This tutorial reviews methods for testing independence between discrete levels of a dose and an ordered categorical response variable. The tests are designed to be powerful for cases in which the response improves monotonically as dosage level increases. First, we show how to apply some standard tests for doubly-ordered contingency tables. Then, we show how to construct tests as part of a model-building strategy. Other topics discussed include generalizations to stratified data, small-sample methods, and sample size and power considerations. © 1997 by John Wiley & Sons, Ltd.