Rayleigh Test for Randomness of Circular Data
David A. Wilkie · Journal of the Royal Statistical Society Series C (Applied Statistics) · 1983
Critical values of the,Rayleigh test for testing whether the population of circular data from which a sample is drawn differs from randomness are sometimes presented in an inconvenient form (Batschelet, 1981) which makes it necessary to interpolate to obtain a value at a chosen probability level. Even when the values are presented at fixed probability levels (Mardia, 1972) it can be useful for computer programming and other purposes to have a simple expression that describes the tables. According to Mardia (1972) a good approximation, based on the work of Pearson (1906) and Greenwood and Durand (1955) for P = P (n R '>K), where is the mean resultant vector of n unit vectors, is given by A study of the tabulated critical values of R reveals that K is quite well represented by a linear function of over a wide range of n for each probability level P (Fig. 1). Substituting K =A t B/n in (1) yields so we choose A =-1nP and B = (2A- A2)/4. ~husapproximate critical values ofnR2 are given by