  We show that the distribution of observed accretion rates is a powerful
diagnostic of protoplanetary disc physics. Accretion due to turbulent
("viscous") transport of angular momentum results in a fundamentally different
distribution of accretion rates than accretion driven by magnetised disc winds.
We find that a homogeneous sample of $\gtrsim$300 observed accretion rates
would be sufficient to distinguish between these two mechanisms of disc
accretion at high confidence, even for pessimistic assumptions. Current samples
of T Tauri star accretion rates are not this large, and also suffer from
significant inhomogeneity, so both viscous and wind-driven models are broadly
consistent with the existing observations. If accretion is viscous, the
observed accretion rates require low rates of disc photoevaporation
($\lesssim$$10^{-9}$M$_{\odot}$yr$^{-1}$). Uniform, homogeneous surveys of
stellar accretion rates can therefore provide a clear answer to the
long-standing question of how protoplanetary discs accrete.
