De bewerking van de resultaten van veldproeven door herleiding van de opbrengstcijfers in beide richtingen van het proefveld

Summary  (The treatment of the results of field experiments by reducing the yields in two directions)
Ir J. J. Dijkveld Stol has shown that good results have been obtained by reducing the yields of field experiments both in columns and in rows.
The mathematical foundation of this method is discussed in the preceding article and it is shown, that the method gives good results if the same supposition may be made as necessary for the application of the methods of Fisher, Knut Vik and the method of the differences.
The variance of Dijkveld Stol's method is identical with Fisher's error variance.     

Assortimentsbepaling van seizoenprodukten

This paper deals with the analysis of a problem often met when determining purchasing policies. From a number of different kinds of goods, which are to be bought, the total quantity is restricted by storing capacity or financial limits. The problem "how much of each kind will be bought" is solved for a discrete as well as for a continuous distribution of demand for the various goods.     

De bewerking van veldproeven volgens de methode van Knut Vik

Summary  (The treatment of field experiments by Knut Vik's method).
Agriculturists and statisticians have studied the problem, how to free the yields in a field experiment from the inequality of the soil. The method of the analysis of variance, due to the English statistician R. A. Fisher has taken an important place in the study of field experiments, so that other methods fell in the background.
The Norwegian agriculturist Knut Vik has suggested a method, which leads to good results without complicated calculations and without the knowledge of a great part of the mathematical statistics.
The mathematical foundation of this method is discussed in this article, which concludes, that the method of Knut Vik is of great importance for agriculturists, who don't want to perform intricate calculations.     

Bepaling van stuwende en verzorgende bedrijfstakken door middel van statistische methoden

Determination of basic and non-basic enterprises by means of statistical methods.
In this article a sketch is given of the various methods used to obtain a clear insight into the meaning of the non-basic enterprises and the enterprises which because of their basic character belong to the factors determining the development of the population. Special attention has been paid to the method which puts the whole problem of the definition of basic and non-basic industries in the framework of a system of equations. This system has been built up from regional social accounts that have been developed for Amsterdam.     

Biologische waardebepalingen van geneesmiddelen

The aim of standardization is to make sure that different batches of a drug do not vary in their potency. With most drugs this can be done by chemical methods, for a certain number of drugs however biological methods are still necessary. The best procedure to standardize a drug is to use a standard preparation. In this lecture it is discussed which demands must be made upon standard and the criterion. The measurement of the pyrogenic activity of drugs is discussed as an example.     

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.     

Een steekproef ter vaststelling van de verdeling van de hoenderstapel

A sample estimate of the poultry distribution
In 1954 a sample survey was carried out of the returns of the agricultural census, May 1954, in order to establish the distribution of the number of holdings and the number of poultry, by size-group of arable land and by size-group of number of poultry. A simple 10 per cent, sample was planned and the expected variances of the numbers of poultry in each size-group were estimated beforehand. The method of estimation is indicated in this paper. This resulted in comparatively high relative errors in the size-groups above 500 hens and also in the size-groups of arable land. Therefore holdings with 500 hens and over were enumerated completely. Some tests were performed with the sample results and finally the efficiency of the stratification is discussed.     

Dimensionering van homogeniseringsinstallaties

Designing of homogenizing equipment
The spread in quality in a large stream of granular material can be sufficiently reduced only by homogenization in mixing heaps and bunker installations. In this treatment each unit of consumption is composed of portions which, at given intervals, are taken from the stream.
The paper indicates how to choose the number and size of the portions and the intervals between them in order to achieve the required reduction in spread at minimum costs.
This determination, elucidated by means of an example, is based on the correlo-gram of the stream referred to thin slices.     

Een systeem van kostenbeheersende productieplanning

In this paper a system of cost-controlled production planning is described. This system considers all kinds of costs associated with a production in phases (e.g. production of units, production of subassemblies, assembly) which may be affected by the planning, such as set-up costs, costs of transport, control, inventories, capacity and changes in capacity.
The mathematical model leads to a linear or mixed discrete-linear programming problem whose solution gives for each time period considered the size of the capacities which should be used and of the series of different products which should be produced. Practical recommendations are given for obtaining a sufficiently satisfying solution.     

Afschatting van verdelingen van kwadratische vormen met toepassingen op aanpassingstoetsen voor normaliteit en exponentialiteit

Summary In this paper a simple approximation is given for the distribution of the quadratic form being a weighted sum of squares of independent, identically distributed standardized normal variates. Using the formulae, the Monte Carlo results concerning some goodness of fit tests for normality and exponentiality are verified and extended.     

Het vergelijken van twee verschillende schatters voor een percentiel P van een normale verdeling

A comparison is made between two different methods to estimate the probability that a normally distributed observation is less than a certain value. One method is based on the binomial distribution, the other one on HALD'S maximum likelihood estimates of the parameters of a censored normal distribution. For large sample sizes a graph of the relative efficiency of these two estimates is constructed. A sampling experiment was performed in order to investigate for one particular situation the possible bias of HALD'S maximum likelihood estimate, which is only asymptotically unbiassed.     

Statistisch onderzoek van contrôle-analyse cijfers: (De verdeling van het droge stofgehalte van het brood tijdens de tweede wereldoorlog)

Summary  (Statistical investigation of the distribution of data for the solids of bread (in loaves analysed in the Food Inspection Laboratory in Amsterdam))
The distributions of the data of the solids of bread as analysed during the years of the war are investigated. The means and the standard deviations are calculated, also χ², kurtosis and skewness supposing the distributions to be normal. An example of calculation is given in table I. Actual numbers for different years are given in table II and in table III. The distributions were tested on normality because former investigations showed that the distribution of under survey prepared loaves did not deviate significantly from the normal.
It is found that generally the investigated distributions cannot be regarded as normal. Though symmetric they show leptokurtosis and the χ²-test for the goodness of fit of normal equation gives values of P 0,01 (or a little more). Similar distributions were found by Clancey¹⁾ in his investigation of numbers of chemical analyses of industrial products (about 10% of the distributions showed this shape, some 10% were truncated leptokurtic curves) and by us for the fat percentage of meals from the governmental eating-houses. The distributions are represented on probability-paper. This way of representing results gives a clear view of the variations of the mean and the standarddeviation in the course of the years (fig. 1). The deviations of the shape of the normal straight line on probability paper by special causes is investigated (fig. 3, fig. 4, fig. 5, fig. 6 to be compared with fig. 2). With this "spectrum" of possibilities of deviations from the normal distribution in mind the special cause for the leptokurtic shape in our special case has been discussed.     

Een noodzakelijke correctie van de overschrijdingsgrenzen voor steekproefgemiddelden bij toepassing van stratified sampling

Summary  (A necessary correction of the control chart limits for averages of samples in the case of stratified sampling).
Application of stratified sampling results in smaller fluctuations of sampling than where the same total number of individuals is drawn at random from the superposed strata.
The proportion of the standard errors of the averages obtained by these two sampling methods may be expressed by a factor φ (o ≤φ≤ 1). The probability limits, between which the random sampling results would be fluctuating normally, should be corrected according to this factor.
A few properties of φ are discussed. This is graphically illustrated. Remarks have been added about the relation between the shape of the population of the sampling averages and the population from which the individuals are drawn, and about the difficulties which arise when the populations are non-Gaussian.     

Afleiding van kwartaalcijfers uit jaartotalen

Summary Quarterly figures may be required when only a sequence of annual totals is available. This article presents two reasonable methods for “interpolating” quarterly figures by means of appropriate minimizing procedures. The first method relates to minimizing the sum of squared second differences of the quarterly figures, the other one is a linear programming procedure which refers to the absolute second differences. Both methods are illustrated by a numerical example, the first one giving somewhat better results.     

Afleiding van kwartaalcijfers uit jaartotalen

Summary  Quarterly figures may be required when only a sequence of annual totals is available. This article presents two reasonable methods for "interpolating" quarterly figures by means of appropriate minimizing procedures.
The first method relates to minimizing the sum of squared second differences of the quarterly figures, the other one is a linear programming procedure which refers to the absolute second differences. Both methods are illustrated by a numerical example, the first one giving somewhat better results.     

Statistische eigenschappen van een vlambeveiliging met behulp van een gasontladingsbuis welke gevoelig is voor ultraviolet licht

Summary The output voltage of a detector circuit containing a gas-filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov-process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special circuit.     

Statistische eigenschappen van een vlambeveiliging met behulp van een gasontladingsbuis welke gevoelig is voor ultraviolet licht

Summary  The output voltage of a detector circuit containing a gas-filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov-process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special circuit.     

Een lading van kraaltjes

Summary An urn containing 200 red beads and 1000 yellow ones is frequently used for demonstration of the hypergeometric or binomial distribution. Experiments show that the practical frequency distribution differs slightly but definitely from the theoretical one. This deviation turned out to be caused by electro-static forces.     

Transformatie van niet-normale verdelingen

In statistical analysis and operational research many techniques are being applied, which are based upon the fact that the phenomenon under consideration has a distribution, which is approximately normal. This distribution-type has got a number of very nice properties and a constant pattern, so that "normal" phenomenona can be predicted. In case of non-normal, but deviated or skew distributions, analysis and forecasting become much more complicated. In this article a method has been described in which some non-normal variables can be transformed into normal ones, so that techniques based on normal distributions may be used.     

De betrouwbaarheid van controleurs

Summary  (The reliability of 100% inspection).
The article of Mr, Enters on The reliability of 100% inspection in the first issue of Statistica is critizised.
The criterion of goodness of control as the sum of the coefficients of correlation between the measurements of the individual inspectors and each of their colleagues does not agree with the everyday use of that criterion, i.e. the correlation between the observed' and the real diameters etc. Nor is this criterion identical with the Spearman criterion of saturation coefficients.
Some suggestions are given for solution of the problem, e.g. psychotechnical testing the inspectors, analysis of the frequency curves of their measurements and computation of the coefficients of correlation between the measurements of each inspector and the corresponding average measurements of all inspectors.