De methoden van De Wolff en Van Heerden voor het nemen van aselecte steekproeven bij accountantscontroles

The procedures suggested by De Wolff and Van Heerden for random sampling in auditing. In recent years two different methods were suggested for taking random samples in typical auditing problems. In this paper these two methods are critically reviewed and compared. In De WoIff's method all large entries in a register are checked, whereas a sample is taken from the smaller ones. Van Heerden does not consider the register as a population of entries, but, if all entries total up to B guilders, as a population of B guilders. He selects guilders randomly and checks the entries to which the selected guilders belong. Both authors only use probability statements if no {severe) mistake is found in the sample. De Wolff uses confidence intervals with a confidence‐level 1‐txfor the fraction p of incorrect small entries and states that, except for a probability α, B will not surpass the correct total value with a fraction ϕ. Van Heerden formulates his conclusions, using the probability β(ϕ) that no mistake will be found in the sample if a fraction ϕ of B is incorrect. In this paper (§ 3), it is shown that the intervals for p, if no mistake is found, cannot be ordinary confidence intervals. However, it is possible to give a somewhat unusual interpretation of De Wolffs results and then it turns out that his conclusions regarding a and ϕ actually are rather pessimistic upper‐limits for the probability of a wrong statement and for the maximal fraction of incorrect guilders respectively. Very often, a priori information is present in auditing problems; § 4 shows how to use this information in order to get shorter intervals for p or smaller values for a. In § 5 a suggestion by V an H e er den to find the optimal sample size is discussed. The suggestion boils down to applying the minimax method to the sum of the checking‐costs nc, c being the costs of checking one entry, and the expected loss if a sample of size n is taken and the fraction tp of incorrect guilders has a probability distribution G(ϕ). For a special case, the optimal value of n is proved to be either the largest integer, smaller than , or the smallest integer, larger than this value. Table 5.III gives these values of n and the corresponding values of β for some values of B/c and ϕ.