Comparison of the robust and Gaussian criteria for all stars with σ_ϖ/ϖ better than 5%. The top panel compares the confidence levels while the bottom panel compares the radial-velocity standard errors σ_vr required to reach a confidence level c = 68.27%. The top panel shows two branches of data points: the linear, one-to-one branch corresponds to stars with a measured radial velocity, whereas the lower, curved branch corresponds to stars without measured radial velocity in the XHIP catalogue. As explained in Sect. 6.2, the latter objects suffer from a bias in the Gaussian confidence level c_Gauss.