The spin-pair compositions at a given point of the position space are defined as the following ratios: that of the parallel spin-pair concentration to the antiparallel spin-pair concentration D-anti(r), to the total spin-pair concentration D-tot(r), and to the single spin-pair concentration D-s(r). The spin-pair concentrations are calculated by the integration of the pair functions pi(alphaalpha)(r(1),r(2)), pi(alphabeta)(r(1),r(2)), pi(betaalpha)(r(1),r(2)), and pi(betabeta)(r(1),r(2)) over an arbitrary volume V(r) around the reference point r. Because the numbers of spin pairs are not proportional to the sampling volume, the dependence of the D(r) functions upon the sample size V(r) has been studied. It is shown that all D(r) functions depend on the population (N) over bar (r) of the sample. For (N) over bar((r) less than or equal to 10(-3), all D(r) functions behave as (N) over bar (2/3)(r); therefore, size-independent spin-pair composition functions are defined as c(pi)(r) = (N) over bar (2/3)(r)D(r). Approximate expressions of the c(pi)(r) functions are proposed, which enable the recovery of the electron localization function of Becke and Edgecombe.