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71-400: Louis Leon Thurstone (May 29, 1887 – September 29, 1955) was an American 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

142-551: A given decision agent. This corresponds to (xPy or xIy) being a total preorder , P being the corresponding strict weak order , and I being the corresponding equivalence relation . Probabilistic models also give rise to stochastic variants of transitivity , all of which can be verified to satisfy (non-stochastic) transitivity within the bounds of errors of estimates of scale locations of entities. Thus, decisions need not be deterministically transitive in order to apply probabilistic models. However, transitivity will generally hold for

213-470: A granular level psychometric research is concerned with the extent and nature of multidimensionality in each of the items of interest, a relatively new procedure known as bi-factor analysis can be helpful. Bi-factor analysis can decompose "an item's systematic variance in terms of, ideally, two sources, a general factor and one source of additional systematic variance." Key concepts in classical test theory are reliability and validity . A reliable measure

284-404: 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

355-559: A large number of comparisons if models such as the BTL can be effectively applied. Using a transitivity test one can investigate whether a data set of pairwise comparisons contains a higher degree of transitivity than expected by chance. Some contend that indifference is not transitive. Consider the following example. Suppose you like apples and you prefer apples that are larger. Now suppose there exists an apple A, an apple B, and an apple C which have identical intrinsic characteristics except for

426-503: A model for pairwise comparisons for chess ranking in incomplete tournaments, which serves as the basis (even though not credited for a while) for methods such as the Elo rating system and is equivalent to the Bradley–Terry model that was proposed in 1952. If an individual or organization expresses a preference between two mutually distinct alternatives, this preference can be expressed as

497-407: A model of intelligence centered on "Primary Mental Abilities" (PMAs), which were independent group factors of intelligence that different individuals possessed in varying degrees. He opposed the notion of a singular general intelligence that factored into the scores of all psychometric tests and was expressed as a mental age . In 1935 Thurstone, together with EL Thorndike and JP Guilford , founded

568-433: 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." 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

639-456: A pairwise comparison. If the two alternatives are x and y , the following are the possible pairwise comparisons: The agent prefers x over y : " x  >  y " or " xPy " The agent prefers y over x : " y  >  x " or " yPx " The agent is indifferent between both alternatives: " x  =  y " or " xIy " In terms of modern psychometric theory probabilistic models, which include Thurstone's approach (also called

710-430: A problem is so involved that no rational formulation is available, then some quantification is still possible by the coefficients of correlation of contingency and the like. But such statistical procedures constitute an acknowledgement of failure to rationalize the problem and to establish functions that underlie the data. We want to measure the separation between the two opinions on the attitude continuum and we want to test

781-481: A property, attribute, or attitude. Methods based on the approach to measurement can be used to estimate such scale values. Thurstone's Law of comparative judgment has important links to modern approaches to social and psychological measurement. In particular, the approach bears a close conceptual relation to the Rasch model (Andrich, 1978), although Thurstone typically employed the normal distribution in applications of

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852-451: A scientific approach to using pairwise comparisons for measurement in 1927, which he referred to as the law of comparative judgment . Thurstone linked this approach to psychophysical theory developed by Ernst Heinrich Weber and Gustav Fechner . Thurstone demonstrated that the method can be used to order items along a dimension such as preference or importance using an interval-type scale. Mathematician Ernst Zermelo (1929) first described

923-699: 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

994-422: A statistical thinking. Precisely here we see the cancer of testology and testomania of today." 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

1065-466: Is preferred , or has a greater amount of some quantitative property , or whether or not the two entities are identical. The method of pairwise comparison is used in the scientific study of preferences , attitudes, voting systems , social choice , public choice , requirements engineering and multiagent AI systems . In psychology literature, it is often referred to as paired comparison . Prominent psychometrician L. L. Thurstone first introduced

1136-563: Is Wundt's influence that paved the way for others to develop psychological testing. 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

1207-429: Is a lack of consensus on appropriate procedures for determining the number of latent factors . A usual procedure is to stop factoring when eigenvalues drop below one because the original sphere shrinks. The lack of the cutting points concerns other multivariate methods, also. Multidimensional scaling is a method for finding a simple representation for data with a large number of latent dimensions. Cluster analysis

1278-403: Is above the just noticeable difference ('jnd') while the size differences between A and B and B and C are below the jnd. You are confronted with the three apples in pairs without the benefit of a sensitive scale. Therefore, when presented A and B alone, you are indifferent between apple A and apple B; and you are indifferent between apple B and apple C when presented B and C alone. However, when

1349-488: Is adjusted with the Spearman–Brown prediction formula to correspond to the correlation between two full-length tests. Perhaps the most commonly used index of reliability is Cronbach's α , which is equivalent to the mean of all possible split-half coefficients. Other approaches include the intra-class correlation , which is the ratio of variance of measurements of a given target to the variance of all targets. There are

1420-519: 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 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

1491-401: 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". Simply put, a test

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1562-657: 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. An alternative method involves the application of unfolding measurement models,

1633-568: Is not valid unless it is used and interpreted in the way it is intended. 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 , or Eysenck Personality Questionnaire . Some of these tests are helpful because they have adequate reliability and validity , two factors that make tests consistent and accurate reflections of

1704-503: 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. Similarly,

1775-409: 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

1846-444: 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 . 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

1917-603: Is the logistic function (the inverse of the logit ). For example, the scale location might represent the perceived quality of a product, or the perceived weight of an object. The BTL model, the Thurstonian model as well as the Rasch model for measurement are all closely related and belong to the same class of stochastic transitivity . Thurstone used the method of pairwise comparisons as an approach to measuring perceived intensity of physical stimuli, attitudes, preferences, choices, and values. He also studied implications of

1988-489: Is the widely used Analytic Hierarchy Process , a structured technique for helping people deal with complex decisions. It uses pairwise comparisons of tangible and intangible factors to construct ratio scales that are useful in making important decisions. Another important application is the Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA) method. The method involves

2059-625: The Standards for Educational and Psychological Testing , 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,

2130-556: 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. Psychological testing has come from two streams of thought:

2201-529: 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. The first psychometric instruments were designed to measure intelligence . One early approach to measuring intelligence

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2272-593: 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. In the field of evaluation , and in particular educational evaluation , the Joint Committee on Standards for Educational Evaluation has published three sets of standards for evaluations. The Personnel Evaluation Standards

2343-441: The additivity criterion for scale differences, a criterion which must be satisfied in order to obtain interval-level measurements. Thurstone received numerous awards, including: Best Article, American Psychological Association (1949); Centennial Award, Northwestern University (1951); Honorary Doctorate, University of Göteborg (1954). Thurstone was President of American Psychological Association (1933) and first President of

2414-598: The 20th century, tied with John Garcia , James J. Gibson , David Rumelhart , Margaret Floy Washburn , and Robert S. Woodworth . Thurstone was born in Chicago , Illinois, to Swedish immigrant parents. His family returned to Stockholm , Sweden, when he was eight years old, before returning to the United States in 1901, settling Jamestown, New York . Thurstone originally received a master's degree in mechanical engineering from Cornell University in 1912. Thurstone

2485-980: The American Psychometric Society (1936). He was elected to the American Academy of Arts and Sciences in 1937, the United States National Academy of Sciences in 1938, and the American Philosophical Society in 1938. Psychometrics Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications, such as degrees or certifications, and most are psychologists with advanced graduate training in psychometrics and measurement theory. In addition to traditional academic institutions, practitioners also work for organizations such as

2556-566: The Law of comparative judgment whereas the Rasch model is a simple logistic function . Thurstone anticipated a key epistemological requirement of measurement later articulated by Rasch, which is that relative scale locations must 'transcend' the group measured; i.e. scale locations must be invariant to (or independent of) the particular group of persons instrumental to comparisons between the stimuli. Thurstone (1929) also articulated what he referred to as

2627-448: The Rasch model, and the broader class of models to which it belongs, was explicitly founded on requirements of measurement in the physical sciences. Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: factor analysis , a method of determining the underlying dimensions of data. One of the main challenges faced by users of factor analysis

2698-473: 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. Because psychometrics is based on latent psychological processes measured through correlations , there has been controversy about some psychometric measures. Critics, including practitioners in the physical sciences , have argued that such definition and quantification

2769-577: The committee also included several psychologists. The committee's report highlighted the importance of the definition of measurement. While Stevens's response was to propose a new definition, which has had considerable influence in the field, this was by no means the only response to the report. Another, notably different, response was to accept the classical definition, as reflected in the following statement: These divergent responses are reflected in alternative approaches to measurement. For example, methods based on covariance matrices are typically employed on

2840-519: The development of modern tests. 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. Herbart was responsible for creating mathematical models of the mind, which were influential in educational practices for years to come. E.H. Weber built upon Herbart's work and tried to prove

2911-418: The disciplines is required. Kept independent, they can give only wrong answers or no answers at all regarding certain important problems." 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

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2982-447: 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

3053-440: The equivalence of different versions of the same measure can be indexed by a Pearson correlation , and is called equivalent forms reliability or a similar term. Internal consistency, which addresses the homogeneity of a single test form, may be assessed by correlating performance on two halves of a test, which is termed split-half reliability ; the value of this Pearson product-moment correlation coefficient for two half-tests

3124-417: 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

3195-421: 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. Charles Darwin was the inspiration behind Francis Galton,

3266-418: The following. Suppose B is larger than A, but it is not discernible without an extremely sensitive scale. Further suppose C is larger than B, but this also is not discernible without an extremely sensitive scale. However, the difference in sizes between apples A and C is large enough that you can discern that C is larger than A without a sensitive scale. In psychophysical terms, the size difference between A and C

3337-770: The journal Psychometrika and also the Psychometric Society, going on to become the society's first president in 1936. Thurstone's contributions to methods of factor analysis have proved valuable in establishing and verifying later psychometric factor structures, and have influenced the hierarchical models of intelligence in use in intelligence tests such as WAIS and the modern Stanford-Binet IQ test . The seven primary mental abilities in Thurstone's model were verbal comprehension , word fluency , number facility , spatial visualization , associative memory , perceptual speed , and reasoning . Despite his contributions to factor analysis, Thurstone (1959, p. 267) cautioned: "When

3408-461: The law of comparative judgment), the Bradley–;Terry–Luce (BTL) model , and general stochastic transitivity models, are more aptly regarded as measurement models. The Bradley–Terry–Luce (BTL) model is often applied to pairwise comparison data to scale preferences. The BTL model is identical to Thurstone's model if the simple logistic function is used. Thurstone used

3479-509: The most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993). Psychometricians have developed a number of different measurement theories. These include classical test theory (CTT) and item response theory (IRT). 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

3550-444: The name of universal psychometrics , has also been proposed. 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. Pairwise comparison (psychology) Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity

3621-522: The normal distribution in applications of the model. The simple logistic function varies by less than 0.01 from the cumulative normal ogive across the range, given an arbitrary scale factor. In the BTL model, the probability that object j is judged to have more of an attribute than object i is: where δ i {\displaystyle \delta _{i}} is the scale location of object i {\displaystyle i} ; σ {\displaystyle \sigma }

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3692-483: The number of alternatives is n, and indifference is not allowed, then the number of possible preference orders for any given n -value is  n !. If indifference is allowed, then the number of possible preference orders is the number of total preorders . It can be expressed as a function of n: where S 2 ( n ,  k ) is the Stirling number of the second kind . One important application of pairwise comparisons

3763-413: The pair A and C are shown, you prefer C over A. If pairwise comparisons are in fact transitive in respect to the four mentioned rules, then pairwise comparisons for a list of alternatives ( A 1 ,  A 2 ,  A 3 , ...,  A n −1 , and A n ) can take the form: For example, if there are three alternatives a , b , and c , then the possible preference orders are: If

3834-441: 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

3905-445: The premise that numbers, such as raw scores derived from assessments, are measurements. Such approaches implicitly entail Stevens's definition of measurement, which requires only that numbers are assigned according to some rule. The main research task, then, is generally considered to be the discovery of associations between scores, and of factors posited to underlie such associations. On the other hand, when measurement models such as

3976-556: 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. In 2014, the American Educational Research Association (AERA), American Psychological Association (APA), and National Council on Measurement in Education (NCME) published a revision of

4047-690: The ratio of some magnitude of a quantitative attribute to a unit of the same attribute" (p. 358) 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,

4118-409: 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

4189-455: 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. 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

4260-404: The sample tested, while, in principle, those derived from item response theory are not. 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

4331-632: The structure of DNA . 1952, he established the L. L. Thurstone Psychometric Laboratory at the University of North Carolina at Chapel Hill . Thurstone was responsible for the standardized mean and standard deviation of IQ scores used today, as opposed to the Intelligence Test system originally used by Alfred Binet . He is also known for the development of the Thurstone scale . Thurstone's work in factor analysis led him to formulate

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4402-491: 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

4473-414: The theory and application of factor analysis , a statistical method developed and used extensively in psychometrics. 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

4544-457: The theory he developed for opinion polls and political voting (Thurstone, 1959). For a given decision agent, if the information, objective, and alternatives used by the agent remain constant, then it is generally assumed that pairwise comparisons over those alternatives by the decision agent are transitive. Most agree upon what transitivity is, though there is debate about the transitivity of indifference. The rules of transitivity are as follows for

4615-464: 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 . The definition of measurement in the social sciences has a long history. A current widespread definition, proposed by Stanley Smith Stevens ,

4686-568: The underlying construct. The Myers–Briggs Type Indicator (MBTI), however, has questionable validity and has been the subject of much criticism. Psychometric specialist Robert Hogan wrote of the measure: "Most personality psychologists regard the MBTI as little more than an elaborate Chinese fortune cookie." Lee Cronbach noted in American Psychologist (1957) that, "correlational psychology, though fully as old as experimentation,

4757-439: The validity of the assumed continuum by means of its internal consistency". Thurstone's approach to measurement was termed the law of comparative judgment . He applied the approach in psychophysics , and later to the measurement of psychological values. The so-called 'Law', which can be regarded as a measurement model, involves subjects making a comparison between each of a number of pairs of stimuli with respect to magnitude of

4828-479: Was offered a brief assistantship in the laboratory of Thomas Edison . In 1914, after two years as an instructor of geometry and drafting at the University of Minnesota , he enrolled as a graduate student in psychology at the University of Chicago (PhD, 1917). He later returned to the University of Chicago (1924–1952) where he taught and conducted research; among his students was James Watson , who co-discovered

4899-635: Was published in 1988, The Program Evaluation Standards (2nd edition) was published in 1994, and The Student Evaluation Standards 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. 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

4970-400: 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

5041-639: Was the test developed in France by Alfred Binet and Theodore Simon . That test was known as the 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 testing . There has been a range of theoretical approaches to conceptualizing and measuring personality, though there

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