Psychometrics: Theory and Psychological Measurement

• Psychometrics is the field of study concerned with the theory and technique of psychological measurement.
• It covers the measurement of knowledge, abilities, attitudes, and personality traits.
• The field primarily focuses on the construction and validation of assessment instruments, such as questionnaires, tests, and personality assessments.

Core Concepts

• Scaling involves the process of creating a continuous scale upon which individuals can be located according to the latent traits they possess.
• Scaling models include classical test theory and item response theory.
• Reliability refers to the consistency and stability of a measurement.
• Validity refers to the accuracy of a measurement and whether it measures what it is supposed to measure.

Reliability

• Test-retest reliability assesses the consistency of results when a test is administered to the same individuals at two different points in time.
• Inter-rater reliability assesses the degree of agreement among different raters or observers.
• Internal consistency assesses the consistency of results across items within a test.
• Cronbach's alpha is a common measure of internal consistency.

Validity

• Content validity assesses whether the content of a test adequately samples the domain it is intended to measure.
• Criterion validity assesses the extent to which a test correlates with a specific criterion or outcome.
• Concurrent validity and predictive validity are types of criterion validity.
• Construct validity assesses the extent to which a test measures a theoretical construct or trait.
• Convergent validity and discriminant validity are types of construct validity.

Item Response Theory (IRT)

• IRT is a family of models that relate examinee's responses to a test item to their latent trait level.
• Item characteristic curves (ICCs) are central to IRT.
• ICCs describe the relationship between the probability of a correct response and the level of the latent trait.
• Item discrimination, difficulty, and pseudo-guessing are parameters often associated with ICCs.
• IRT provides item-level information, allowing for the development of tailored and adaptive tests.

Classical Test Theory (CTT)

• CTT is a traditional approach to psychometrics that assumes each test score is composed of a true score and an error component.
• Observed score = True score + Error.
• CTT focuses on the overall reliability and validity of a test.
• CTT is simpler to apply compared to IRT but has limitations, such as sample dependency.

Factor Analysis

• Factor analysis is a statistical method used to reduce a large number of variables into a smaller number of factors.
• Exploratory factor analysis (EFA) is used to discover the underlying structure of a set of variables.
• Confirmatory factor analysis (CFA) is used to test a pre-specified factor structure.

Bias

• Measurement bias occurs when a test yields systematically different results for different groups, even when they have the same level of the underlying trait.
• Differential item functioning (DIF) analysis is used to identify items that function differently for different groups.

Applications

• Educational testing and assessment.
• Personnel selection and placement.
• Clinical psychology and mental health assessment.
• Market research and consumer behavior.
• Program evaluation.

Challenges and Future Directions

• Adapting to diverse populations and cultural contexts.
• Use of technology in assessment.
• Addressing issues of test security and cheating.
• Development of new statistical methods.
• Ethical considerations in testing and assessment.