  We present an analysis of the relative bias between early- and late-type
galaxies in the Two-degree Field Galaxy Redshift Survey (2dFGRS). Our analysis
examines the joint counts in cells between early- and late-type galaxies, using
approximately cubical cells with sides ranging from 7h^{-1}Mpc to 42h^{-1}Mpc.
We measure the variance of the counts in cells using the method of Efstathiou
et al. (1990), which we find requires a correction for a finite volume effect.
We fit lognormal models to the one-point density distribution and develop
methods of dealing with biases in the recovered variances resulting from this
technique. We directly fit deterministic models for the joint density
distribution function, f(delta_E,delta_L), to the joint counts in cells using a
maximum likelihood technique. Our results are consistent with a scale invariant
relative bias factor on all scales studied. Linear bias is ruled out on scales
less than l=28h^{-1}Mpc. A power-law bias model is a significantly better fit
to the data on all but the largest scales studied; the relative goodness of fit
of this model as compared to that of the linear bias model suggests that any
nonlinearity is negligible for l>~40h^{-1}Mpc, consistent with the expectation
from theory that the bias should become linear on large scales. (abridged)
