Criterion Variable

Criterion variable is a name used to describe the dependent variable in a variety of statistical modeling contexts, including multiple regression, discriminant analysis, and canonical correlation. The goal of much statistical modeling is to investigate the relationship between a (set of) criterion variable(s) and a set of predictor variables. The outcomes of such analyses are myriad and include as possibilities the development of model formulas, prediction rules, and classification rules. Criterion variables are also known under a number of other names, such as dependent variable, response variable, predictand, and Y. Similarly, predictor variables are often referred to using names such as independent variable, explanatory variable, and X. While such names are suggestive of a cause-and-effect relationship between the predictors and the criterion variable(s), great care should be taken in assessing causality. In general, statistical modeling alone does not establish a causal relationship between the variables but rather reveals the existence or otherwise of an observed association, where changes in the predictors are concomitant, whether causally or not, with changes in the criterion variable(s). The determination of causation typically requires further investigation, ruling out the involvement of confounding variables (other variables that affect both explanatory and criterion variables, leading to a significant association between them), and, often, scientifically explaining the process that gives rise to the causation. Causation can be particularly difficult to assess in the context of observational studies (experiments in which both explanatory and criterion variables are observed). In designed experiments, where, for example, the values of the explanatory variables might be fixed at particular, prechosen levels, it may be possible to assess causation more effectively as the research design more readily permits the adjustment of certain explanatory variables in isolation from the others, allowing a clearer judgment to be made about the nature of the relationship between the response and predictors. This entry's focus is on types of criterion variables and analysis involving criterion variables.