Developers often create common tests and special tests, which exercise common behaviors and special behaviors of the class under test, respectively. Although manually created tests are valuable, developers often overlook some special or even common tests. We have developed a new approach for automatically identifying special and common unit tests for a class without requiring any specification. Given a class, we automatically generate test inputs and identify common and special tests among the generated tests. Developers can inspect these identified tests and use them to augment existing tests. Our approach is based on statistical algebraic abstractions, program properties (in the form of algebraic specifications) dynamically inferred based on a set of predefined abstraction templates. We use statistical algebraic abstractions to characterize program behaviors and identify special and common tests. Our initial experience has shown that a relatively small number of common and special tests can be identified among a large number of generated tests and these identified tests expose common and special behaviors that deserve developers' attention.