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circ_rtest.m
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circ_rtest.m
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function [pval, z] = circ_rtest(alpha, w, d)
%
% [pval, z] = circ_rtest(alpha,w,d)
% Computes Rayleigh test for non-uniformity of circular data.
% H0: the population is uniformly distributed around the circle
% HA: the populatoin is not distributed uniformly around the circle
% Assumption: the distribution has maximally one mode and the data is
% sampled from a von Mises distribution!
%
% Input:
% alpha sample of angles in radians
% [w number of incidences in case of binned angle data]
% [d spacing of bin centers for binned data, if supplied
% correction factor is used to correct for bias in
% estimation of r, in radians (!)]
%
% Output:
% pval p-value of Rayleigh's test
% z value of the z-statistic
%
% PHB 7/6/2008
%
% References:
% Statistical analysis of circular data, N. I. Fisher
% Topics in circular statistics, S. R. Jammalamadaka et al.
% Biostatistical Analysis, J. H. Zar
%
% Circular Statistics Toolbox for Matlab
% By Philipp Berens, 2009
% [email protected] - www.kyb.mpg.de/~berens/circStat.html
if size(alpha,2) > size(alpha,1)
alpha = alpha';
end
if nargin < 2
r = circ_r(alpha);
n = length(alpha);
else
if length(alpha)~=length(w)
error('CIRCSTAT:circ_rtest:InputSizeMismatch', 'Input dimensions do not match: alpha and w should be the same size.')
end
if nargin < 3
d = 0;
end
r = circ_r(alpha,w(:),d);
n = sum(w);
end
% compute Rayleigh's R (equ. 27.1)
R = n*r;
% compute Rayleigh's z (equ. 27.2)
z = R^2 / n;
% compute p value using approxation in Zar, p. 617
pval = exp(sqrt(1+4*n+4*(n^2-R^2))-(1+2*n));
% outdated version:
% compute the p value using an approximation from Fisher, p. 70
% pval = exp(-z);
% if n < 50
% pval = pval * (1 + (2*z - z^2) / (4*n) - ...
% (24*z - 132*z^2 + 76*z^3 - 9*z^4) / (288*n^2));
% end
end