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	Figure 1: Variation of the deepness of the Cepheid samples with distance. The (normalized) apparent V magnitude limit of the Cepheid samples first grows with distance (radial velocity ) but, after a certain point, tends to bend where we have seen the bias appearing in derived Cepheid distances. We show the positions for an unbiased galaxy (NGC 3351) and a biased one (NGC 1425).
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In the text

	Figure 2: V-band period luminosity relation for NGC 3351, an unbiased galaxy ( top panel) and NGC 1425, a biased galaxy ( bottom panel). These galaxies are shown in Fig. 6, where we compare the corrected and uncorrected distance moduli.
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In the text

Figure 3: Observed Hubble values in log scale against normal ( top panel) and normalized ( bottom panel) limiting absolute magnitude. These absolute magnitudes are calculated from Eq. (1), using corrected radial velocity . Top panel: the observed depends on the limiting absolute magnitude. One may recognize the classical shape of a bias curve with a plateau of constant near the faint limiting absolute magnitudes ( . Bottom panel: after the normalization, all the data are put on a same bias curve. The plateau is more clearly visible.

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In the text

Figure 4: Observed Hubble values in log scale against normal ( top panel) and normalized ( bottom panel) limiting absolute magnitude. These absolute magnitudes are calculated from Eq. (2), using observed distance moduli . Top panel: the correlation of the observed with the limiting absolute magnitude is still visible, as in Fig. 3a, although it should be canceled by the inverse correlation of errors (see text). However it is difficult to recognize the classical shape of a bias curve because of the uncertainties on . Bottom panel: after the normalization, all the data are put on the same bias curve.

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In the text

Figure 5: Application of the cluster incompleteness bias curve fitting to the Cepheid bias. Top panel: the fit of Fig. 3b with the bias curve following the method described in the text. Bottom panel: the same figure as the previous one, when the bias fit is applied to Fig. 4b. We have added on both figures the recent measurement of the galaxy M 83 (filled star) by Thim et al. (2003). It is in the unbiased plateau.

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In the text

Figure 6: Comparison of corrected and uncorrected distance moduli for HST (light gray or red) and ground-based (dark gray or blue) observations. The ground-based (open circles) and HST observations (filled circles) show the same trend (dashed lines) at different distances as explained by the systematic error in Cepheid distances. From the ground, the bias starts soon beyond the closest galaxy (M 31), except for the new VLT result on M 83 (filled star). From space, the bias appears beyond the distance of closest galaxy groups (M 81). At the distance of the closest large galaxy cluster (Virgo) it has a large incidence. The identified galaxies (NGC 3351 and NGC 1425) were used above (Fig. 2) to show the PL relation for an unbiased and biased galaxy.

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In the text

Figure 7: Local Hubble diagrams for uncorrected ( top) and corrected ( bottom) distances. Top panel: the clear curvature in the uncorrected relation is now understood to be caused by the bias that moves the galaxies up from the Hubble line. Open circles show the galaxies observed from the ground with a velocity  km s-1. Bottom panel: the linearity, which is the property of the large-scale Hubble law as shown by secondary distance indicators (e.g., supernovae Ia), is revealed here, locally, by Cepheid stars. The line corresponds to a local value H= 56 km s-1 Mpc-1. The filled star represents the recent VLT measurement of the galaxy M 83 (see text).

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In the text

Figure A.1: Simulation of the bias. Top panel: calculation of from a simulation, in the case where there is no selection effect on magnitudes. Bottom panel: the same calculation as above, but a with a realistic selection on magnitudes (the limiting magnitude includes the amplitude of the Cepheid light curve).


In the text

Figure A.2: Simulation of the bias when we add a velocity dispersion increasing with distance. Top panel: case where the correlation of errors due to the velocity reinforces the bias trend. Bottom panel: case where the correlation of errors due to should produce a trend opposite to the trend produced by the bias.


In the text