The quality of representation is the key. Content validity is generally established by logical means, statistical evidence is secondary. It is established by comparing items and patterns of answers to a test plan and definition of the underlying domain. Criterion-Related Validity Concern is how well the test estimates or predicts something else. The something else is a criterion, operationalized as a criterion measure.
Predictive validity involves estimating a future criterion.
Concurrent validity relates to current status on a criterion. Key Issues in Criterion-Related Validity Generalizability should be demonstrated through cross validation. Carefully consider the adequacy of criterion measures . There are usually multiple ways to represent a criterion, rarely is one perfect. Small samples have correlation coefficients that tend to bounce around a great deal.