Diagnostic assessments are "small scale" tests, usually one-on-one, with the purpose to gather specific data to help plan a child's specific learning path. These may be, but are not limited to, assessments that help identify specific learning disabilities. They are often, but not exclusively, used for students with special needs. They are typically given by highly trained staff members who understand the benefits and limits of these tests.
See the list of district approved diagnostic assessments.