Within many ecological systems, relationships between controlling factors and associated response variables are complex. In many cases, the response should vary little when the controlling factor exerts strong effects. Conversely, when the effect of the controlling factor is weak or absent, the response may vary greatly with effects of other factors. Correlation or regression analyses often may not be appropriate for testing these relationships, because variance of the response changes with values of the controlling factor. We suggest using a technique from the astronomy literature, a two-dimensional Kolmogorov- Smirnov (2DKS) test, to detect relationships in bivariate data with these patterns of variance. This technique successfully identified simulated bivariate data composed of paired independent values as having nonsignificant relationships and simulated bivariate data in which mean and variance of y was constrained at high levels of x as having significant relationships. Using these simulations and examples from aquatic and terrestrial systems, we demonstrate that the 2DKS is a robust test for detecting nonrandom patterns in bivariate distributions that commonly arise in many ecological systems.