Abstract: The common practice of ranking a group of animals in the closest possible order to a linear dominance hierarchy assumes that dominance among those animals is generally transitive. In fact, analysis of groups in which dominance relationships are random shows that this method has a surprisingly high probability of producing an apparently linear or near-linear hierarchy by chance. As such, the existence of transitive dominance should be tested before it is used in ranking. A suitable statistical test is described here. Chance may also contribute to the linear appearance of hierarchies based on other factors.