Microarrays are a powerful new technology that allow for the measurement of the expression of thousands of genes simultaneously. Owing to relatively high costs, sample sizes tend to be quite small. If investigators apply a correction for multiple testing, a very small p-value will be required to declare significance. We use modifications to Chebyshev's inequality to develop a testing procedure that is nonparametric and yields p-values on the interval [0, 1]. We evaluate its properties via simulation and show that it both holds the type I error rate below nominal levels in almost all conditions and can yield p-values denoting significance even with very small sample sizes and stringent corrections for multiple testing.