Variation in the A₂ fraction with source X-ray luminosity in CDFS (solid line with hatched uncertainty region) and COSMOS (solid line with shaded uncertainty region). The ratio is A₂/(A₁ + A₂), where A₁ and A₂ are the numbers of type-1 and type-2 sources, respectively. Here, the two samples are considered individually and at two different redshift ranges (middle and right columns). The different panels show the effect of different assumptions while assessing the luminosity and obscuration classes. The upper two panels show the difference between considering HR or N_H to separate the population into type-1 (unobscured) and type-2 (obscured) sources. The middle lower panel shows the effect of adopting the intrinsic luminosity () instead of the observed luminosity (, upper panels). Finally, the bottom panel shows the effect of correcting for the N_H bias when derived via flux-ratios (Paper I). A moving bin is used as described in Fig. 1. The horizontal dotted line shows the overall A₂ fraction in each case, .