Recent statistical constitutive models of suspensions of neutrally buoyant, noncolloidal, solid spheres in Newtonian fluids suggest that the particles migrate in response to gradients in "suspension temperature," defined as the average kinetic energy contained in the particle velocity fluctuations. These models have not yet been compared systematically with experimental data. In addition the "temperature" models assume isotropic particle velocity fluctuations, since the suspension temperature is given as a scalar. However, highly anisotropic particle velocity fluctuations have been observed experimentally, which suggests that a suspension temperature tensor is more realistic. We use laser Doppler velocimetry to measure particle velocity, fluctuations arising from interparticle collisions in a concentrated suspension under nearly homogeneous shear flow in a narrow-gap concentric cylinder Couette device. We compare the relative sizes of the fluctuating velocity components and determine the variation of each component with particle volume fraction and shear rate. The data indicate that the suspension temperature is anisotropic. The flow direction component is overwhelmingly the largest at every concentration and shear rate, followed in order of magnitude by the neutral-direction and velocity-gradient-direction components. Additionally, over the region of the flow accessible to measurement, each fluctuating velocity component demonstrates a distinct variation with shear rate and particle volume fraction. Finally, we explain the observed anisotropy and variation of the suspension temperature in terms of the dynamics of interparticle interactions.