Psychmetrics

Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement. The field is primarily concerned with the construction and validation of measurement instruments such as questionnaires, tests, and personality assessments.

It involves two major research tasks, namely: (i) the construction of instruments and procedures for measurement; and (ii) the development and refinement of theoretical approaches to measurement. Those who practice psychometrics are known as psychometricians. All psychometricians possess a specific psychometric qualification, and while many are clinical psychologists, others work as human resources or learning and development professionals.

Origins and background
Much of the early theoretical and applied work in psychometrics was undertaken in an attempt to measure intelligence. Francis Galton, often referred to as "the father of psychometrics", devised and included mental tests among his anthropometric measures. However, the origin of psychometrics also has connections to the related field of psychophysics. Two other pioneers of psychometrics obtained doctorates in the Leipzig Psychophysics Laboratory under Wilhelm Wundt: James McKeen Cattell in 1886 and Charles Spearman in 1906.

The psychometrician L. L. Thurstone, founder and first president of the Psychometric Society in 1936, 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.

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."

Figures who made significant contributions to psychometrics include Karl Pearson, Henry F. Kaiser, L. L. Thurstone, Georg Rasch, Johnson O'Connor, Frederic M. Lord, Ledyard R Tucker, Arthur Jensen, and David Andrich.

Psychometric, psychometrician and psychometrist appreciation week is the first week in November.

Definition of measurement in the social sciences
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, which is that measurement is the numerical estimation and expression of the magnitude of one quantity relative to another (Michell, 1997).

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)

These divergent responses are reflected in alternative approaches to measurement. For example, methods based on covariance matrices are typically employed on the premise that numbers, such as raw scores derived from assessments, are measurements. Such approaches implicitly entail Stevens's definition of measurement, which requires only that numbers are assigned according to some rule. The main research task, then, is generally considered to be the discovery of associations between scores, and of factors posited to underlie such associations.

On the other hand, when measurement models such as the Rasch model are employed, numbers are not assigned based on a rule. Instead, in keeping with Reese's statement above, specific criteria for measurement are stated, and the goal is to construct procedures or operations that provide data that meet the relevant criteria. Measurements are estimated based on the models, and tests are conducted to ascertain whether the relevant criteria have been met.

Instruments and procedures
The first psychometric instruments were designed to measure the concept of intelligence. The best known historical approach involved the Stanford-Binet IQ test, developed originally by the French psychologist Alfred Binet. Nevertheless, intelligence tests are useful tools for various purposes. 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.

Psychometrics is applied widely in educational assessment to measure abilities in domains such as reading, writing, and mathematics. The main approaches in applying tests in these domains have been Classical Test Theory and the more recent Item Response Theory and Rasch measurement models. These latter approaches permit joint scaling of persons and assessment items, which provides a basis for mapping of developmental continua by allowing descriptions of the skills displayed at various points along a continuum. Such approaches provide powerful information regarding the nature of developmental growth within various domains.

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. 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).

Theoretical approaches
Psychometricians have developed a number of different measurement theories. These include classical test theory (CTT) and item response theory (IRT)  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.

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; multidimensional scaling, a method for finding a simple representation for data with a large number of latent dimensions; and data clustering, an approach to finding objects that are like each other. All these multivariate descriptive methods try to distill large amounts of data into 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.

One of the main deficiencies in various factor analyses is a lack of consensus in cutting points 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.

Key concepts
Key concepts in classical test theory are reliability and validity. A reliable measure is one that measures a construct consistently across time, individuals, and situations. A valid measure is one that measures what it is intended to measure. A measure may be reliable without being valid. However, 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,  the equivalence of different versions of the same measure can be indexed by a Pearson correlation, and is called equivalent forms reliability or a similar term.

Internal consistency, which addresses the homogeneity of a single test form, may be assessed by correlating performance on two halves of a test, which is termed split-half reliability; the value of this Pearson product-moment correlation coefficient for two half-tests is adjusted with the Spearman–Brown prediction formula to correspond to the correlation between two full-length tests. Perhaps the most commonly used index of reliability is Cronbach's α, which is equivalent to the mean of all possible split-half coefficients. Other approaches include the intra-class correlation, which is the ratio of variance of measurements of a given target to the variance of all targets.

There are a number of different forms of validity. Criterion-related validity can be assessed by correlating a measure with a criterion measure known to be valid. 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 are drawn from the domain being measured. In a personnel selection example, test content is based on a defined statement or set of statements of knowledge, skill, ability, or other characteristics obtained from a job analysis.

Item response theory models the relationship between latent traits and responses to test items. Among other advantages, IRT provides a basis for obtaining an estimate of the location of a test-taker on a given latent trait as well as the standard error of measurement of that location. For example, a university student's knowledge of history can be deduced from his or her score on a university test and then be compared reliably with a high school student's knowledge deduced from a less difficult test. Scores derived by classical test theory do not have this characteristic, and assessment of actual ability (rather than ability relative to other test-takers) must be assessed by comparing scores to those of a "norm group" randomly selected from the population. In fact, all measures derived from classical test theory are dependent on the sample tested, while, in principle, those derived from item response theory are not.

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

Testing standards
In this field, the Standards for Educational and Psychological Testing place standards about validity and reliability, along with errors of measurement and related considerations under the general topic of test construction, evaluation and documentation. The second major topic covers standards related to fairness in testing, including fairness in testing and test use, the rights and responsibilities of test takers, testing individuals of diverse linguistic backgrounds, and testing individuals with disabilities. The third and final major topic covers standards related to testing applications, including the responsibilities of test users, psychological testing and assessment, educational testing and assessment, testing in employment and credentialing, plus 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 has published three sets of standards for evaluations. The Personnel Evaluation Standards 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 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.