Radio spectral index () of star-forming sources detected at 3 GHz as a function of redshift. As in Fig. 3, the median values within each redshift bin, derived from a single-censored survival analysis, are shown by the black squares. The predicted evolution in the spectral index due to the contamination of free-free emission based on the M82 model of Condon (1992) is shown by the thick, dashed blue line. Our assumed value of α = − 0.7 for non-detections at 1.4 GHz is shown by the black dashed line.