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.
Quantitative marketing research is the application of quantitative research techniques to the field of marketing research. It has roots in both the positivist view of the world, and the modern marketing viewpoint that marketing is an interactive process in which both the buyer and seller reach a satisfying agreement on the "four Ps" of marketing: Product, Price, Place (location) and Promotion.
Cronbach's alpha, also known as tau-equivalent reliability or coefficient alpha, is a reliability coefficient and a measure of the internal consistency of tests and measures. It was named after the American psychologist Lee Cronbach.
The Spearman–Brown prediction formula, also known as the Spearman–Brown prophecy formula, is a formula relating psychometric reliability to test length and used by psychometricians to predict the reliability of a test after changing the test length. The method was published independently by Spearman (1910) and Brown (1910).
Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological testing such as the difficulty of items or the ability of test-takers. It is a theory of testing based on the idea that a person's observed or obtained score on a test is the sum of a true score (error-free score) and an error score. Generally speaking, the aim of classical test theory is to understand and improve the reliability of psychological tests.
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.
In statistics and research, internal consistency is typically a measure based on the correlations between different items on the same test. It measures whether several items that propose to measure the same general construct produce similar scores. For example, if a respondent expressed agreement with the statements "I like to ride bicycles" and "I've enjoyed riding bicycles in the past", and disagreement with the statement "I hate bicycles", this would be indicative of good internal consistency of the test.
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.
In psychometrics, the Kuder–Richardson formulas, first published in 1937, are a measure of internal consistency reliability for measures with dichotomous choices. They were developed by Kuder and Richardson.
Lee Joseph Cronbach was an American educational psychologist who made contributions to psychological testing and measurement.
In statistics, inter-rater reliability is the degree of agreement among independent observers who rate, code, or assess the same phenomenon.
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.
Psychometric software refers to specialized programs used for the psychometric analysis of data obtained from tests, questionnaires, polls or inventories that measure latent psychoeducational variables. Although some psychometric analyses can be performed using general statistical software such as SPSS, most require specialized tools designed specifically for psychometric purposes.
The Revised NEO Personality Inventory is a personality inventory that assesses an individual on five dimensions of personality. These are the same dimensions found in the Big Five personality traits. These traits are openness to experience, conscientiousness, extraversion(-introversion), agreeableness, and neuroticism. In addition, the NEO PI-R also reports on six subcategories of each Big Five personality trait.
In statistical models applied to psychometrics, congeneric reliability a single-administration test score reliability coefficient, commonly referred to as composite reliability, construct reliability, and coefficient omega. is a structural equation model (SEM)-based reliability coefficients and is obtained from on a unidimensional model. is the second most commonly used reliability factor after tau-equivalent reliability(; also known as Cronbach's alpha), and is often recommended as its alternative.
Goldine C. Gleser was an American psychologist and statistician known for her research on the statistics of psychological testing, on generalizability theory, on defence mechanisms, on the psychological effects on child survivors of the Buffalo Creek flood, for her work with Mildred Trotter on estimation of stature, and for her participation in the Cincinnati Radiation Experiments. She was a professor of psychiatry and psychology at the University of Cincinnati.
