Cope's Rule states that the size of species tends to increase along an evolutionary lineage. A basic statistical framework is elucidated for testing Cope's Rule and some surprising complications are pointed out. If Cope's Rule is formulated in terms of mean size, then it is not invariant to the way in which size is measured. If Cope's Rule is formulated in terms of median size, then it is not invariant to the degree of separation between ancestral and descendant species. Some practical problems in assessing Cope's Rule are also described. These results have implications for the empirical assessment of Cope's Rule.