Criterion Variable in statistics is the variable whose value we predict based on the predictor variables. The predictor variables are the independent variables and the criterion variables are the dependent variables.
Example 1: Criterion variable is a term used for dependent variables in the context of linear regression. Suppose you construct a linear regression model to study the relationship between the number of hours spent studying and marks obtained in an exam.
Since the marks obtained depend on the number of hours spent studying, the marks obtained are the dependent/criterion variable. The number of hours spent studying is the predictor (independent) variable since we can use it to predict the marks obtained.
Note that in the above example there is an actual causal relationship between the two variables. This need not be the case every time we see a correlation between two variables.
Example 2: Consider the two variables – Height of a person and shoe size of a person. There is definitely a relationship between these two variables. Generally speaking, as a person grows up his shoe size increases and his height also increases.
Hence, we can construct a linear regression model between these two variables taking the predictor variable to be the shoe size of the person and the criterion variable to be the height of the person. We can obtain predictions for the height by inputting the shoe size in our regression.
Notice then in this example we cannot infer a causal relationship between the two variables. Indeed it would be absurd to claim that the increase in shoe size caused a corresponding increase in the height of the person.