Evaluating order-constrained hypotheses for circular data from a between-within subjects design

Researchers in psychology often encounter data measured in angles (e.g., directions, or measurements on circular scales such as the circumplex model of affect). Due to periodicity, the evaluation of these circular data requires special statistical methods. This article introduces new tests for the analysis of order-constrained hypotheses for circular data. Through these tests, researchers can evaluate their expectations regarding the outcome of an experiment directly by representing their ideas in the form of a hypothesis containing inequality constraints. The resulting data analysis is generally more powerful than one using null hypothesis testing. An example of circular data from psychology is presented to illustrate the use of the tests. Results from a simulation study show that the tests perform well in terms of type I error and power.