Cronbach's coefficient alpha has been widely known and used in educational research. Many education research practitioners, however, may not be aware of the potential issues when the main assumptions for coefficient alpha are violated in research practice. This paper provides a brief discussion about two assumptions that may make the use and interpretation of coefficient alpha less appropriate in education research: violations of the tau-equivalence model assumption and the error independence assumption. Violation of either or both of these assumptions will have negative effects on the precision of coefficient alpha as reliability estimate. The paper further presents two alternative reliability estimates without the assumptions of tau-equivalence or error independence. Research practitioners may consider these and other alternatives, when measurement data may not satisfy the assumptions for coefficient alpha.