In conventional continuum mechanics, the yield behavior of a material is size independent. However, in nanoindentation, plasticity size effects have been observed for many years, where a higher hardness is measured for smaller indentation size. In this paper we show that there was a size effect in the initiation of plasticity, by using spherical indenters with different radii, and that the length scale at which the size effect became significant depended on the mechanism of plastic deformation. For yield by densification (fused silica), there was no size effect in the nanoindentation regime. For phase transition (silicon), the length scale was of the order tens of nanometers. For materials that deform by dislocations (InGaAs/InP), the length scale was of the order a micrometer, to provide the space required for a dislocation to operate. We show that these size effects are the result of yield initiating over a finite volume and predict the length scale over which each mechanism should become significant.