 As Theorem 1 makes clear, the lack of correlation between \(\r{M}\) and \(\r{T}\) is sufficient to rule out association reversals (and thus YAP as well). Does it also rule out the more general amalgamation paradox? The answer to this depends on which measure of association one chooses for \(\alpha\). Discussions of Simpson’s Paradox commonly treat association as the difference in the success rate between the treated and the untreated, but this is only one of many possibilities (Fitelson 1999). While the lack of association between \(M\) and \(T\) is sufficient to rule out AMP for most measures (including the difference measure) it does not rule it out for all measures, as we will now explain. Readers not interested the specific details may skip to the following section.