[pval, k, K] = circ_kuipertest(sample1, sample2, res, vis_on)
The Kuiper two-sample test tests whether the two samples differ
significantly.The difference can be in any property, such as mean
location and dispersion. It is a circular analogue of the
Kolmogorov-Smirnov test.
H0: The two distributions are identical.
HA: The two distributions are different.
Input:
alpha1 fist sample (in radians)
alpha2 second sample (in radians)
res resolution at which the cdf is evaluated
vis_on display graph
Output:
pval p-value; the smallest of .10, .05, .02, .01, .005, .002,
.001, for which the test statistic is still higher
than the respective critical value. this is due to
the use of tabulated values. if p>.1, pval is set to 1.
k test statistic
K critical value
References:
Batschelet, 1980, p. 112
Circular Statistics Toolbox for Matlab0001 function [pval, k, K] = circ_kuipertest(alpha1, alpha2, res, vis_on) 0002 0003 % [pval, k, K] = circ_kuipertest(sample1, sample2, res, vis_on) 0004 % 0005 % The Kuiper two-sample test tests whether the two samples differ 0006 % significantly.The difference can be in any property, such as mean 0007 % location and dispersion. It is a circular analogue of the 0008 % Kolmogorov-Smirnov test. 0009 % 0010 % H0: The two distributions are identical. 0011 % HA: The two distributions are different. 0012 % 0013 % Input: 0014 % alpha1 fist sample (in radians) 0015 % alpha2 second sample (in radians) 0016 % res resolution at which the cdf is evaluated 0017 % vis_on display graph 0018 % 0019 % Output: 0020 % pval p-value; the smallest of .10, .05, .02, .01, .005, .002, 0021 % .001, for which the test statistic is still higher 0022 % than the respective critical value. this is due to 0023 % the use of tabulated values. if p>.1, pval is set to 1. 0024 % k test statistic 0025 % K critical value 0026 % 0027 % References: 0028 % Batschelet, 1980, p. 112 0029 % 0030 % Circular Statistics Toolbox for Matlab 0031 0032 % By Marc J. Velasco and Philipp Berens, 2009 0033 % velasco@ccs.fau.edu 0034 0035 0036 if nargin < 3 0037 res = 100; 0038 end 0039 if nargin < 4 0040 vis_on = 0; 0041 end 0042 0043 n = length(alpha1(:)); 0044 m = length(alpha2(:)); 0045 0046 % create cdfs of both samples 0047 [phis1 cdf1 phiplot1 cdfplot1] = circ_samplecdf(alpha1, res); 0048 [phis2 cdf2 phiplot2 cdfplot2] = circ_samplecdf(alpha2, res); 0049 0050 % maximal difference between sample cdfs 0051 [dplus, gdpi] = max([0 cdf1-cdf2]); 0052 [dminus, gdmi] = max([0 cdf2-cdf1]); 0053 0054 % calculate k-statistic 0055 k = n * m * (dplus + dminus); 0056 0057 % find p-value 0058 [pval K] = kuiperlookup(min(n,m),k/sqrt(n*m*(n+m))); 0059 K = K * sqrt(n*m*(n+m)); 0060 0061 0062 % visualize 0063 if vis_on 0064 figure 0065 plot(phiplot1, cdfplot1, 'b', phiplot2, cdfplot2, 'r'); 0066 hold on 0067 plot([phis1(gdpi-1), phis1(gdpi-1)], [cdf1(gdpi-1) cdf2(gdpi-1)], 'o:g'); 0068 plot([phis1(gdmi-1), phis1(gdmi-1)], [cdf1(gdmi-1) cdf2(gdmi-1)], 'o:g'); 0069 hold off 0070 set(gca, 'XLim', [0, 2*pi]); 0071 set(gca, 'YLim', [0, 1.1]); 0072 xlabel('Circular Location') 0073 ylabel('Sample CDF') 0074 title('CircStat: Kuiper test') 0075 h = legend('Sample 1', 'Sample 2', 'Location', 'Southeast'); 0076 set(h,'box','off') 0077 set(gca, 'XTick', pi*0:.25:2) 0078 set(gca, 'XTickLabel', {'0', '', '', '', 'pi', '', '', '', '2pi'}) 0079 end 0080 0081 0082 0083 end 0084 0085 function [p K] = kuiperlookup(n, k) 0086 0087 load kuipertable.mat; 0088 alpha = [.10, .05, .02, .01, .005, .002, .001]; 0089 nn = ktable(:,1); %#ok<COLND> 0090 0091 % find correct row of the table 0092 [easy row] = ismember(n, nn); 0093 if ~easy 0094 % find closest value if no entry is present) 0095 row = length(nn) - sum(n<nn); 0096 if row == 0 0097 error('N too small.'); 0098 else 0099 warning('N=%d not found in table, using closest N=%d present.',n,nn(row)) %#ok<WNTAG> 0100 end 0101 end 0102 0103 % find minimal p-value and test-statistic 0104 idx = find(ktable(row,2:end)<k,1,'last'); 0105 if ~isempty(idx) 0106 p = alpha(idx); 0107 else 0108 p = 1; 0109 end 0110 K = ktable(row,idx+1); 0111 0112 end