The detection rate of gamma-ray burst (GRB) afterglows is only 30% at
radio wavelengths, much lower than in the X-ray ( 95%) or optical (
70%) bands. The cause of this low radio detection rate has previously been attributed to limited observing sensitivity. We use visibility stacking to test this idea, and conclude that the low detection rate is instead due to two intrinsically different populations of GRBs, radio bright and radio faint. The radio bright GRBs also have higher gamma-ray fluence, isotropic energies, X-ray fluxes and optical fluxes than the radio faint GRBs, confirming the existence of two physically distinct populations. We suggest that the gamma-ray efficiency of the prompt emission is responsible for the difference between the two populations.