Justification for optimum choice of statistical tests for solving test tasks with statistical processing of results psychological research

We study the conditions of applicability of the statistical criteria of Student and Wilcoxon in solving the single-sample position problem. The consequences of a violation of the correspondence of the distribution of data to the normal law are estimated by the Monte Carlo method, followed by an evaluation of the first kind error rates. Shown, that when severe asymmetry of the distribution of the trait has been, the use of Student's criterion for solving single sample tasks can lead to erroneous interpretation of results when summing up the results of psychological research. An algorithm for a non-parametric solution of a single-sample problem in computer statistical packages which include the Wilcoxon nonpara-metric criterion for paired (dependent) samples is given.