The paper presents an original statistical approach dedicated to the evaluation of two time intervals which are useful in various chaotic applications, namely: the transient time and the minimum statistical independence sampling distance. The overall procedure relies on Smirnov tests based on two-sample statistic, Kolmogorov-Smirnov tests based on one-sample statistic, a Monte Carlo analysis and an original statistical independence test. The experimental study was performed on the logistic map for different values of its parameter, values considered of much interest in the literature. The proposed statistical approach may guide another experimenter to extend the analysis for other logistic map parameters and also for other chaotic maps.