Completeness functions (left column) and PDFs of observed projected proper lengths L_p, obs (right column). Selection effects leave imprints on the distribution of radio galaxies’ L_p, obs. In the top row, we show how imposing an angular length threshold in a GRG search campaign leads to incompleteness (left), which causes the PDF f_Lp, obs(right) to differ from f_Lp. We assume RGs with angular length ϕ < ϕ_min have probability 0 to be included in a sample, whilst RGs with angular length ϕ > ϕ_max have probability 1. The inclusion probability is assumed to increase linearly between ϕ_min and ϕ_max. In the left panel, we fix ϕ_min = 3′ and vary ϕ_max; in the right panel, we also fix ϕ_max = 7′. In the bottom row, we show how a survey’s surface brightness limitations lead to incompleteness (left), which causes the PDF f_Lp, obs(right) to differ from f_Lp. We assume that lobe surface brightnesses are lognormally distributed; we parametrise the distribution for RGs of intrinsic length l_ref = 0.7 Mpc at z = 0 observed at ν_obs = 144 MHz with a median b_ν, ref and dispersion parameter σ_ref. In the left panel, we fix σ_ref = 1.5 and vary b_ν, ref; in the right panel, we also fix b_ν, ref = 1000 Jy deg⁻². We assume a lobe spectral index α = −1, a surface brightness detection threshold b_ν, th = 25 Jy deg⁻², and self-similar growth: ζ = −2. For both selection effects, we consider RGs up to cosmological redshift z_max = 0.5 only.