 This fact follows directly from the Law of Total Probability (proof omitted) and it gives us a simple necessary condition for the occurrence of Association Reversal (AR): turning to  Figure 1  again, it implies that the overall success rate per condition has to be on the solid lines. Thus AR cannot occur in the right part of  Figure 1,  but it can occur if the proportions are ordered as in the left part of  Figure 1.  Generally, AR is avoided when the following condition holds: 