This note presents an alternative proof of a result on statistical dominance first given by Fishburn. The proof is simpler than the original, and avoids the use of the rather complex Abel's summation identity. A criterion of "weak" dominance is then proposed in order to deal with situations where it is not possible to establish Fishburn's "strict" dominance. It is also shown that "strict" dominance is a special case of the more general concept of "weak" dominance.