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Summary Parametric and non-parametric methods and their applications The rapid development of non-parametric methods in statistics raises the question of the difference between these methods and the classical parametric methods and of their different fields of application. This paper, read at a meeting of the “Vereniging voor Statistiek” on March 6, 1952, attempts to throw some light on this problem by means of two examples. A short exposition of an application of the method of moments of K. Pearson to the estimation of a population is given for a case, where this method is quite adequate and where it would be difficult to find an equally adequate parameterfree method. On the other hand a method of determination of histamine in human blood is described, which is based on an application of the method of m rankings of M. Friedman and M. G. Kendall. In this case the transition from the classical methods to parameterfree methods constitutes a real gain in rigour and efficiency.