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Psychological statistics is application of formulas, theorems, numbers and laws to psychology. Statistical methods for psychology include development and application statistical theory and methods for modeling psychological data. These methods include psychometrics, factor analysis, experimental designs, and Bayesian statistics. The article also discusses journals in the same field.
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. Psychometrics is concerned with the objective measurement of latent constructs that cannot be directly observed. Examples of latent constructs include intelligence, introversion, mental disorders, and educational achievement. The levels of individuals on nonobservable latent variables are inferred through mathematical modeling based on what is observed from individuals' responses to items on tests and scales.
In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:
"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 and 1.00, are usually used to indicate the amount of error in the scores."
Validity is the main extent to which a concept, conclusion, or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence described in greater detail below.
In the social sciences, scaling is the process of measuring or ordering entities with respect to quantitative attributes or traits. For example, a scaling technique might involve estimating individuals' levels of extraversion, or the perceived quality of products. Certain methods of scaling permit estimation of magnitudes on a continuum, while other methods provide only for relative ordering of the entities.
The g factor is a construct developed in psychometric investigations of cognitive abilities and human intelligence. It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the fact that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks. The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores based on many tests are frequently regarded as estimates of individuals' standing on the g factor. The terms IQ, general intelligence, general cognitive ability, general mental ability, and simply intelligence are often used interchangeably to refer to this common core shared by cognitive tests. However, the g factor itself is a mathematical construct indicating the level of observed correlation between cognitive tasks. The measured value of this construct depends on the cognitive tasks that are used, and little is known about the underlying causes of the observed correlations.
In psychometrics, item response theory (IRT) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments". By contrast, item response theory treats the difficulty of each item as information to be incorporated in scaling items.
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions".
A Likert scale is a psychometric scale named after its inventor, American social psychologist Rensis Likert, which is commonly used in research questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term is often used interchangeably with rating scale, although there are other types of rating scales.
A personality test is a method of assessing human personality constructs. Most personality assessment instruments are in fact introspective self-report questionnaire measures or reports from life records (L-data) such as rating scales. Attempts to construct actual performance tests of personality have been very limited even though Raymond Cattell with his colleague Frank Warburton compiled a list of over 2000 separate objective tests that could be used in constructing objective personality tests. One exception however, was the Objective-Analytic Test Battery, a performance test designed to quantitatively measure 10 factor-analytically discerned personality trait dimensions. A major problem with both L-data and Q-data methods is that because of item transparency, rating scales and self-report questionnaires are highly susceptible to motivational and response distortion ranging all the way from lack of adequate self-insight to downright dissimulation depending on the reason/motivation for the assessment being undertaken.
Construct validity concerns how well a set of indicators represent or reflect a concept that is not directly measurable. Construct validation is the accumulation of evidence to support the interpretation of what a measure reflects. Modern validity theory defines construct validity as the overarching concern of validity research, subsuming all other types of validity evidence such as content validity and criterion validity.
A questionnaire is a research instrument that consists of a set of questions for the purpose of gathering information from respondents through survey or statistical study. A research questionnaire is typically a mix of close-ended questions and open-ended questions. Open-ended, long-term questions offer the respondent the ability to elaborate on their thoughts. The Research questionnaire was developed by the Statistical Society of London in 1838.
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. There are five major research areas in mathematical psychology: learning and memory, perception and psychophysics, choice and decision-making, language and thinking, and measurement and scaling.
Quantitative psychology is a field of scientific study that focuses on the mathematical modeling, research design and methodology, and statistical analysis of psychological processes. It includes tests and other devices for measuring cognitive abilities. Quantitative psychologists develop and analyze a wide variety of research methods, including those of psychometrics, a field concerned with the theory and technique of psychological measurement.
A computerized classification test (CCT) refers to, as its name would suggest, a Performance Appraisal System that is administered by computer for the purpose of classifying examinees. The most common CCT is a mastery test where the test classifies examinees as "Pass" or "Fail," but the term also includes tests that classify examinees into more than two categories. While the term may generally be considered to refer to all computer-administered tests for classification, it is usually used to refer to tests that are interactively administered or of variable-length, similar to computerized adaptive testing (CAT). Like CAT, variable-length CCTs can accomplish the goal of the test with a fraction of the number of items used in a conventional fixed-form test.
The Millon Clinical Multiaxial Inventory – Fourth Edition (MCMI-IV) is the most recent edition of the Millon Clinical Multiaxial Inventory. The MCMI is a psychological assessment tool intended to provide information on personality traits and psychopathology, including specific mental disorders outlined in the DSM-5. It is intended for adults with at least a 5th grade reading level who are currently seeking mental health services. The MCMI was developed and standardized specifically on clinical populations, and the authors are very specific that it should not be used with the general population or adolescents. However, there is evidence base that shows that it may still retain validity on non-clinical populations, and so psychologists will sometimes administer the test to members of the general population, with caution. The concepts involved in the questions and their presentation make it unsuitable for those with below average intelligence or reading ability.
Measuring the Mind: Conceptual Issues in Contemporary Psychometrics is a book by Dutch academic Denny Borsboom, Assistant Professor of Psychological Methods at the University of Amsterdam, at time of publication. The book discusses the extent to which psychology can measure mental attributes such as intelligence and examines the philosophical issues that arise from such attempts.
Psychometric software is software that is used for psychometric analysis of data from tests, questionnaires, or inventories reflecting latent psychoeducational variables. While some psychometric analyses can be performed with standard statistical software like SPSS, most analyses require specialized tools.
In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale and serves to identify a set of latent constructs underlying a battery of measured variables. It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables. Measured variables are any one of several attributes of people that may be observed and measured. Examples of measured variables could be the physical height, weight, and pulse rate of a human being. Usually, researchers would have a large number of measured variables, which are assumed to be related to a smaller number of "unobserved" factors. Researchers must carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.
Klaus D. Kubinger, is a psychologist as well as a statistician, professor for psychological assessment at the University of Vienna, Faculty of Psychology. His main research work focuses on fundamental research of assessment processes and on application and advancement of Item response theory models. He is also known as a textbook author of psychological assessment on the one hand and on statistics on the other hand.
References
- Guilford, J. P. (1936). Psychometric methods. New York: McGraw-Hill.
- Kline, P. (1986). A handbook of test construction. London: Methuen