The β − M₁₆₀₀ diagram for our B-dropout sample. Open triangles and filled squares represent individual objects in the ERS and HUDF fields, respectively. Error bars on the observed points are given by the uncertainty on the linear fit on their observed magnitudes. Blue and red circles and lines indicate the result of the statistical analysis described in Sect. 5, which takes systematic effects into account. Blue open circles and error bars indicate the average ⟨ β ⟩  and intrinsic r.m.s of the best-fit Gaussian distributions in each of the four bins: uncertainties on ⟨ β ⟩  are much lower and are not visible in this scale. Red filled circles show the best-fit log-normal distributions. The Gaussians best-fit values are plotted at the average magnitude of the observed points in the relevant bins, log-normal ones with a small magnitude offset for clarity. The green continuous line is the β − UV relation by Bouwens et al. (2009). We show for comparison a linear fit on the Gaussian and log-normal best-fit points (blue dashed and red continous lines), but underline that our analysis indicates a significant difference only between the first and second magnitude bins.