Correlation of divergency: c delta. Being different in a similar way or not

Matched sets may have unlike mean scores and spreads yet share the same way in which some scores stand apart. Mean gaps and raw-score correlations do not answer this question. Correlation of divergency, c delta, is put forward to fill that gap. For every score in each of two equally sized, matched sets, it finds how far that score lies from every other score in its own set. It then draws these gaps into one divergence score through a power mean. The Pearson correlation between the two lists of divergence scores is c delta, which lies between-1 and 1. A high positive value means that the same people or things stand out in both sets, no matter which way their raw scores point. A negative value means that a score far from the rest in one set tends to be matched with a score near the rest in the other, whilst a value near zero shows little linear link. As c delta stems from within-set gaps, it is unchanged by shifts in overall level or units. It can show whether the same people feel sharply shut out in matched neighbourhood sets, whether the same bacterial strains grow oddly under two drugs, or whether the same proteins stand out in two drug-binding fingerprints. It should sit alongside means and raw-score correlations rather than take their place: c delta does not show whether an outlier is high or low, nor why it arose. The power p sets the weight given to wide gaps. With p=1 it uses Gini distance, and with p=2 root-mean-square distance. Higher p gives more weight to the furthest gaps but cuts Kish's effective sample size. The raw scores and the choice of p must therefore be read with care.