Campbell and Fiske (1959) developed the Multitrait-Multimethod Matrix to assess the construct validity of a set of measures in a study.
[2] The approach stresses the importance of using both discriminant and convergent validation techniques when assessing new tests.
In other words, in order to establish construct validity, you have to demonstrate both convergence and discrimination.
High correlations between the test scores would be evidence of convergent validity.
For example, in order to test the convergent validity of a measure of self-esteem, a researcher may want to show that measures of similar constructs, such as self-worth, confidence, social skills, and self-appraisal are also related to self-esteem, whereas non-overlapping factors, such as intelligence, should not relate.