Type I error calibration curves for continuous fractal patterns generated through Fourier synthesis of 32×32 pixels images [27] (see Fig. 1 for examples).

<p>Observed versus expected type I error probabilities resulting from independence tests on 1000 pairs of simulated images, are plotted for every combination of method (colour curves) and degree of spatial autocorrelation (panels) as measured by the energy spectrum exponent, <i>β</i>. Methods compared are random reassignments, random shifts, corrected <i>t</i>-test of Dutilleul (ModT), iterative amplitude adjusted Fourier transform (IAAFT), and wavelet-based image synthesis. Each bin is 0.05 wide. The Kolmogorov-Smirnov (K.-S.) maximum difference statistic which measures the departure from the line of identity (dashed line) is indicated for each curve along with results of the derived test of the departure: *** = <i>p</i>-value<0.001; * = 0.01≤<i>p</i>-value<0.05; NS = not significant.