Spike trains without obvious serial dependencies are commonly described as reflecting a renewal process, in which the intervals are randomly and independently generated. We present a simple, straightforward but statistically rigorous way to test for randomness and stationarity in neuronal spike trains. This method is based on quantile analysis of cumulative probability distributions. The method can be used to test null hypotheses about any two interval distributions. Application of the method for spike trains from rat cerebellar cortex revealed that randomness and independence can be separate phenomena that require separate evaluation.