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Numerous interestingness measures have been proposed in statistics and data mining to assess object relationships. This is especially important in recent studies of association or correlation pattern mining. However, it is still not clear whether there is any intrinsic relationship among many proposed measures, and which one is truly effective at gauging object relationships in large data sets. Recent studies have identified a critical property, null-(transaction) invariance, for measuring associations among events in large data sets, but many measures do not have this property. In this study, we re-examine a set of null-invariant interestingness measures and find that they can be expressed as the generalized mathematical mean, leading to a total ordering of them. Such a unified framework provides insights into the underlying philosophy Responsible editor: M.J. Zaki. 123 372 T. Wu et al.of the measures and helps us understand and select the proper measure for different applications. Moreover, we propose a new measure called Imbalance Ratio to gauge the degree of skewness of a data set. We also discuss the efficient computation of interesting patterns of different null-invariant interestingness measures by proposing an algorithm, GAMiner, which complements previous studies. Experimental evaluation verifies the effectiveness of the unified framework and shows that GAMiner speeds up the state-of-the-art algorithm by an order of magnitude.