This probability table is based on the number of runs of signs of first differences in ordered series, or expressed differently, the number of rises and falls in ordered series, that would occur under this nonparametric null hypothesis: the relative magnitude of an observation is independent of its position in the series. The runs test used in conjunction with the probability table in this article is probably less sensitive than rank order correlation techniques for detecting monotonic correlations, but much better for rejecting the above null hypothesis in dealing with series involving cycles or some other non-monotonic systematic rise and fall in the magnitude of the observations, such asU-shaped or invertedU-shaped series of observations.