[pval, m] = circ_otest(alpha,sz,w)
Computes Omnibus or Hodges-Ajne test for non-uniformity of circular data.
H0: the population is uniformly distributed around the circle
HA: the population is not distributed uniformly around the circle
Alternative to the Rayleigh and Rao's test. Works well for unimodal,
bimodal or multimodal data. If requirements of the Rayleigh test are
met, the latter is more powerful.
Input:
alpha sample of angles in radians
[sz step size for evaluating distribution, default 1 degree
[w number of incidences in case of binned angle data]0001 function [pval m] = circ_otest(alpha, sz, w) 0002 % 0003 % [pval, m] = circ_otest(alpha,sz,w) 0004 % Computes Omnibus or Hodges-Ajne test for non-uniformity of circular data. 0005 % H0: the population is uniformly distributed around the circle 0006 % HA: the population is not distributed uniformly around the circle 0007 % 0008 % Alternative to the Rayleigh and Rao's test. Works well for unimodal, 0009 % bimodal or multimodal data. If requirements of the Rayleigh test are 0010 % met, the latter is more powerful. 0011 % 0012 % Input: 0013 % alpha sample of angles in radians 0014 % [sz step size for evaluating distribution, default 1 degree 0015 % [w number of incidences in case of binned angle data] 0016 0017 % Output: 0018 % pval p-value 0019 % m minimum number of samples falling in one half of the circle 0020 % 0021 % PHB 3/16/2009 0022 % 0023 % References: 0024 % Biostatistical Analysis, J. H. Zar 0025 % A bivariate sign test, J. L. Hodges et al., 1955 0026 % A simple test for uniformity of a circular distribution, B. Ajne, 1968 0027 % 0028 % Circular Statistics Toolbox for Matlab 0029 0030 % By Philipp Berens, 2009 0031 % berens@tuebingen.mpg.de - www.kyb.mpg.de/~berens/circStat.html 0032 0033 if size(alpha,2) > size(alpha,1) 0034 alpha = alpha'; 0035 end 0036 0037 if nargin < 2 || isempty(sz) 0038 sz = circ_ang2rad(1); 0039 end 0040 0041 if nargin < 3 0042 w = ones(size(alpha)); 0043 else 0044 if length(alpha)~=length(w) 0045 error('Input length does not match.') 0046 end 0047 w =w(:); 0048 end 0049 0050 alpha = mod(alpha,2*pi); 0051 n = sum(w); 0052 dg = 0:sz:pi; 0053 0054 m = zeros(size(dg)); 0055 for i=1:length(dg) 0056 m(i) = sum((alpha > dg(i) & alpha < pi + dg(i)).*w); 0057 end 0058 m = min(m); 0059 0060 if n > 50 0061 % approximation by Ajne (1968) 0062 A = pi*sqrt(n) / 2 / (n-2*m); 0063 pval = sqrt(2*pi) / A * exp(-pi^2/8/A^2); 0064 else 0065 % exact formula by Hodges (1955) 0066 pval = 2^(1-n) * (n-2*m) * nchoosek(n,m); 0067 end 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079