View source for Psychometrics

{{short description|Theory and technique of psychological measurement}}
{{distinguish|text=[[psychrometrics]], the measurement of the heat and water vapor properties of air}}
{{For|other uses of this term and similar terms|Psychometry (disambiguation)}}
{{About|the theory and technique of measurement of psychological attributes|research design and methodology in psychology|Psychological statistics|the mathematical modeling of psychological theories and phenomena|Mathematical psychology}}<!-- definitions loosely taken from the three articles and https://dictionary.apa.org/ -->

{{Psychology sidebar|applied}}
'''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.<ref>{{Cite web|url=http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorP|title=Glossary1|date=22 July 2017|archive-url=https://web.archive.org/web/20170722194028/http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorP |access-date=28 June 2022|archive-date=2017-07-22 }}</ref> Psychometrics is concerned with the objective measurement of [[Latent variable|latent constructs]] that cannot be directly observed. Examples of latent constructs include [[intelligence]], [[personality]] factors (e.g., [[introversion]]), [[mental disorder]]s, and [[Educational measurement|educational achievement]].<ref name=":0">{{cite book|last1=Tabachnick|first1=B.G.|title=Using Multivariate Analysis|last2=Fidell|first2=L.S.|publisher=Allyn and Bacon|year=2001|isbn=978-0-321-05677-1|location=Boston}}{{Page needed|date=November 2010}}</ref> The levels of individuals on nonobservable latent variables are [[Statistical inference|inferred]] through [[mathematical model]]ing based on what is observed from individuals' responses to items on tests and scales.<ref name=":0" /> 

Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Most psychometricians are [[psychologists]] with advanced graduate training in psychometrics and measurement theory. According to the ''Dictionary of Psychology'' a psychometrician "is an individual with a theoretical knowledge of measurement techniques who is qualified to develop, evaluate, and improve psychological tests."<ref>American Psychological Association. (2015). ''Dictionary of Psychology''. Author. doi:10.1037/14646-000 [https://dictionary.apa.org/psychometrician]</ref> In addition to traditional academic institutions, psychometricians also work for organizations, such as [[Pearson Education|Pearson]] and the [[Educational Testing Service]] as well as independent consultants. Some psychometric researchers focus on the construction and validation of assessment instruments, including [[Survey sampling|surveys]], [[Scale invariance|scales]], and [[Open-ended question|open]]- or [[Closed-ended question|close-ended]] [[questionnaire]]s. Others focus on research relating to measurement theory (e.g., [[item response theory]], [[intraclass correlation]]) or specialize as [[learning and development]] professionals.

==Etymology==
The word psychometry derives from [[Greek language|Greek]]: ψυχή, ''psukhē'', "spirit, soul" and μέτρον, ''metron'', "measure"). The American academic [[Joseph Rodes Buchanan]] is credited as having first coined the word "psychometry" in 1842 but in connection with his investigation of the [[Psychometry (paranormal)|paranormal]] illusion rather than the  rational quantification of [[psychological]] criteria.

== Historical foundation ==
Rational psychological testing has come from two streams of thought: the first, from [[Charles Darwin|Darwin]], [[Sir Francis Galton|Galton]], and [[James McKeen Cattell|Cattell]], on the measurement of individual differences and the second, from [[J.E. Herbart|Herbart]], [[E.H. Weber|Weber]], [[Gustav Fechner|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.<ref name="kap" />

=== Victorian stream ===
Charles Darwin was the inspiration behind 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 how to measure those differences.

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 (trait)|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.<ref name="kap">{{Cite book |last1=Kaplan |first1=Robert M. |title=Psychological Testing: Principles, Applications, and Issues |last2=Saccuzzo |first2=Dennis P. |date=2012-05-01 |publisher=Cengage Learning |isbn=978-1-133-49201-6 |edition=8th}}</ref>

=== 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.<ref name="kap" /> Herbart was responsible for creating mathematical models of the mind, which were influential in educational practices for years to come.

[[Ernst Heinrich Weber|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 nervous system|sensory system]]. After Weber, [[Gustav Fechner|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.<ref name="kap" />

=== 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.<ref>{{Cite book |last1=Nunnally |first1=Jum C. |title=Psychometric Theory |last2=Bernstein |first2=Ira H. |date=1994 |publisher=McGraw-Hill Humanities/Social Sciences/Languages |isbn=978-0-07-047849-7 |edition=3rd |publication-place=New York, NY}}</ref> In the late 1950s, [[Leopold Szondi]] made a historical and epistemological assessment of the impact of statistical thinking on 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."<ref>[[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: {{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.}}</ref>

More recently, psychometric theory has been applied in the measurement of [[wikt:personality|personality]], [[Attitude (psychology)|attitudes]] and [[belief]]s, 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 (journal)|Science]]'' article in which Stevens proposed four [[levels of measurement]].<ref name="Stevens 1946">{{cite journal|last=Stevens|first=S. S.|author-link=Stanley Smith Stevens|date=7 June 1946|title=On the Theory of Scales of Measurement|journal=[[Science (journal)|Science]]|volume=103|issue=2684|pages=677–680|bibcode=1946Sci...103..677S|doi=10.1126/science.103.2684.677|pmid=17750512|s2cid=4667599}}</ref> 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.&nbsp;358)<ref>{{cite journal|last1=Michell|first1=Joel|title=Quantitative science and the definition of measurement in psychology|journal=British Journal of Psychology|date=August 1997|volume=88|issue=3|pages=355–383|doi=10.1111/j.2044-8295.1997.tb02641.x}}</ref>

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 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).<ref>{{Cite journal |last=Resse |first=Thomas Whelan |date=1943 |title=The application of the theory of physical measurement to the measurement of psychological magnitudes, with three experimental examples. |url=https://doi.apa.org/doi/10.1037/h0093539 |journal=Psychological Monographs |volume=55 |issue=3 |pages=i–89 |doi=10.1037/h0093539 |issn=0096-9753|url-access=subscription }}</ref>

These divergent responses are reflected in alternative approaches to measurement. For example, methods based on [[covariance matrix|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.<ref>{{Cite web|url=http://www.assessmentpsychology.com/psychometrics.htm|title=Psychometrics|website=Assessmentpsychology.com|access-date=28 June 2022}}</ref>

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|date=March 2015}}

== Instruments and procedures ==
The first psychometric instruments were designed to measure [[intelligence (trait)|intelligence]].<ref>{{cite book |title=Massachusetts General Hospital comprehensive clinical psychiatry |date=2016 |location=London |isbn=978-0323295079 |page=73 |edition=Second |url=https://books.google.com/books?id=y5nTBgAAQBAJ&pg=PA74 |access-date=31 October 2021|last1=Stern |first1=Theodore A. |last2=Fava |first2=Maurizio |last3=Wilens |first3=Timothy E. |last4=Rosenbaum |first4=Jerrold F. }}</ref> One early approach to measuring intelligence was the test developed in France by [[Alfred Binet]] and [[Theodore Simon]]. That test was known as the {{ill|Test Binet-Simon|fr}}.The French test was adapted for use in the U. S. by [[Lewis Terman]] of Stanford University, and named the [[Stanford-Binet IQ test]].

Another major focus in psychometrics has been on [[personality test]]ing. 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 [[Big five personality traits|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|date=March 2015}}<ref>{{Cite book |title=The Gale Encyclopedia of Psychology |publisher=Gale |year=2022 |isbn=9780028683867 |editor-last=Longe |editor-first=Jacqueline L. |edition=4th |volume=2 |location=Farmington Hills, Michigan |pages=1000}}</ref> An alternative method involves the application of unfolding measurement models, the most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993).<ref>{{Cite journal |last1=Andrich |first1=David |last2=Luo |first2=Guanzhong |date=1993-09-01 |title=A Hyperbolic Cosine Latent Trait Model For Unfolding Dichotomous Single-Stimulus Responses |url=https://journals.sagepub.com/doi/abs/10.1177/014662169301700307 |journal=Applied Psychological Measurement |language=EN |volume=17 |issue=3 |pages=253–276 |doi=10.1177/014662169301700307 |issn=0146-6216}}</ref>

== Theoretical approaches ==
Psychometricians have developed a number of different measurement theories. These include [[classical test theory]] (CTT) and [[item response theory]] (IRT).<ref>{{Cite book |last1=Embretson |first1=Susan E. |title=Item Response Theory for Psychologists |last2=Reise |first2=Steven Paul |date=2000 |publisher=L. Erlbaum Associates |isbn=978-0-8058-2818-4}}</ref><ref>Hambleton, R.K., & Swaminathan, H. (1985). ''Item Response Theory: Principles and Applications.'' Boston: Kluwer-Nijhoff.</ref> An approach that 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.<ref>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.</ref>

Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: [[factor analysis]],<ref>Thompson, B.R. (2004). ''Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications.'' American Psychological Association.</ref> 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 [[Factor analysis#Criteria for determining the number of factors|determining the number of latent factors]].<ref name="Zwick1986">{{cite journal |last1=Zwick |first1=William R. |last2=Velicer |first2=Wayne F. |title=Comparison of five rules for determining the number of components to retain. |journal=Psychological Bulletin |date=1986 |volume=99 |issue=3 |pages=432–442 |doi=10.1037/0033-2909.99.3.432}}</ref> A usual procedure is to stop factoring when [[Eigenvalues and eigenvectors|eigenvalues]] drop below one because the original sphere shrinks. The lack of the cutting points concerns other multivariate methods, also.<ref>{{Cite book |last=Singh |first=Manoj Kumar |url=https://books.google.com/books?id=wodCEAAAQBAJ&dq=A+usual+procedure+is+to+stop+factoring+when+eigenvalues+drop+below+one+because+the+original+sphere+shrinks.&pg=PA107 |title=Introduction to Social Psychology |date=2021-09-11 |publisher=K.K. Publications |language=en}}</ref>

[[Multidimensional scaling]]<ref>[[Mark L. Davison|Davison, M.L.]] (1992). ''Multidimensional Scaling.'' Krieger.</ref> 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]]<ref>Kaplan, D. (2008). ''Structural Equation Modeling: Foundations and Extensions'', 2nd ed. Sage.</ref> and [[path analysis (statistics)|path analysis]] represent more sophisticated approaches to working with large [[Covariance matrix|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<ref>{{Cite journal |last=DeMars |first=Christine E. |date=2013-10-01 |title=A Tutorial on Interpreting Bifactor Model Scores |url=https://www.tandfonline.com/doi/abs/10.1080/15305058.2013.799067 |journal=International Journal of Testing |volume=13 |issue=4 |pages=354–378 |doi=10.1080/15305058.2013.799067 |issn=1530-5058|url-access=subscription }}</ref><ref>{{Cite journal |last=Reise |first=Steven P. |date=2012-09-01 |title=The Rediscovery of Bifactor Measurement Models |journal=Multivariate Behavioral Research |volume=47 |issue=5 |pages=667–696 |doi=10.1080/00273171.2012.715555 |issn=0027-3171 |pmc=3773879 |pmid=24049214}}</ref><ref>{{Cite journal |last1=Rodriguez |first1=Anthony |last2=Reise |first2=Steven P. |last3=Haviland |first3=Mark G. |date=June 2016 |title=Evaluating bifactor models: Calculating and interpreting statistical indices. |url=https://doi.apa.org/doi/10.1037/met0000045 |journal=Psychological Methods |language=en |volume=21 |issue=2 |pages=137–150 |doi=10.1037/met0000045 |pmid=26523435 |issn=1939-1463|url-access=subscription }}</ref> 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."<ref>{{Cite journal |last1=Schonfeld |first1=Irvin Sam |last2=Verkuilen |first2=Jay |last3=Bianchi |first3=Renzo |date=August 2019 |title=An exploratory structural equation modeling bi-factor analytic approach to uncovering what burnout, depression, and anxiety scales measure. |url=https://doi.apa.org/doi/10.1037/pas0000721 |journal=Psychological Assessment |language=en |volume=31 |issue=8 |pages=1073–1079 |doi=10.1037/pas0000721 |pmid=30958024 |issn=1939-134X|url-access=subscription }}</ref>

=== Key concepts ===
Key concepts in classical test theory are [[Reliability (psychometric)|reliability]] and [[Test validity|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.''<ref name="gifted.uconn">{{cite web|url=http://www.gifted.uconn.edu/Siegle/research/Instrument+Reliability+and+Validity/Reliability.htm|title=Home – Educational Research Basics by Del Siegle|website=www.gifted.uconn.edu|date=17 February 2015}}</ref> Similarly, the equivalence of different versions of the same measure can be indexed by a [[Pearson product-moment correlation coefficient|Pearson correlation]], and is called ''equivalent forms reliability'' or a similar term.<ref name="gifted.uconn"/>

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.<ref name="gifted.uconn"/> 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 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."<ref>Nunnally, J.C. (1978). ''Psychometric theory'' (2nd ed.). New York: McGraw-Hill.</ref> 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 trait]]s 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 (statistics)|validity]] and [[Reliability (statistics)|reliability]] typically are viewed as essential elements for determining the [[Quality (business)|quality]] of any test. However, professional and practitioner associations frequently have placed these concerns within broader contexts when developing [[Standards organization|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.<ref>[http://psychology.tamu.edu/Faculty/blanton/bj.2006.arbitrary.pdf Blanton, H., & Jaccard, J. (2006). Arbitrary metrics in psychology.] {{webarchive|url=https://web.archive.org/web/20060510182915/http://psychology.tamu.edu/Faculty/blanton/bj.2006.arbitrary.pdf |date=2006-05-10 }} ''American Psychologist, 61''(1), 27–41.</ref>

=== 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]]'',<ref>{{cite web|url=http://www.apa.org/science/standards.html#overview|title=The Standards for Educational and Psychological Testing|website=apa.org}}</ref> 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|psychological testing and assessment]], workplace testing and [[Professional certification|credentialing]], [[Test (student assessment)|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]]<ref>{{Cite web|url=http://www.wmich.edu/evalctr/jc/|archiveurl=https://web.archive.org/web/20091015044732/http://www.wmich.edu/evalctr/jc/|url-status=dead|title=Joint Committee on Standards for Educational Evaluation|archive-date=15 October 2009|access-date=28 June 2022}}</ref> has published three sets of standards for evaluations. ''The Personnel Evaluation Standards''<ref>Joint Committee on Standards for Educational Evaluation. (1988). ''[http://www.wmich.edu/evalctr/jc/PERSTNDS-SUM.htm The Personnel Evaluation Standards: How to Assess Systems for Evaluating Educators.] {{webarchive|url=https://web.archive.org/web/20051212001638/http://www.wmich.edu/evalctr/jc/PERSTNDS-SUM.htm |date=2005-12-12 }}'' Newbury Park, CA: Sage Publications.</ref> was published in 1988, ''The Program Evaluation Standards'' (2nd edition)<ref>Joint Committee on Standards for Educational Evaluation. (1994). ''[http://www.wmich.edu/evalctr/jc/PGMSTNDS-SUM.htm The Program Evaluation Standards, 2nd Edition.] {{webarchive|url=https://web.archive.org/web/20060222025348/http://www.wmich.edu/evalctr/jc/PGMSTNDS-SUM.htm |date=2006-02-22 }}'' Newbury Park, CA: Sage Publications.</ref> was published in 1994, and ''The Student Evaluation Standards''<ref>Committee on Standards for Educational Evaluation. (2003). ''[http://www.wmich.edu/evalctr/jc/briefing/ses/ The Student Evaluation Standards: How to Improve Evaluations of Students.] {{webarchive|url=https://web.archive.org/web/20060524144621/http://www.wmich.edu/evalctr/jc/briefing/ses/ |date=2006-05-24 }}'' Newbury Park, CA: Corwin Press.</ref> 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.<ref>[{{cite journal|url=https://www.academia.edu/2395969 |title=Author guidelines for reporting scale development and validation results in the Journal of the Society for Social Work and Research]|volume=1|issue=2|pages=99–103|author=E. Cabrera-Nguyen|journal=Academia.edu|year=2010}}</ref> 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 variable|latent psychological processes]] measured through [[correlation]]s, there has been controversy about some psychometric measures.<ref>{{cite book|last1=Tabachnick|first1=B.G.|title=Using Multivariate Analysis|last2=Fidell|first2=L.S.|publisher=Allyn and Bacon|year=2001|isbn=978-0-321-05677-1|location=Boston}}</ref>{{Page needed|date=November 2010}} 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".<ref name="1999standards">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.</ref> Simply put, a test is not valid unless it is used and interpreted in the way it is intended.<ref>{{Cite book|last=Bandalos|first=Deborah L.|title=Measurement theory and applications for the social sciences|date=2018|isbn=978-1-4625-3215-5|location=New York|pages=261|oclc=1015955756}}</ref> 

Two types of tools used to measure [[personality traits]] are [[objective test]]s and [[Projective test|projective measures]]. Examples of such tests are the: [[Big Five personality traits|Big Five Inventory]] (BFI), [[Minnesota Multiphasic Personality Inventory]] (MMPI-2), [[Rorschach test|Rorschach Inkblot test]], [[Neurotic Personality Questionnaire KON-2006]],<ref><span lang="PL">{{Cite journal|vauthors=Aleksandrowicz JW, Klasa K, Sobański JA, Stolarska D|year=2009|title=KON-2006 Neurotic Personality Questionnaire|url=http://www.archivespp.pl/uploads/images/2009_11_1/21_p_Archives_1_09.pdf|journal=Archives of Psychiatry and Psychotherapy|volume=1|pages=21–22}}</span></ref> or [[Eysenck Personality Questionnaire]]. Some of these tests are helpful because they have adequate [[Reliability (research methods)|reliability]] and [[Test validity|validity]], two factors that make tests consistent and accurate reflections of the underlying construct. [[Myers–Briggs Type Indicator|The Myers–Briggs Type Indicator]] (MBTI), however, has questionable validity and has been the subject of much criticism. Psychometric specialist [[Robert Hogan (psychologist)|Robert Hogan]] wrote of the measure: "Most personality psychologists regard the MBTI as little more than an elaborate Chinese fortune cookie."<ref>{{cite book|last=Hogan|first=Robert|title=Personality and the fate of organizations|date=2007|publisher=[[Lawrence Erlbaum Associates]]|isbn=978-0-8058-4142-8|location=Mahwah, NJ|page=28|oclc=65400436|author-link=Robert Hogan (psychologist)}}</ref>

[[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&nbsp;... 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."<ref>{{Cite journal|last=Cronbach|first=L. J.|date=1957|title=The two disciplines of scientific psychology.|journal=American Psychologist|volume=12|issue=11|pages=671–684|doi=10.1037/h0043943|via=EBSCO}}</ref>

== 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.<ref name="Humphreys">{{Cite journal | author = Humphreys, L.G.
 | year = 1987
 | title = Psychometrics considerations in the evaluation of intraspecies differences in intelligence
 | journal = Behav Brain Sci
 | volume = 10
 | issue = 4
 | pages = 668–669
 | doi=10.1017/s0140525x0005514x
 }}</ref><ref name="Eysenck">{{Cite journal | author = Eysenck, H.J.
 | year = 1987
 | title = The several meanings of intelligence
 | journal = Behav Brain Sci
 | volume = 10
 | issue = 4
 | pages = 663
 | doi=10.1017/s0140525x00055060
 }}</ref><ref name="Locurto">{{Cite journal |author1=Locurto, C. |author2=Scanlon, C
 |name-list-style=amp | year = 1987
 | title = Individual differences and spatial learning factor in two strains of mice
 | journal = Behav Brain Sci
 | volume = 112
 | pages = 344–352
 }}</ref><ref name="king1997five">{{Cite journal |author1=King, James E |author2=Figueredo, Aurelio Jose
 |name-list-style=amp | year = 1997
 | title = The five-factor model plus dominance in chimpanzee personality
 | journal = Journal of Research in Personality
 | volume = 31
 | issue = 2
 | pages = 257–271
 | doi=10.1006/jrpe.1997.2179
 }}</ref>

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.<ref name="upsycho">{{Cite journal |author1=J. Hernández-Orallo |author2=D.L. Dowe |author3=M.V. Hernández-Lloreda | year = 2013
|title = Universal Psychometrics: Measuring Cognitive Abilities in the Machine Kingdom
|journal = Cognitive Systems Research
|volume=27 |pages=50–74 |hdl=10251/50244|doi=10.1016/j.cogsys.2013.06.001 |s2cid=26440282 |url=https://riunet.upv.es/bitstream/10251/50244/3/upsycho.pdf |hdl-access=free }}</ref><ref>{{Cite book |last=Hernández-Orallo |first=José |url=https://www.cambridge.org/core/books/measure-of-all-minds/DC3DFD0C1D5B3A3AD6F56CD6A397ABCA |title=The Measure of All Minds: Evaluating Natural and Artificial Intelligence |date=2017 |publisher=[[Cambridge University Press]] |isbn=978-1-107-15301-1 |location=Cambridge}}</ref>

== See also ==
{{portal|border=no|Psychology}}
{{columns-list|colwidth=30em|
*[[Cattell–Horn–Carroll theory]]
*[[Classical test theory]]
*[[Computational psychometrics]]
*[[Concept inventory]]
*[[Cronbach's alpha]]
*[[Educational assessment]]
*[[Educational psychology]]
*[[Factor analysis]]
*[[Flynn effect]]
*[[Item response theory]]
*[[Likert scale]]
*[[List of international databases on individual student achievement tests]]
*[[List of psychometric software]]
*[[List of schools for quantitative psychology|List of schools for psychometrics]]
*[[Congeneric reliability|Omega]]
*[[Operationalisation]]
*[[Quantitative psychology]]
*[[Psychometric Society]]
*[[Psychological testing]]
*[[Rasch model]]
*[[Scale (social sciences)]]
*[[School psychology]]
*[[Standardized test]]
}}

== References ==
{{Reflist}}

=== Bibliography ===
{{refbegin}}
*{{Cite journal | doi = 10.1177/014662169301700307 | author1 = Andrich, D. | author2 = Luo, G. | name-list-style = amp | year = 1993 | title = A hyperbolic cosine model for unfolding dichotomous single-stimulus responses | url = http://apm.sagepub.com/content/19/3/269.full.pdf | journal = Applied Psychological Measurement | volume = 17 | issue = 3 | pages = 253–276 | citeseerx = 10.1.1.1003.8107 | s2cid = 120745971 }}
*Michell, J. (1999). ''Measurement in Psychology''. Cambridge: Cambridge University Press. {{doi|10.1017/CBO9780511490040}}
*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.
*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}}
*{{Cite journal | doi = 10.1126/science.103.2684.677 | author = Stevens, S. S. | year = 1946 | title = On the theory of scales of measurement | journal = Science | volume = 103 | issue = 2684| pages = 677–80 | pmid = 17750512 | bibcode = 1946Sci...103..677S }}
*{{Cite journal | author = Thurstone, L.L. | year = 1927 | title = A law of comparative judgement | journal = Psychological Review | volume = 34 | issue = 4| pages = 278–286 | doi=10.1037/h0070288}}
*Thurstone, L.L. (1929). The Measurement of Psychological Value. In T.V. Smith and W.K. Wright (Eds.), ''Essays in Philosophy by Seventeen Doctors of Philosophy of the University of Chicago''. Chicago: Open Court.
*Thurstone, L.L. (1959). ''The Measurement of Values''. Chicago: The University of Chicago Press.
*{{Cite journal | author = S.F. Blinkhorn | year = 1997 | title = Past imperfect, future conditional: fifty years of test theory | journal = British Journal of Mathematical and Statistical Psychology | volume = 50 | issue = 2| pages = 175–185 | doi = 10.1111/j.2044-8317.1997.tb01139.x | author-link = Steve Blinkhorn }}
*{{Cite web|url=https://www.linkedin.com/pulse/cambridge-just-told-me-big-data-doesnt-work-yet-david-sanford/|title=Cambridge just told me Big Data doesn't work yet|last=Sanford|first=David|date=18 November 2017|website=LinkedIn}}
{{refend}}

== Further reading ==
*{{cite book|author=Robert F. DeVellis|title=Scale Development: Theory and Applications|url=https://books.google.com/books?id=48ACCwAAQBAJ|year=2016|publisher=SAGE Publications|isbn=978-1-5063-4158-3}}
*{{cite book |author=Borsboom, Denny |title=Measuring the Mind: Conceptual Issues in Contemporary Psychometrics |location=Cambridge |publisher=[[Cambridge University Press]] |isbn=978-0-521-84463-5 |year=2005 |title-link=Measuring the Mind }}
*{{cite book|author1=Leslie A. Miller|author2=Robert L. Lovler|title=Foundations of Psychological Testing: A Practical Approach|url=https://books.google.com/books?id=8EYdCAAAQBAJ|year=2015|publisher=SAGE Publications|isbn=978-1-4833-6927-3}}
*{{cite book|author=Roderick P. McDonald|title=Test Theory: A Unified Treatment|url=https://books.google.com/books?id=_feqA2RdyOoC|year=2013|publisher=Psychology Press|isbn=978-1-135-67530-1}}
*{{cite book|author=Paul Kline|title=The Handbook of Psychological Testing|url=https://books.google.com/books?id=lm2RxaKaok8C|year=2000|publisher=Psychology Press|isbn=978-0-415-21158-1}}
*{{cite book|author1=Rush AJ Jr|author2=First MB|author3=Blacker D|title=Handbook of Psychiatric Measures|year=2008|publisher=American Psychiatric Publishing|url=https://books.google.com/books?id=ddyZUcaGaRIC|isbn=978-1-58562-218-4|oclc=85885343}}
*{{cite book|author=Ann C Silverlake|title=Comprehending Test Manuals: A Guide and Workbook|url=https://books.google.com/books?id=zl8PDQAAQBAJ|year=2016|publisher=Taylor & Francis|isbn=978-1-351-97086-0}}

== External links ==
{{wikiversity}}
{{wiktionary}}
{{Library resources box
|by=no
|onlinebooks=no
|others=no
|about=yes
|label=psychometrics}}
*[https://www.apa.org/science/programs/testing/standards APA Standards for Educational and Psychological Testing]
*[http://ipip.ori.org/ International Personality Item Pool]
*[https://web.archive.org/web/20091015044732/http://www.wmich.edu/evalctr/jc/ Joint Committee on Standards for Educational Evaluation]
*[http://www.psychometrics.cam.ac.uk/ The Psychometrics Centre, University of Cambridge] 
*[https://www.psychometricsociety.org/ Psychometric Society and Psychometrika homepage]
*[http://www.psychometriclab.com/ London Psychometric Laboratory]

{{Human intelligence topics}}
{{Psychology}}
{{Statistics|applications}}

[[Category:Psychometrics| ]]
[[Category:Applied psychology]]
[[Category:Educational research]]
[[Category:Psychological testing]]
[[Category:Metrics]]
[[Category:Educational assessment and evaluation]]