Simulations of three plane-parallel ionization chambers have been used to determine directly the chamber- and quality-dependent factors fc,Q, instead of the product (Sw,air p)Q, and kQ,Q0 (or kQ,Q,int) for a broad range of electron beam qualities (4-20 MeV) using divergent monoenergetic beams and phase-space data from two accelerators. An original calculation method has been used which circumvents the weakness of the so far assumed independence between stopping-power ratios and perturbation factors. Very detailed descriptions of the geometry and materials of the chambers have been obtained from the manufacturers, and prepared as input to the PENELOPE 2003 Monte Carlo system using a computer code that includes correlated sampling and particle splitting. Values of the beam quality factors have been determined for the case of an electron reference beam. The calculated values have been compared with those in the IAEA TRS-398 dosimetry protocol and the differences analysed. The results for a NACP-02 chamber show remarkably good agreement with TRS-398 at high electron beam qualities but differ slightly at low energies. Arguments to explain the differences include questioning the undemonstrated assumption that the NACP is a 'perturbation-free' chamber even at very low electron beam energies. Results for Wellhöfer PPC-40 and PPC-05 chambers cannot be compared with data from others for these chambers because no calculations or reliable experimental data exist. It has been found that the results for the PPC-40 are very close to those of a Roos chamber, but the values for the PPC-05 are considerably different from those of a Markus chamber, and rather approach those of a Roos chamber. Results for monoenergetic electrons and accelerator phase-space data have been compared to assess the need for detailed and costly simulations, finding very small differences. This questions the emphasis given in recent years to the use of 'realistic' source data for accurate electron beam dosimetry.