Het opinieonderzoek en de verkiezingen

The comment on the public opinion poll concerning the results of the election 1946 is discussed. It is shown that the mean error, being dependent on the number of parties, cannot be used to express numerically the goodness of the forecast.     

Het begrip Universum in de Statistica

Summary  (The meaning of population in statistics).
The general opinion, that a population consists of a number of objects of observation is shown to be incorrect.
It is pointed out that a series of similar individual discriminations of observation has to be called a population.     

Het probleem van de ruïnering der spelers

The gambler's ruin.
When a single trial has two possible outcomes A and B, with probabilities p and q( p +q= 1), a succession of these trials forms a so-called Bernoulli chain. The well-known result for the probability of n times A and m times B is
In this article we consider the ruin problem, in which the initial capitals of the gamblers are a and b, respectively. In stead of a Bernoulli chain we then have a Markoff chain, with coefficients that are less simple than the ordinary binomial coefficients.
A more general expression (formula 1) is obtained for the probability distribution of the gambler's profit after a certain number of games, provided none of them became ruined beforehand. The probability for ruin after a certain number of games is a special case, similar to the results of Lagrange, Laplace and others, but appears in a form, more suitable for numerical calculations.
Some other results, obtained through the same method as developed in this paper are indicated.     

Het oordeel van een bedrijfsleider over de toepassing van de statistiek in het bedrijf

A manager's view on the application of statistics in the concern.
To be able to judge of the correct dosing of statistical methods in his concern a manager should discriminate between incidental research and systemetical application of statistics. A sound job limitation and good information are indispensable to the success of a statistical check system.
The cost of the introduction of statistical check methods into a concern with a variated manufacturing programme in the field of electrical engineering (350 people) was estimated to be Djls 18,000 in one year. In the next year more than this amount will be earned back through the savings and the improvements obtained.     

Het voorspellen van levertijden uit gegevens over de voort-gang van een project

Estimation of dates of delivery by extrapolation of progress-data for a project.
The problem can be put in mathematical form with the aid of some assumptions with regard to the occurrence of interruptions.
The progress of the project is supposed to be interrupted by time-intervals during which progress is fully stopped. These intervals start at irregularly distributed moments and have a variable size. The points on the time axis corresponding with the moments of stagnation will show a constant average density, if a constant average production capacity or development capacity is available. This means that the results are valid only if no alterations are made which influence the general progress of the project involved.
The application of probability theory to problems connected with promises of delivery may, in general, look unacceptable.
Many projects, however, have an experimental character and unforeseen technical and organisational troubles are unavoidable.
In such cases the theory makes it possible to obtain a maximum amount of information contained in the progress-data and may help management to make the best decisions.     

Het examen Statistisch Analist 1959

This paper is a report on the examination for "Statistisch Analist (Algemeen gedeelte)", 1959. It presents the examination papers and brief solutions.     

Het examen Statistisch Analist 1960

This paper is a report on the examination for „Statistisch Analist (Algemeen gedeelte)”, 196o. It presents the examination papers and brief solutions.     

Het examen Statistisch Analist 1965

Summary
This paper contains a report on the examination for "Statistisch Analist (Alge-meen Gedeelte)" 1965, sponsored by the "Vereniging voor Statistiek". It presents the examination problems and brief solutions.     

Het Examen Statistisch Analist 1964

This paper contains a report on the examination for "Statistisch Analist (Algemeen Gedeelte)"sponsored by the "Vereniging voor Statistiek". It presents the examination problems and brief solutions.     

Het examen Statistisch Analist 1962

This paper contains a report on the examination for "Statistisch Analist (Algemeen Gedeelte)" 1962, sponsored by the "Vereniging voor Statistiek". It presents the examination problems and brief solutions.     

Het object van het opinie-onderzoek

In research of public opinion the selection of the subjects is of the greatest importance, which makes it necessary to raise as much as possible the level of this research-work, not in the least by restraint.     

Het examen Statistisch Analist 1961

This paper is a report on the examination for „Statistisch Analist (Algemeen Gedeelte)” 1961, sponsored by the „Vereniging voor Statistiek”. It presents the examination papers and brief solutions.     

Het examen Statistisch Analist 1963

This paper contains a report on the examination for "Statistisch Analist (Algemeen Gedeelte)" 1963, sponsored by the "Vereniging voor Statistiek". It presents the examination problems and brief solutions.     

Het statistische verband tussen arbeidsproduktiviteit en produktie

The statistical relation between labour-productivity and production.
Rising labour productivity can be induced by increases in output, or result from "autonomous" factors. Many induced increases will be irreversible, in particular those associated with "learning" processes. Under conditions of continuous economic growth the learning curve hypothesis leads to a simple exponential relation between labour demand and output in the long run.
In the short run, current and past profits and the profitability of import substitution join output as explanatory factors of labour demand.
In the long run, the effect of growth of capital must be taken into account. Autonomous factors can be represented by an exponential trend. With United States data, increasing returns to scale are still found. Under conditions of a constant savings ratio and continuous population growth a production function, which takes account of all these factors, can be shown to be compatible with a constant labour-output elasticity, however.     

Het verdelen van steekproeven over subpopulaties bij accountantscontroles

Summary  "Stratificationprocedures for a typical auditing problem".
During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n ₀ is determined in such a way that the probability β not to find any mistake in the sample, if a fraction p ₀ or more of T is incorrect, is smaller than a preassigned value β₀. So n ₀ should satisfy (l- p )ⁿ⁰≤β₀ for p ≥ p ₀. A complication arises if it is not possible to postpone sampling until the whole population T is available. One then wants to take samples from a population which is growing up to T . Suppose one is going to take samples n _i from e.g. r subpopulations

Using the minimax procedure, it is shown, that in this case one should choose the sizes n _i equal to ( T _i/ T ) n ₀. The minimax-value of the probability not to find any incorrect guilder in the r samples, taken together is equal to β₀.     

Het verdelen van steekproeven over subpopulaties bij accountantscontroles

Summary “Stratificationprocedures for a typical auditing problem”. During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n₀ is determined in such a way that the probability β not to find any mistake in the sample, if a fraction p₀ or more of T is incorrect, is smaller than a preassigned value β₀. So n₀ should satisfy (l-p)ⁿ⁰≤β₀ for p≥p₀. A complication arises if it is not possible to postpone sampling until the whole population T is available. One then wants to take samples from a population which is growing up to T. Suppose one is going to take samples n_i from e.g. r subpopulations Using the minimax procedure, it is shown, that in this case one should choose the sizes n_i equal to (T_i/T)n₀. The minimax-value of the probability not to find any incorrect guilder in the r samples, taken together is equal to β₀.