Statistical randomization test for QCD intermittency in a single-event distribution

Abstract

A randomization test was developed to determine the statistical significance of QCD intermittency in single-event distributions. A total of 96 simulated intermittent distributions based on standard normal Gaussian distributions of size N=500, 1000, 1500, 2000, 4000, 8000, 16000, and 32000 containing induced holes and spikes were tested for intermittency. Non-intermittent null distributions were also simulated as part of the test. A log-linear model was developed to simultaneously test the significance of fit coefficients for the y-intercept and slope contribution to ln(F_2) vs. ln(M) from both the intermittent and null distributions. Statistical power was also assessed for each fit coefficient to reflect the proportion of times out of 1000 tests each coefficient was statistically significant, given the induced effect size and sample size of the Gaussians. Results indicate that the slope of ln(F_2) vs. ln(M) for intermittent distributions increased with decreasing sample size, due to artificially-induced holes occurring in sparse histograms. For intermittent Gaussians with 4000 variates, there was approximately 70% power to detect a slope difference of 0.02 between intermittent and null distributions. For sample sizes of 8000 and greater, there was more than 70% power to detect a slope difference of 0.01. The randomization test performed satisfactorily since the power of the test for intermittency decreased with decreasing sample size. Power was near-zero when the test was applied to null distributions. The randomization test can be used to establish the statistical significance of intermittency in empirical single-event Gaussian distributions.