Non-normal statistics applied to diffusivity calculations accelerate screening of ionic conductors for electrochemical devices such as electric storage batteries, fuel cells, and sensors. Displacements of atomic species within a crystalline structure for a candidate ionic conductor material are analyzed using a Skellam distribution optionally combined with Gaussian noise to calculate values for the standard deviation, upper error bound, and lower error bound for predicted values of diffusivity (D). When the predicted values of D have sufficient statistical precision, the diffusivity calculation is terminated and the calculated diffusivity is compared to a threshold value of diffusivity. When the threshold has been exceeded, the candidate ionic conductor may be listed as a preferred good conductor. When the calculated diffusivity fails to exceed the threshold, the material may be listed as a poor conductor and may be eliminated from further consideration.