  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 0.44\pm0.02 and 0.27\pm0.05 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.
