watson               package:CircStats               R Documentation

_W_a_t_s_o_n'_s _T_e_s_t

_D_e_s_c_r_i_p_t_i_o_n:

     Performs a Watson's goodness of fit test for the von Mises or
     circular uniform distribution.

_U_s_a_g_e:

     watson(x, alpha=0, dist='uniform')

_A_r_g_u_m_e_n_t_s:

       x: vector of angular measurements in radians.

   alpha: significance level of the test.  Valid levels are 0.01, 0.05,
          0.1.  This argument may be ommited, in which case, a range
          for the p-value will be returned.

    dist: distribution to test for.  The default is the uniform
          distribution. To test for the von Mises distribution, set
          dist = 'vm'.

_V_a_l_u_e:

     NULL

_N_o_t_e:

     If dist = 'uniform', Watson's one-sample test for the circular
     uniform distribution is performed, and the results are printed to
     the screen.  If alpha is specified and non-zero, the test
     statistic is printed along with the critical value and decision. 
     If alpha is omitted, the test statistic is printed and a range for
     the p-value of the test is given.

     If dist = 'vm', estimates of the population parameters are used to
     evaluate the von Mises distribution function at all data points,
     thereby arriving at a sample of approximately uniformly
     distributed data, if the original observations have a von Mises
     distribution. The one-sample Watson test is then applied to the
     transformed data as above.

_R_e_f_e_r_e_n_c_e_s:

     Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular
     Statistics, Section 7.2, World Scientific Press, Singapore.

     Stephens, M. (1970).  Use of the Kolmogorov-Smirnov, Cramer-von
     Mises and related statistics without extensive tables.  Journal of
     the Royal Statistical Society, B32, 115-122.

_S_e_e _A_l_s_o:

     circ.range, kuiper, rao.spacing, r.test, v0.test

_E_x_a_m_p_l_e_s:

     # Generate data from the uniform distribution on the circle.
     data <- runif(100, 0, 2*pi)  
     watson(data)
     # Generate data from a von Mises distribution.
     data <- rvm(50, 0, 4) 
     watson(data, 0.05, dist='vm')

