Het nut van waarshijnlijkheidspapier voor de variatiestatistiek

The utility of probability paper in studying the statistics of biological variations. This paper mainly deals with various applications and theorems concerning arithmetic probability paper. It is pointed out that the so‐called ‘normal function’ introduced by Kapteyn and Van Uven [1,2] is the same function as that which would be obtained by plotting the corresponding distribution on arithmetic probability paper. For a normal distribution the ‘normal function’ is a straight line, for a logarithmiconormal distribution it is a logarithmic curve. Galton's well‐known apparatus for demonstrating the genesis of a normal distribution (fig. 5) was modijied by Kapteyn (fig. 6) so as to produce a skew distribution. The latter apparatus can be transformed into the former by a process of stretching and compressing in a horizontal direction, and this transformation is again described by the ‘normal function’ of the non‐normal distribution shown in fig. 6. If the dividing blocks in these apparatus are conceived infinitesimally small and all of equal height, the path of those grains of small shot which always fall towards the right, or always towards the left, is again the ‘normal function’, or its image with respect to a horizontal line. Further some applications of probability paper in correlation studies and for the representation of certain laws of growth are discussed. In ‘Appendix I’ a method for χ2‐testing the reliability of a normal distribution fitted by means of probability paper is described, white in ‘Appendix II’ a mathematical proof is given of a number of theorems that were merely enunciated in the main paper.