  We prove an almost sure weak limit theorem for simple linear rank statistics
for samples with continuous distributions functions. As a corollary the result
extends to samples with ties, and the vector version of an a.s. central limit
theorem for vectors of linear rank statistics. Moreover, we derive such a weak
convergence result for some quadratic forms. These results are then applied to
quantile estimation, and to hypothesis testing for nonparametric statistical
designs, here demonstrated by the c-sample problem, where the samples may be
dependent. In general, the method is known to be comparable to the bootstrap
and other nonparametric methods (\cite{THA, FRI}) and we confirm this finding
for the c-sample problem.
