  Many experiments can be interpreted in terms of random processes operating
according to some internal protocols. When experiments are costly or cannot be
repeated only one or a few finite samples are available. In this paper we study
data generated by pseudo-random computer experiments operating according to
particular internal protocols. We show that the standard statistical analysis
performed on a sample, containing 100000 data points or more, may sometimes be
highly misleading and statistical errors largely underestimated. Our results
confirm in a dramatic way the dangers of standard asymptotic statistical
inference if a sample is not homogenous. We demonstrate that analyzing various
subdivisions of samples by multiple chi-square tests and chi-square frequency
graphs is very effective in detecting sample inhomogeneity. Therefore to assure
correctness of the statistical inference the above mentioned chi-square tests
and other non-parametric sample homogeneity tests should be incorporated in any
statistical analysis of experimental data. If such tests are not performed the
reported conclusions and estimates of the errors cannot be trusted.
