It is well known that the clustering of galaxies depends on galaxy type.Such relative bias complicates the inference of cosmological parameters from galaxy redshift surveys, and is a challenge to theories of galaxy formation and evolution. In this paper we perform a joint counts-in-cells analysis on galaxies in the 2dF Galaxy Redshift Survey, classified by both colour and spectral type, eta, as early or late type galaxies. We fit three different models of relative bias to the joint probability distribution of the cell counts, assuming Poisson sampling of the galaxy density field. We investigate the nonlinearity and stochasticity of the relative bias, with cubical cells of side 10Mpc leq L leq 45Mpc (h=0.7). Exact linear bias is ruled out with high significance on all scales. Power law bias gives a better fit, but likelihood ratios prefer a bivariate lognormal distribution, with a non-zero `stochasticity - i.e. scatter that may result from physical effects on galaxy formation other than those from the local density field. Using this model, we measure a correlation coefficient in log-density space (r_LN) of 0.958 for cells of length L=10Mpc, increasing to 0.970 by L=45Mpc. This corresponds to a stochasticity sigma_b/bhat of 0.44pm0.02 and 0.27pm0.05 respectively. For smaller cells, the Poisson sampled lognormal distribution presents an increasingly poor fit to the data, especially with regard to the fraction of completely empty cells. We compare these trends with the predictions of semianalytic galaxy formation models: these match the data well in terms of overall level of stochasticity, variation with scale, and fraction of empty cells.
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