  Statistical methods are frequently built upon assumptions that limit their
applicability to certain problems and conditions. Failure to recognize these
limitations can lead to conclusions that may be inaccurate or biased. An
example of such methods is the non-parametric Efron-Petrosian test statistic
used in the studies of truncated data. We argue and show how the inappropriate
use of this statistical method can lead to biased conclusions when the
assumptions under which the method is valid do not hold. We do so by
reinvestigating the evidence recently provided by multiple independent reports
on the evolution of the luminosity/energetics distribution of cosmological
Long-duration Gamma-Ray Bursts (LGRBs) with redshift. We show that the effects
of detection threshold has been likely significantly underestimated in the
majority of previous studies. This underestimation of detection threshold leads
to severely-incomplete LGRB samples that exhibit strong apparent
luminosity-redshift or energetics-redshift correlations. We further confirm our
findings by performing extensive Monte Carlo simulations of the cosmic rates
and the luminosity/energy distributions of LGRBs and their detection process.
