Distribution of the distance from the M(H₂) vs. M_star relations Δ(y) plotted in Figs. 2 and 3 determined assuming a constant X_CO factor (panel a)) or the luminosity-dependent X_CO factor given in Boselli et al. (2002) (panel b)). Negative values are for galaxies below the fitted relation. The black empty histogram gives the distribution of galaxies with Hi − def ≤ 0.3, the filled grey histogram that of the most Hi-deficient objects of the sample (Hi − def > 0.6). Non-detected galaxies are included at their upper limits. The red empty histogram shows the distribution of the spiral galaxies mapped in CO by Kuno et al. (2007) with Hi − def ≤ 0.4, the blue dashed histogram that of the Hi-deficient galaxies (Hi − def > 0.4). The black dotted and red dashed vertical lines give the one-sigma dispersion in the distribution determined for the whole sample of Hi-normal (Hi − def ≤ 0.4) galaxies (black) and for the subsample of objects mapped by Kuno et al. (2007; red). σ indicates the mean dispersion of the different distributions of unperturbed galaxies. KS indicates the probability that the two galaxy populations are driven by the same parent population (Kolmogorov-Smirnov test).