Abstract. In the literature of data mining and statistics, numerous interestingness measures have been proposed to disclose succinct object relationships of association patterns. However, it is still not clear when a measure is truly effective in large data sets. Recent studies have identified a critical property, null-(transaction) invariance, for measuring event associations in large data sets, but many existing measures do not have this property. We thus re-examine the null-invariant measures and find interestingly that they can be expressed as a generalized mathematical mean, and there exists a total ordering of them. This ordering provides insights into the underlying philosophy of the measures and helps us understand and select the proper measure for different applications.