Verdelingsvrije toetsen voor twee steekproeven en de methode der 2 × 2 ‐tabel

Distributionfree two sample tests and the method of the 2 × 2 ‐ table. The method of the 2 × 2 ‐ table may be used for testing the hypothesis that two probabilities pAand pBare equal. This test is based on two independent series A and B of independent trials, each trial resulting in a success or a failure with probabilities pAand qA= 1—pAfor series A, pBand qB= 1—pBfor series B. Each of these trials may be considered as an observation of a random variable which may take the two values“: success and failure, which may be denoted by two symbols e.g. z 1 and z 2. Then the two series A and B are two independent series of observations of two random variables x (for A) and y (for B), taking the value z1, with probability pA (respectively pB) and the value z2with probability qA (respectively qB). The hypothesis pA=pBis then identical with the hypothesis that x and y possess the same probability distribution. This hypothesis may be tested by means of a distributionfree two sample test. A class of distributionfree two sample tests mentioned in [1] (cf. p. 251) is considered. It contains i.a. the tests of E. J. G. Pitman, F. Wilcoxon, M. E. Terry and B. L. van der Waerden. In this mainly expository paper it is shown that each test belonging to this class, when applied to the series of observations mentioned above, is identical with the method of the 2 × 2 ‐ table.