AbstractClimbing ripple cross-laminae were used to obtain two-dimensional palaeocurrent data from glaciofluvial and glaciolacustrine sands. These data were then compared to the Gaussian, von Mises and circular uniform frequency distributions for goodness-of-fit atα= 0.05 andα= 0.01. Individual sample distributions taken from sampling units of one cubic metre were best described by the Gaussian and von Mises distributions. Atα= 0.05, only the Gaussian provided an adequate fit for samples with relatively small standard deviations (∼14°to 18°). For samples with larger standard deviations (∼20°to 40°) both the Gaussian and von Mises distributions were satisfactory fits atα= 0.01, but atα= 0.05 the Gaussian was the better fit for most of the samples. None of the three theoretical distributions adequately described the sampling distribution, which had a standard deviation of 50°. The best fit distribution for samples with standard deviations around 50°is probably transitional between a von Mises and a circular uniform distribution at bothα= 0.05 and 0.01.In future studies of similar deposits, if the same size of sampling unit (1 cubic metre) is used and if the same average flow variability is assumed, a minimum of about 25 observations will be necessary in each sample in order to estimate the sample vector resultant to within±10°of the true average flow direction atα= 0.05; and atα= 0.01, at least 45 observations will be necessary.Analysis-of-variance of the data in their vectorial form gaveω= 4.273 andβ= 0.5399 for the within and between-site estimates of the population variance. The concentration parameter,χ, was 6.998 for the grand vector resultant and gaveψ≃56°for the semi-angle of confidence,ψ, around the grand resultant. Several combinations of sample size and number were calculated (a) to achieve the same value forχin estimating the grand vector resultant in separate investigations, and (b) to increase the valueχ.