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		Not to be confused with psychrometrics, the measurement of the heat and water vapor properties of air.

For other uses of this term and similar terms, see Psychometry (disambiguation).

theory and technique of psychological measurement

	
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Psychometrics is a field of study concerned with the theory and technique of psychological measurement. As defined by the US National Council on Measurement in Education (NCME), psychometrics refers to psychological measurement. Generally, it refers to the field in psychology and education that is devoted to testing, measurement, assessment, and related activities.[1]

The field is concerned with the objective measurement of skills and knowledge, abilities, attitudes, personality traits, and educational achievement. Some psychometric researchers focus on the construction and validation of assessment instruments such as questionnaires, tests, raters' judgments, psychological symptom scales, and personality tests. Others focus on research relating to measurement theory (e.g., item response theory; intraclass correlation).

Practitioners are described as psychometricians. Psychometricians usually possess a specific qualification, and most are psychologists with advanced graduate training. In addition to traditional academic institutions, many psychometricians work for the government or in human resources departments. Others specialize as learning and development professionals.


Contents


	1 Historical foundation
	1.1 Victorian stream
	1.2 German stream
	1.3 20th century



	2 Definition of measurement in the social sciences
	3 Instruments and procedures
	4 Theoretical approaches
	4.1 Key concepts



	5 Standards of quality
	5.1 Testing standards
	5.2 Evaluation standards



	6 Non-human: animals and machines
	7 See also
	8 References
	8.1 Bibliography
	8.2 Notes



	9 Further reading
	10 External links





Historical foundation[edit]

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.[2]


Victorian stream[edit]

Charles Darwin was the inspiration behind Sir Francis Galton who led to the creation of psychometrics. In 1859, Darwin published his book On the Origin of Species, which was devoted to the role of natural selection in the emergence over time of different populations of species of plants and animals. The book discussed how individual members of a species differ and how they possess characteristics that are more or less adaptive to their environment. Those with more adaptive characteristics are more likely to procreate and give rise to another generation. Those with less adaptive characteristics are less likely to procreate. This idea 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 about different characteristics that people possess and how those characteristics make them 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, who is considered a pioneer of psychometrics went on to extend Galton's work. Cattell also coined the term mental test, and is responsible for the research and knowledge which ultimately led to the development of modern tests.[3]


German stream[edit]

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.[3] 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.[3]


20th century[edit]

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.[citation needed] 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."[4]

More recently, psychometric theory has been applied in the measurement of personality, attitudes, and beliefs, and academic achievement.  Measurement of these unobservable phenomena is difficult, and much of the research and accumulated science in this discipline has been developed in an attempt to properly define and quantify such phenomena.  Critics, including practitioners in the physical sciences and social activists, have argued that such definition and quantification is impossibly difficult, and that such measurements are often misused, such as with psychometric personality tests used in employment procedures:


	"For example, an employer wanting someone for a role requiring consistent attention to repetitive detail will probably not want to give that job to someone who is very creative and gets bored easily."[5]


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, and Jane Loevinger.


Definition of measurement in the social sciences[edit]

The definition of measurement in the social sciences has a long history.  A currently widespread definition, proposed by Stanley Smith Stevens (1946), is that measurement is "the assignment of numerals to objects or events according to some rule."  This definition was introduced in the paper in which Stevens proposed four levels of measurement.  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)[6]

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).[7]


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.[8]

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[edit]

The first[citation needed]psychometric instruments were designed to measure the concept of intelligence.[9]  One historical approach involved the Stanford-Binet IQ test, developed originally by the French psychologist Alfred Binet. An alternative conception of intelligence is that cognitive capacities within individuals are a manifestation of a general component, or general intelligence factor, as well as cognitive capacity specific to a given domain.[citation needed]

Another major focus in psychometrics has been on personality testing.  There have been a range of theoretical approaches to conceptualizing and measuring personality.  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]  A common method in the measurement of attitudes is the use of the Likert scale.  An alternative method involves the application of unfolding measurement models, the most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993).[10]


Theoretical approaches[edit]

Psychometricians have developed a number of different measurement theories.  These include classical test theory (CTT) and item response theory (IRT).[11][12]  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.[13]

Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: factor analysis,[14] 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.[15] 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[16] 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[17] 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[18][19][20] 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."[21]


Key concepts[edit]

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.[22]  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.[22]

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.[22]  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."[23] 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.

Many psychometricians are also concerned with finding and eliminating test bias from their psychological tests. Test bias is a form of systematic (i.e., non-random) error which leads to examinees from one demographic group having an unwarranted advantage over examinees from another demographic group.[24] According to leading experts, test bias may cause differences in average scores across demographic groups, but differences in group scores are not sufficient evidence that test bias is actually present because the test could be measuring real differences among groups.[25][24] Psychometricians use sophisticated scientific methods to search for test bias and eliminate it. Research shows that it is usually impossible for people reading a test item to accurately determine whether it is biased or not.[26]


Standards of quality[edit]

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.[27]


Testing standards[edit]

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,[28] 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[edit]

In the field of evaluation, and in particular educational evaluation, the Joint Committee on Standards for Educational Evaluation[29] has published three sets of standards for evaluations. The Personnel Evaluation Standards[30] was published in 1988, The Program Evaluation Standards (2nd edition)[31] was published in 1994, and The Student Evaluation Standards[32] 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.[33]  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.


Non-human: animals and machines[edit]

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.[34][35][36]
[37]

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.[38]


See also[edit]


	Cattell–Horn–Carroll theory
	Classical test theory
	Computational psychometrics
	Concept inventory
	Cronbach's alpha
	Data mining
	Educational assessment
	Educational psychology
	Factor analysis
	Item response theory
	List of psychometric software
	List of schools for psychometrics
	Operationalisation
	Quantitative psychology
	Psychometric Society
	Rasch model
	Scale (social sciences)
	School counselor
	School psychology
	Standardized test




References[edit]

Bibliography[edit]


	Andrich, D. & Luo, G. (1993). "A hyperbolic cosine model for unfolding dichotomous single-stimulus responses" (PDF). Applied Psychological Measurement. 17 (3): 253–276. CiteSeerX 10.1.1.1003.8107. doi:10.1177/014662169301700307. 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
	Stevens, S. S. (1946). "On the theory of scales of measurement". Science. 103 (2684): 677–80. Bibcode:1946Sci...103..677S. doi:10.1126/science.103.2684.677. PMID 17750512.

	Thurstone, L.L. (1927). "A law of comparative judgement". Psychological Review. 34 (4): 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.
	S.F. Blinkhorn (1997). "Past imperfect, future conditional: fifty years of test theory". Br. J. Math. Statist. Psychol. 50 (2): 175–185. doi:10.1111/j.2044-8317.1997.tb01139.x.

	Sanford, David (18 November 2017). "Cambridge just told me Big Data doesn't work yet". LinkedIn.





Notes[edit]


	^ 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

	^ Kaplan, R.M., & Saccuzzo, D.P. (2010). Psychological Testing: Principles, Applications, and Issues. (8th ed.). Belmont, CA: Wadsworth, Cengage Learning.

	^ a b c Kaplan, R.M., & Saccuzzo, D.P. (2010). Psychological tresting: Principles, applications, and issues (8th ed.). Belmont, CA: Wadsworth, Cengage Learning.

	^ 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.



	^ Psychometric Assessments. Psychometric Assessments . University of Melbourne.

	^ 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.


	^ 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

	^ http://www.assessmentpsychology.com/psychometrics.htm

	^ "Los diferentes tipos de tests psicometricos - examen psicometrico". examenpsicometrico.com.


	^ Andrich, D. & Luo, G. (1993). A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement, 17, 253-276.

	^ Embretson, S.E., & Reise, S.P. (2000). Item Response Theory for Psychologists. Mahwah, NJ: Erlbaum.

	^ Hambleton, R.K., & Swaminathan, H. (1985). Item Response Theory: Principles and Applications. Boston: Kluwer-Nijhoff.

	^ 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.

	^ Thompson, B.R. (2004). Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications. American Psychological Association.

	^ 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.


	^ Davison, M.L. (1992). Multidimensional Scaling. Krieger.

	^ Kaplan, D. (2008). Structural Equation Modeling: Foundations and Extensions, 2nd ed. Sage.

	^ 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

	^ 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

	^ 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

	^ 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

	^ a b c "Home - Educational Research Basics by Del Siegle". www.gifted.uconn.edu.


	^ Nunnally, J.C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill.

	^ a b Warne, Russell T.; Yoon, Myeongsun; Price, Chris J. (2014). "Exploring the various interpretations of "test bias"". Cultural Diversity and Ethnic Minority Psychology. 20 (4): 570–582. doi:10.1037/a0036503. PMID 25313435.


	^ Reynolds, C. R. (2000). Why is psychometric research on bias in mental testing so often ignored? Psychology, Public Policy, and Law, 6, 144-150. doi:10.1037/1076-8971.6.1.144

	^ Reschly, D. J. (1980) Psychological evidence in the Larry P. opinion: A case of right problem-wrong solution? School Psychology Review, 9, 123-125.

	^ Blanton, H., & Jaccard, J. (2006). Arbitrary metrics in psychology. Archived 2006-05-10 at the Wayback Machine American Psychologist, 61(1), 27-41.

	^ "The Standards for Educational and Psychological Testing". apa.org.


	^ Joint Committee on Standards for Educational Evaluation Archived 2009-10-15 at the Wayback Machine

	^ 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.

	^ 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.

	^ 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.

	^ [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.


	^ 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.


	^ Eysenck, H.J. (1987). "The several meanings of intelligence". Behav Brain Sci. 10 (4): 663. doi:10.1017/s0140525x00055060.


	^ Locurto, C. & Scanlon, C (1987). "Individual differences and spatial learning factor in two strains of mice". Behav Brain Sci. 112: 344–352.


	^ 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.


	^ 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.






Further reading[edit]

	Robert F. DeVellis (2016). Scale Development: Theory and Applications. SAGE Publications. ISBN 978-1-5063-4158-3.

	Borsboom, Denny (2005). Measuring the Mind: Conceptual Issues in Contemporary Psychometrics. Cambridge: Cambridge University Press. ISBN 978-0-521-84463-5. Lay summary (28 June 2010).

	Leslie A. Miller; Robert L. Lovler (2015). Foundations of Psychological Testing: A Practical Approach. SAGE Publications. ISBN 978-1-4833-6927-3.

	Roderick P. McDonald (2013). Test Theory: A Unified Treatment. Psychology Press. ISBN 978-1-135-67530-1.

	Paul Kline (2000). The Handbook of Psychological Testing. Psychology Press. ISBN 978-0-415-21158-1.

	Rush AJ Jr; First MB; Blacker D (2008). Handbook of Psychiatric Measures. American Psychiatric Publishing. ISBN 978-1-58562-218-4. OCLC 85885343.

	Ann C Silverlake (2016). Comprehending Test Manuals: A Guide and Workbook. Taylor & Francis. ISBN 978-1-351-97086-0.

	Fenton H (2019). "Top 10 Tips on how to prepare for a psychometric test to get that job!". Business Optimization Training Institute.

	Dr. Snigdha Rai (2018). "An Ultimate Guide to Psychometric Tests". Mercer Mettl.

	Radhika Kulkarni (2019). "Hiring Using Online Psychometric Tests". Psychometrica.

	Saville, P. & Hopton, T. (2014). "Psychometrics@Work". CPI Books.CS1 maint: multiple names: authors list (link)



External links[edit]

		Wikiversity has learning resources about Psychometrics


		Look up psychometrics in Wiktionary, the free dictionary.


	APA Standards for Educational and Psychological Testing
	International Personality Item Pool
	Joint Committee on Standards for Educational Evaluation
	The Psychometrics Centre, University of Cambridge
	Psychometric Society and Psychometrika homepage
	London Psychometric Laboratory


	Library resources about 
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	Psychologists
	
	Wilhelm Wundt (1832–1920)
	William James (1842–1910)
	Ivan Pavlov (1849–1936)
	Sigmund Freud (1856–1939)
	Edward Thorndike (1874–1949)
	Carl Jung (1875–1961)
	John B. Watson (1878–1958)
	Clark L. Hull (1884–1952)
	Kurt Lewin (1890–1947)
	Jean Piaget (1896–1980)
	Gordon Allport (1897–1967)
	J. P. Guilford (1897–1987)
	Carl Rogers (1902–1987)
	Erik Erikson (1902–1994)
	B. F. Skinner (1904–1990)
	Donald O. Hebb (1904–1985)
	Ernest Hilgard (1904–2001)
	Harry Harlow (1905–1981)
	Raymond Cattell (1905–1998)
	Abraham Maslow (1908–1970)
	Neal E. Miller (1909–2002)
	Jerome Bruner (1915–2016)
	Donald T. Campbell (1916–1996)
	Hans Eysenck (1916–1997)
	Herbert A. Simon (1916–2001)
	David McClelland (1917–1998)
	Leon Festinger (1919–1989)
	George A. Miller (1920–2012)
	Richard Lazarus (1922–2002)
	Stanley Schachter (1922–1997)
	Robert Zajonc (1923–2008)
	Albert Bandura (b. 1925)
	Roger Brown (1925–1997)
	Endel Tulving (b. 1927)
	Lawrence Kohlberg (1927–1987)
	Noam Chomsky (b. 1928)
	Ulric Neisser (1928–2012)
	Jerome Kagan (b. 1929)
	Walter Mischel (1930–2018)
	Elliot Aronson (b. 1932)
	Daniel Kahneman (b. 1934)
	Paul Ekman (b. 1934)
	Michael Posner (b. 1936)
	Amos Tversky (1937–1996)
	Bruce McEwen (b. 1938)
	Larry Squire (b. 1941)
	Richard E. Nisbett (b. 1941)
	Martin Seligman (b. 1942)
	Ed Diener (b. 1946)
	Shelley E. Taylor (b. 1946)
	John Anderson (b. 1947)
	Ronald C. Kessler (b. 1947)
	Joseph E. LeDoux (b. 1949)
	Richard Davidson (b. 1951)
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	Roy Baumeister (b. 1953)




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Statistics

	
	Outline
	Index




	
	Descriptive statistics

	
	Continuous data	
	Center	
	Mean
	arithmetic
	geometric
	harmonic


	Median
	Mode




	Dispersion	
	Variance
	Standard deviation
	Coefficient of variation
	Percentile
	Range
	Interquartile range




	Shape	
	Central limit theorem
	Moments
	Skewness
	Kurtosis
	L-moments









	Count data	
	Index of dispersion




	Summary tables	
	Grouped data
	Frequency distribution
	Contingency table




	Dependence	
	Pearson product-moment correlation
	Rank correlation
	Spearman's ρ
	Kendall's τ


	Partial correlation
	Scatter plot




	Graphics	
	Bar chart
	Biplot
	Box plot
	Control chart
	Correlogram
	Fan chart
	Forest plot
	Histogram
	Pie chart
	Q–Q plot
	Run chart
	Scatter plot
	Stem-and-leaf display
	Radar chart
	Violin plot










	
	Data collection

	
	Study design	
	Population
	Statistic
	Effect size
	Statistical power
	Optimal design
	Sample size determination
	Replication
	Missing data




	Survey methodology	
	Sampling
	stratified
	cluster


	Standard error
	Opinion poll
	Questionnaire




	Controlled experiments	
	Scientific control
	Randomized experiment
	Randomized controlled trial
	Random assignment
	Blocking
	Interaction
	Factorial experiment




	Adaptive Designs	
	Adaptive clinical trial
	Up-and-Down Designs
	Stochastic approximation




	Observational Studies	
	Cross-sectional study
	Cohort study
	Natural experiment
	Quasi-experiment










	
	Statistical inference

	
	Statistical theory	
	Population
	Statistic
	Probability distribution
	Sampling distribution
	Order statistic


	Empirical distribution
	Density estimation


	Statistical model
	Model specification
	Lp space


	Parameter
	location
	scale
	shape


	Parametric family
	Likelihood (monotone)
	Location–scale family
	Exponential family


	Completeness
	Sufficiency
	Statistical functional
	Bootstrap
	U
	V


	Optimal decision
	loss function


	Efficiency
	Statistical distance
	divergence


	Asymptotics
	Robustness




	Frequentist inference	
	Point estimation	
	Estimating equations
	Maximum likelihood
	Method of moments
	M-estimator
	Minimum distance


	Unbiased estimators
	Mean-unbiased minimum-variance
	Rao–Blackwellization
	Lehmann–Scheffé theorem


	Median unbiased


	Plug-in




	Interval estimation	
	Confidence interval
	Pivot
	Likelihood interval
	Prediction interval
	Tolerance interval
	Resampling
	Bootstrap
	Jackknife






	Testing hypotheses	
	1- & 2-tails
	Power
	Uniformly most powerful test


	Permutation test
	Randomization test


	Multiple comparisons




	Parametric tests	
	Likelihood-ratio
	Score/Lagrange multiplier
	Wald







	Specific tests	
	
	Z-test (normal)
	Student's t-test
	F-test




	Goodness of fit	
	Chi-squared
	G-test
	Kolmogorov–Smirnov
	Anderson–Darling
	Lilliefors
	Jarque–Bera
	Normality (Shapiro–Wilk)
	Likelihood-ratio test
	Model selection
	Cross validation
	AIC
	BIC






	Rank statistics	
	Sign
	Sample median


	Signed rank (Wilcoxon)
	Hodges–Lehmann estimator


	Rank sum (Mann–Whitney)
	Nonparametric anova
	1-way (Kruskal–Wallis)
	2-way (Friedman)
	Ordered alternative (Jonckheere–Terpstra)









	Bayesian inference	
	Bayesian probability
	prior
	posterior


	Credible interval
	Bayes factor
	Bayesian estimator
	Maximum posterior estimator












	
		Correlation
	Regression analysis




	
	Correlation	
	Pearson product-moment
	Partial correlation
	Confounding variable
	Coefficient of determination




	Regression analysis	
	Errors and residuals
	Regression validation
	Mixed effects models
	Simultaneous equations models
	Multivariate adaptive regression splines (MARS)




	Linear regression	
	Simple linear regression
	Ordinary least squares
	General linear model
	Bayesian regression




	Non-standard predictors	
	Nonlinear regression
	Nonparametric
	Semiparametric
	Isotonic
	Robust
	Heteroscedasticity
	Homoscedasticity




	Generalized linear model	
	Exponential families
	Logistic (Bernoulli) / Binomial / Poisson regressions




	Partition of variance	
	Analysis of variance (ANOVA, anova)
	Analysis of covariance
	Multivariate ANOVA
	Degrees of freedom










	
	Categorical / Multivariate / Time-series / Survival analysis

	
	Categorical	
	Cohen's kappa
	Contingency table
	Graphical model
	Log-linear model
	McNemar's test




	Multivariate	
	Regression
	Manova
	Principal components
	Canonical correlation
	Discriminant analysis
	Cluster analysis
	Classification
	Structural equation model
	Factor analysis


	Multivariate distributions
	Elliptical distributions
	Normal








	Time-series	
	General	
	Decomposition
	Trend
	Stationarity
	Seasonal adjustment
	Exponential smoothing
	Cointegration
	Structural break
	Granger causality




	Specific tests	
	Dickey–Fuller
	Johansen
	Q-statistic (Ljung–Box)
	Durbin–Watson
	Breusch–Godfrey




	Time domain	
	Autocorrelation (ACF)
	partial (PACF)


	Cross-correlation (XCF)
	ARMA model
	ARIMA model (Box–Jenkins)
	Autoregressive conditional heteroskedasticity (ARCH)
	Vector autoregression (VAR)




	Frequency domain	
	Spectral density estimation
	Fourier analysis
	Wavelet
	Whittle likelihood







	Survival	
	Survival function	
	Kaplan–Meier estimator (product limit)
	Proportional hazards models
	Accelerated failure time (AFT) model
	First hitting time




	Hazard function	
	Nelson–Aalen estimator




	Test	
	Log-rank test













	
	Applications

	
	Biostatistics	
	Bioinformatics
	Clinical trials / studies
	Epidemiology
	Medical statistics




	Engineering statistics	
	Chemometrics
	Methods engineering
	Probabilistic design
	Process / quality control
	Reliability
	System identification




	Social statistics	
	Actuarial science
	Census
	Crime statistics
	Demography
	Econometrics
	Jurimetrics
	National accounts
	Official statistics
	Population statistics
	Psychometrics




	Spatial statistics	
	Cartography
	Environmental statistics
	Geographic information system
	Geostatistics
	Kriging










	
	Category
	 Mathematics portal
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Retrieved from "https://en.wikipedia.org/w/index.php?title=Psychometrics&oldid=992845105"


		Categories: 	Psychometrics
	Applied psychology
	Branches of psychology
	Educational assessment and evaluation
	Educational psychology
	Educational research
	Psychological testing
	Applied statistics


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