Many analytical techniques in locational archaeology and spatial geography involve comparing observed distributions of point patterns with theoretically-modelled random distributions. This paper suggests that comparing observed data with large numbers of empirically generated random distributions offers a more accurate, robust, and intuitively obvious estimate of deviations from randomness in distributional data. Specifically, the nearest-neighbor and linear nearest-neighbor statistics are discussed, and a randomization method of generating random patterns of data is applied to both theoretical models of point pattern distributions and to archaeological data. It is found that the theoretical values associated with a random point distribution (e.g. about 1.00 for the nearest-neighbor statistic) only hold for very specific site geometries and that the randomization approach is more widely applicable to real archaeological data. Similarily, the randomization routine provides a more robust test of the statistical significance of deviations from randomness, which are not burdened by the underlying assumptions of statistical models regularly applied to this question.