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Psychological researchers in different fields sometimes encounter circular or directional data. Circular data are data measured in the form of angles or two-dimensional orientations. As an example, experiments investigating the development of spatial memory and the influence of visual experience on haptic orientation perception are presented. Three permutation tests are proposed for the evaluation of ordered hypotheses. The quality of the permutation tests is investigated by means of several simulation studies. The results of these studies show the expected increase in power when the permutation tests for ordered hypotheses are compared to a common non-directional test for circular data. The differences in power between the three tests for ordered alternatives are small.