  Differences in clustering properties between galaxy subpopulations complicate
the cosmological interpretation of the galaxy power spectrum, but can also
provide insights about the physics underlying galaxy formation. To study the
nature of this relative clustering, we perform a counts-in-cells analysis of
galaxies in the Sloan Digital Sky Survey (SDSS) in which we measure the
relative bias between pairs of galaxy subsamples of different luminosities and
colours. We use a generalized chi-squared test to determine if the relative
bias between each pair of subsamples is consistent with the simplest
deterministic linear bias model, and we also use a maximum likelihood technique
to further understand the nature of the relative bias between each pair. We
find that the simple, deterministic model is a good fit for the
luminosity-dependent bias on scales above ~2 Mpc/h, which is good news for
using magnitude-limited surveys for cosmology. However, the colour-dependent
bias shows evidence for stochasticity and/or non-linearity which increases in
strength toward smaller scales, in agreement with previous studies of
stochastic bias. Also, confirming hints seen in earlier work, the
luminosity-dependent bias for red galaxies is significantly different from that
of blue galaxies: both luminous and dim red galaxies have higher bias than
moderately bright red galaxies, whereas the biasing of blue galaxies is not
strongly luminosity-dependent. These results can be used to constrain galaxy
formation models and also to quantify how the colour and luminosity selection
of a galaxy survey can impact measurements of the cosmological matter power
spectrum.
