Very accurate energies can be computed by the fixed-node diffusion Monte Carlo method. They are affected only by the nodal error due to the approximate description of the nodal surfaces by the trial wave function. We examine the cancellation of nodal errors in molecular electron affinity calculations. Ground state energies of the anions of first-row hydrides AH (A = Li-O) have been computed using the fixed-node diffusion Monte Carlo method with a determinant times a correlation factor as the trial wave function. The energies are among the lowest to date. Using the energy values for the neutral molecules computed by Luchow and Anderson [A. Luchow and J. B. Anderson, J. Chem. Phys. 105, 7573 (1996)] we computed adiabatic electron affinity values and found them in agreement with the experimental data. As a consequence, the values of the anion dissociation energies are also correctly evaluated.