A reinterpretation of the Boyd-Coulson [R. J. Boyd and C. A. Coulson, J. Phys. B 7, 1805 (1974)] definition of the Fermi hole is presented. Through this reinterpretation, which makes no reference to the hypothetical Hartree level, we are able to show the essentially identical character of the Boyd-Coulson definition with the one based on a conditional probability analysis. The basis-set dependence of the Fermi hole is emphasized and the effect of canonical, localized and delocalized Kohn-Sham and Hartree-Fock basis sets is examined for selected atoms and molecules. (C) 2004 American Institute of Physics.