Purpose Diffusional kurtosis imaging (DKI) is an approach to characterizing the non‐Gaussian fraction of water diffusion in biological tissue. However, DKI is highly susceptible to the low signal‐to‐noise ratio of diffusion‐weighted images, causing low precision and a significant bias due to Rician noise distribution. Here, we evaluate precision and bias using weighted linear least squares fitting of different acquisition schemes including several multishell schemes, a diffusion spectrum imaging (DSI) scheme, as well as a compressed sensing reconstruction of undersampled DSI scheme. Methods Monte Carlo simulations were performed to study the three‐dimensional distribution of the apparent kurtosis coefficient (AKC). Experimental data were acquired from one healthy volunteer with multiple repetitions, using the same acquisition schemes as for the simulations. Results The angular distribution of the bias and precision were very inhomogeneous. While axial kurtosis was significantly overestimated, radial kurtosis was underestimated. The precision of radial kurtosis was up to 10‐fold lower than axial kurtosis. Conclusion The noise bias behavior of DKI is highly complex and can cause overestimation as well as underestimation of the AKC even within one voxel. The acquisition scheme with three shells, suggested by Poot et al, provided overall the best performance. Magn Reson Med 76:1684–1696, 2016. © 2016 International Society for Magnetic Resonance in Medicine