As shown in Fig. the confidence intervals obtained from 300 Monte Carlo simulations with each simulation performed with 5000 steps using BS or random errors and different σ MC differ. As σ MC increases, the confidence interval gets broader and standard deviation of the IPR increases. However, the differences between bootstrapping and random error with σ MC = σ f it are very small but since the Kruskal-Wallis-test results in a p-value = 0.002 < 0.05 for lgK 11 and p = 0.023 < 0.05 for lgK 12 , the differences are significant for the given example. The corresponding plots for lgK 12 are presented in Fig. .