 Applying all this to our dataset in  Table 1,  we see that \(\alpha(D) = 0\) although \(\alpha(D_1) &gt; 0\) and \(\alpha(D_2) &gt; 0\). This is a special case of what Samuels (1993) calls Association Reversal (AR). Association reversal occurs if and only if there is a population such that the association in all partitioned subpopulations is either (i) positive (ii) negative, or (iii) zero, and the type of association in the population does not match that of the subpopulations. Writing this out mathematically, this means for a dataset \(D = \sum_{i=1}^N D_i\) that one of the following two conditions holds, 