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Psychometrics

Psychometrics is the systematic application of mathematical principles in order to measure (quantify) psychological constructs. Measurement consists of rules for assigning symbols to objects to (a) represent quantities of attributes numerically (scaling), or (b) define whether the objects fall in the same or different categories with respect to a given attribute (classification). The objects of study in psychometrics are usually people, but many studies involve other animals, or basic biological or psychological processes. Accurate measurement is essential for the development of any science because it permits objective quantification and communication of findings. Standardized measurement specifies the concept in which we are interested so that others can replicate or refute our work. Psychometric theory has been applied in a wide range of fields, including the measurement of intelligence, personality, attitudes and beliefs, and achievement, as well as in health-related disciplines.

Primary Approaches

Psychometric theory has evolved into several areas of study. Early psychometric work was in the area of intelligence testing. This work gave rise to classical test theory (CTT). More recently, item response theory has emerged to address some of the shortcomings of the CTT approaches.

Classical Test Theory

Core to the CTT approach are the concepts of reliability and validity. Reliability is the study of consistency in measurements. All measures contain some degree of error or imprecision, and CTT procedures are used to evaluate the amount of error present in a measure and whether the observed error is systematic or random. Reliability is assessed statistically, often with correlational techniques. For example, test-retest reliability (stability) of a test or the reliability of alternate forms of a test is evaluated with the Pearson coefficient.

Validity, which is dependent on a measure first being reliable, refers to whether a measure is measuring what it is supposed to measure. Validity often is a multifaceted and ongoing research process that involves establishing various aspects of a measure's validity. For example, concurrent validity refers to a measure's correlation with a known criterion measure collected at the same time, whereas predictive validity is the ability of a measure to predict a criterion at some future point in time.

Item Response Theory

Item response theory (IRT) models the relationship between latent traits and responses to test items. In contrast to CTT approaches, IRT methods have the potential to produce measures that are (a) sample independent—item parameters can be created independent of the sample taking a test; (b) falsifiable models—direct tests are available to evaluate whether a specific IRT model is appropriate for a particular data set; and (c) directly addressing measurement bias at the individual item level before these items are combined to form a scale score.

Statistical Methods

The field of psychometrics uses a number of statistical procedures, particularly correlation and regression techniques. Multivariate descriptive methods frequently are used and include factor analysis to uncover underlying dimensions in a test data set, cluster analyses to find test items or test respondents similar to each other, and multidimensional scaling to find simple representations for complex test data. More complex nonlinear regression models are used to test IRT models.

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