A note on measuring overlap

In measuring the overlap between two sets A and B (e.g. libraries, databases) one is obliged to calculate the overlap O(A|B) of A with respect to B (i.e. the fraction of elements of B that are also in A) and of O(B|A) of B with respect to A (i.e. the fraction of elements in A that are also in B). Theoretically this requires two samples. In this paper we explain that one sample can suffice to determine confidence intervals for both O(A|B) and O(B|A). The paper closes with the example of measuring the overlap between the secondary sources in mathematics MathSciNet and Zentralblatt MATH and with a remark on the estimation of the Jaccard index.