Cumulative distribution functions for the GCNS background distribution (dashed blue), the GCNS × TESS flare distribution (solid blue), the V-LoTSS × GCNS sample (green), the LoTSS × GCNS sample (orange), and the VLASS × GCNS sample (grey), shown as a function of effective temperature T_eff. The solid blue line is the product of the dashed blue line and TESS flare rate curve according to Fig. 1d. The shaded regions correspond to the 95% confidence level based on a binomial distribution. The stars with T_eff < 2800 K (around spectral type M6; shaded red box) are excluded in our analysis due to their incompleteness in TESS. The top axis of the CDF plots indicates the nominal stellar spectral types (Pecaut & Mamajek 2013).