Stern, Theodore A.; Fava, Maurizio; Wilens, Timothy E.; Rosenbaum, Jerrold F. (2016). Massachusetts General Hospital comprehensive clinical psychiatry (Second ed.). London. p. 73. ISBN   978-0323295079 . Retrieved 31 October 2021.
  12. Andrich, D. & Luo, G. (1993). A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement, 17, 253–276.
  13. Embretson, S.E., & Reise, S.P. (2000). Item Response Theory for Psychologists. Mahwah, NJ: Erlbaum.
  14. Hambleton, R.K., & Swaminathan, H. (1985). Item Response Theory: Principles and Applications. Boston: Kluwer-Nijhoff.
  15. Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. Copenhagen, Danish Institute for Educational Research, expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago: The University of Chicago Press.
  16. Thompson, B.R. (2004). Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications. American Psychological Association.
  17. Zwick, William R.; Velicer, Wayne F. (1986). "Comparison of five rules for determining the number of components to retain". Psychological Bulletin. 99 (3): 432–442. doi:10.1037//0033-2909.99.3.432.
  18. Davison, M.L. (1992). Multidimensional Scaling. Krieger.
  19. Kaplan, D. (2008). Structural Equation Modeling: Foundations and Extensions, 2nd ed. Sage.
  20. DeMars, C. E. (2013). A tutorial on interpreting bi-factor model scores. International Journal of Testing, 13, 354–378. http://dx.doi.org/10 .1080/15305058.2013.799067
  21. Reise, S. P. (2012). The rediscovery of bi-factor modeling. Multivariate Behavioral Research, 47, 667–696. http://dx.doi.org/10.1080/00273171.2012.715555
  22. Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016). Evaluating bifactor models: Calculating and interpreting statistical indices. Psychological Methods, 21, 137–150. http://dx.doi.org/10.1037/met0000045
  23. Schonfeld, I.S., Verkuilen, J. & Bianchi, R. (2019). An exploratory structural equation modeling bi-factor analytic approach to uncovering what burnout, depression, and anxiety scales measure. Psychological Assessment, 31, 1073–1079. http://dx.doi.org/10.1037/pas0000721 p. 1075
  24. 1 2 3 "Home – Educational Research Basics by Del Siegle". www.gifted.uconn.edu. 17 February 2015.
  25. Nunnally, J.C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill.
  26. Blanton, H., & Jaccard, J. (2006). Arbitrary metrics in psychology. Archived 2006-05-10 at the Wayback Machine American Psychologist, 61(1), 27–41.
  27. "The Standards for Educational and Psychological Testing". apa.org.
  28. Joint Committee on Standards for Educational Evaluation Archived 2009-10-15 at the Wayback Machine
  29. Joint Committee on Standards for Educational Evaluation. (1988). The Personnel Evaluation Standards: How to Assess Systems for Evaluating Educators. Archived 2005-12-12 at the Wayback Machine Newbury Park, CA: Sage Publications.
  30. Joint Committee on Standards for Educational Evaluation. (1994). The Program Evaluation Standards, 2nd Edition. Archived 2006-02-22 at the Wayback Machine Newbury Park, CA: Sage Publications.
  31. Committee on Standards for Educational Evaluation. (2003). The Student Evaluation Standards: How to Improve Evaluations of Students. Archived 2006-05-24 at the Wayback Machine Newbury Park, CA: Corwin Press.
  32. [E. Cabrera-Nguyen. "Author guidelines for reporting scale development and validation results in the Journal of the Society for Social Work and Research]". Academia.edu. 1 (2): 99–103.
  33. Tabachnick, B.G.; Fidell, L.S. (2001). Using Multivariate Analysis. Boston: Allyn and Bacon. ISBN   978-0-321-05677-1.
  34. American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (1999) Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
  35. Bandalos, Deborah L. (2018). Measurement theory and applications for the social sciences. New York. p. 261. ISBN   978-1-4625-3215-5. OCLC   1015955756.
  36. Aleksandrowicz JW, Klasa K, Sobański JA, Stolarska D (2009). "KON-2006 Neurotic Personality Questionnaire" (PDF). Archives of Psychiatry and Psychotherapy. 1: 21–22.
  37. Hogan, Robert (2007). Personality and the fate of organizations. Mahwah, NJ: Lawrence Erlbaum Associates. p. 28. ISBN   978-0-8058-4142-8. OCLC   65400436.
  38. Cronbach, L. J. (1957). "The two disciplines of scientific psychology". American Psychologist. 12 (11): 671–684. doi:10.1037/h0043943 via EBSCO.
  39. Humphreys, L.G. (1987). "Psychometrics considerations in the evaluation of intraspecies differences in intelligence". Behav Brain Sci. 10 (4): 668–669. doi:10.1017/s0140525x0005514x.
  40. Eysenck, H.J. (1987). "The several meanings of intelligence". Behav Brain Sci. 10 (4): 663. doi:10.1017/s0140525x00055060.
  41. Locurto, C. & Scanlon, C (1987). "Individual differences and spatial learning factor in two strains of mice". Behav Brain Sci. 112: 344–352.
  42. King, James E & Figueredo, Aurelio Jose (1997). "The five-factor model plus dominance in chimpanzee personality". Journal of Research in Personality. 31 (2): 257–271. doi:10.1006/jrpe.1997.2179.
  43. J. Hernández-Orallo; D.L. Dowe; M.V. Hernández-Lloreda (2013). "Universal Psychometrics: Measuring Cognitive Abilities in the Machine Kingdom" (PDF). Cognitive Systems Research. 27: 50–74. doi:10.1016/j.cogsys.2013.06.001. hdl: 10251/50244 . S2CID   26440282.

Bibliography

Further reading