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.
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