This paper considers advantages of measures of confirmation or evidential support in the context of interestingness of association rules. In particular, it is argued that the way in which they characterize positive/negative association has advantages over other measures such as null-invariant measures. Several properties are reviewed and proposed as requirements for an adequate confirmation measure in a data mining context. While none of the well-known confirmation measures satisfy all of these requirements, two new measures are proposed which do and one of these is shown to have a further advantage. Some results suggest that these measures are relatively stable when the number of null transactions varies.