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The Hermans–Rasson test as a powerful alternative to the Rayleigh test for circular statistics in biology

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Fig. 1 Estimated type I error rates for random samples of specified size drawn from a uniform population based on 10,000 replicates in each case
Fig. 3 Estimated power of random samples (n = 20) drawn from bimodal distributions von Mises distributions [symmetrical: (a) and asymmetrical: (b)] and from bimodal wrapped skew normal distributions [symmetrical: (c) and asymmetrical: (d)], with a range of
Fig. 4 Estimated power of random samples (n = 20) drawn from bimodal distributions. In a, c we vary the central concentration points of the two identical constituent distributions (changing from exactly coincident with each other at the left extreme to exa
Fig. 5 Estimated power of random samples (n = 60) drawn from multimodal Von Mises distributions [3 symmetrical modes: (a) and 4 symmetrical modes: (b)] and from multimodal wrapped skew normal distribution [3 symmetrical modes: (d) and 4 symmetrical modes: (d)]

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