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- function [h mu ul ll] = circ_mtest(alpha, dir, xi, w, d)
- %
- % [pval, z] = circ_mtest(alpha, dir, w, d)
- % One-Sample test for the mean angle.
- % H0: the population has mean dir.
- % HA: the population has not mean dir.
- %
- % Note: This is the equvivalent to a one-sample t-test with specified
- % mean direction.
- %
- % Input:
- % alpha sample of angles in radians
- % dir assumed mean direction
- % [xi alpha level of the test]
- % [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:
- % h 0 if H0 can not be rejected, 1 otherwise
- % mu mean
- % ul upper (1-xi) confidence level
- % ll lower (1-xi) confidence level
- %
- % PHB 7/6/2008
- %
- % References:
- % Biostatistical Analysis, J. H. Zar
- %
- % Circular Statistics Toolbox for Matlab
- % By Philipp Berens, 2009
- % berens@tuebingen.mpg.de - www.kyb.mpg.de/~berens/circStat.html
- if size(alpha,2) > size(alpha,1)
- alpha = alpha';
- end
- if nargin<3
- xi = 0.05;
- end
- if nargin<4
- % if no specific weighting has been specified
- % assume no binning has taken place
- w = ones(size(alpha));
- else
- if size(w,2) > size(w,1)
- w = w';
- end
- if length(alpha)~=length(w)
- error('Input dimensions do not match.')
- end
- end
- if nargin<5
- % per default do not apply correct for binned data
- d = 0;
- end
- % compute ingredients
- mu = circ_mean(alpha,w);
- t = circ_confmean(alpha,xi,w,d);
- ul = mu + t;
- ll = mu - t;
- % compute test via confidence limits (example 27.3)
- h = abs(circ_dist2(dir,mu)) > t;
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