If a Cepheid luminosity at given period depends on metallicity , then the P-L relation in galaxies with higher metallicities may show a higher dispersion if these galaxies also sample a wider range of intrinsic metallicities .
Using published HST Cepheid data from 25 galaxies , we have found such a correlation between the the P-L dispersion and host galaxy metallicity which is significant at the \approx 3 \sigma level in the V band .
In the I band the correlation is less significant , although the tighter intrinsic dispersion of the P-L relation in I makes it harder to detect such a correlation in the HST sample .
We find that these results are unlikely to be explained by increased dust absorption in high metallicity galaxies .
The data support the suggestion of Hoyle et al .
that the metallicity dependence of the Cepheid P-L relation may be stronger than expected , with \Delta M / [ O / H ] \approx - 0.66 mag dex ^ { -1 } at fixed period .

The high observed dispersions in the HST Cepheid P-L relations have the further consequence that the bias due to incompleteness in the P-L relation at faint magnitudes is more significant than previously thought .
Using a maximum likelihood technique which takes into account the effect on the P-L relations of truncation by consistently defined magnitude completeness limits , we re-derive the Cepheid distances to the 25 galaxies and find that the average distance is increased by \approx 0.1mag .
However , in the cases of two high metallicity galaxies at large distances the effect is severe , with the published distance modulus underestimating the true distance modulus by \approx 0.5mag .

In the HST sample , galaxies at higher distance tend to have higher metallicity .
This means that when a full metallicity correction is made , a scale error in the published Cepheid distances is seen in the sense that the published distance moduli are increasingly underestimates at larger distances , with the average difference now being \approx 0.3mag .
This results in the average distance modulus to the four galaxies in the Virgo cluster core increasing from ( m - M ) _ { 0 } = 31.2 \pm 0.19 to ( m - M ) _ { 0 } = 31.8 \pm 0.17 with similar increases for the Fornax and Ursa Major clusters .
For the 18 HST galaxies with good Tully-Fisher distances and m - M _ { 0 } > 29.5 the Cepheid-TF distance modulus average residual increases from 0.44 \pm 0.09 mag to 0.82 \pm 0.1mag indicating a significant scale error in TF distances and resulting in the previous Pierce & Tully TF estimate of H _ { 0 } =85 \pm 10 kms ^ { -1 } Mpc ^ { -1 } reducing to H _ { 0 } =58 \pm 7 kms ^ { -1 } Mpc ^ { -1 } , assuming a still uncertain Virgo infall model .
Finally , for the 8 HST galaxies with SNIa , the metallicity corrected Cepheid distances now imply a metallicity dependence of SNIa peak luminosity in the sense that metal-poor hosts have lower luminosity SNIa .
Thus SNIa Hubble diagram estimates of both H _ { 0 } and q _ { 0 } may also require significant metallicity corrections .