One common example for the use of circular statistics is in orientation biology (see many examples in Batschelet 5). Such data cannot be analyzed using standard linear statistics therefore, circular statistical methods have been formulized to detect non-random patterns in periodically recorded data (for discussions on circular data see for example Jammalamadaka and Sengupta 1, Mardia and Jupp 2, Mello 3 and Pewsey et al. Instead, they are recorded on a cyclical scale, for example time of day or compass directions. Many variables in biology are circular, i.e. Hence, we recommend the routine use of either Watson’s U 2 test or MANOVA approach when comparing two samples of circular data. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Of these eight, we were able to identify the Watson’s U 2 test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. We found that only eight tests offered good control of Type-I error in all our simulated situations. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. Many biological variables are recorded on a circular scale and therefore need different statistical treatment.