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.     

De invloed van de keuze der gewichten op de hoogte van een gewogen indexcijfer

The influence of the choice of the weights on the value of an indexnumber.
Price and quantity indexnumbers are weighted averages of groups of price and quantity ratios and they are convenient instruments to indicate the general tendency of such groups, especially if the number of basic ratios is considerable. The frequent use of indexnumbers is due to the fact that they can often be applied to problems for which, strictly speaking, an indexnumber had to be used derived from the same group of ratios but based on a different set of weights.
Two typical examples of such problems are given.
The use of a set of weights differing from the appropriate one is only justified, however, when the indexnumber is rather insensitive to changes in the set of weights. A simple formula is derived showing that the relative change of an index-number due to a change in the set of weights is equal to the product of the (weighted) coefficient of variation of the basic ratios, the (weighted) standard deviation of the relative changes of the weights and the (weighted) coefficient of correlation of the ratios and of the relative changes. The system of weights used in the calculation of these three factors is the same and is equal to the set of true weights belonging to the problem under consideration.
The practical use of the formula is demonstrated at the problem of index-numbers of costs frequently encountered in the practice of cost accounting.     

De theoretische zijde van de methode der kleinste kwadraten

The theoretical aspect of least squares.
This article contains a slightly modified presentation of the Markoff theory of least squares as developed along different lines by Aitken and by David and Neyman. The modifications aim at a more complete treatment and a geometrical illustration of the connection between best linear estimates and generalized least squares. The unbiasedness of ordinary least squares estimates in the case of heteroscedastic and correlated errors is stressed and the loss of efficiency is shown to be generally small. Topics like orthogonalization, partial correlation and what is called "over-correlation" are treated in passing.
Matrices are constantly used, being the adequate tools in this matter. In the appendix a special relevant matrix theorem is derived, viz. a generalization of the well known Cauchy inequality.     

De frequentistische opbouw van de waarschijnlijkheids-rekening volgens R. von Mises

R. von M ises publiceerde zijn frequentistische opbouw van de waarschijnlijkheidsleer voor het eerst in 1919. De daarbij naar voren gebrachte inzichten verschilden zeer van de in die tijd algemeen geaccepteerde ideeén omtrent de grondslagen van de waarschijnlijkheidsleer. Onder invloed van (zowel opbouwende als abrekende) kritieken, alsmede door eigen gewijzigde inzichten, evolueerde zijn theorie zich, via diverse publikaties, tot die, weke wij aantreffen in zijn in 1964 posthuum verschenen, laatste werk.
In dit artikel wordt nader ingegaan op de theorie van V on M ises , zoals die in het zojuist genoemde werk behandeld wordt. Hiertoe is het soms nodig in te gaan op vroegere publikaties van zijn hand.
In vele boeken en artikelen (zie bijv. C ramer (1966) p. 150 en H emelrijk (1968) p. 13) worden enige zinnen gewijd aan het feit, dat V on M ises zich met de grondslagen van de waarschijnlijkheidsleer heeft bezig gehouden. Bijna nooit krijgt men echter te lezen, wat hij precies gezegd heeft.     

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.     

Naar aseptische en realistische methoden in de toegepaste statistiek

Summary
Applied statistics is not pure mathematics but the application of suitable methods of mathematical statistics to practical problems.
In choosing the method one should be extremely suspicious in regard to septic methods and give strong preference to realistic methods.
Septic methods are those which by their very nature introduce properties alien to the magnitudes concerned e.g. addition of non-additive variables, differentiation of stochastic variables, stochastic treatment of indeterminate variables, etc. Realistic methods are those based on a preliminary analysis of the practical problem which should bring to light the essential mutually independent variables controlling the outcome of the problem. Undue simplification at the cost of the accuracy required in actual practice should be avoided; especially weak correlations between variables shown by the deductive analysis as being essentially mutually independent should be discarded.
On the other hand the mathematical treatment should be as simple and direct as possible.
The professional mathematician can become a real danger if he wants to guide the application of mathematical statistics to certain fields of applied science in which he is not sufficiently specialised and experienced. Contrariwise, if he acquires this knowledge in business, the highest positions are open to him.     

De bepaling van de nauwkeurigheid, waarmede metingen of beoor-delingen worden verricht.

Summary  (Discussion of the accuracy of measurements and judgments).
In this paper a Summary is given of the methods, which are used or can be used to determine the accuracy, with which measurements, which can be expressed in concrete units (lengths, weights, percentages etc.), can be made.
An account is also given of a method, which can be used, when expression in concrete units is not possible (e.g. grading the odor or taste of butter or wine, judging the achievements of pupils by means of test-work).     

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.     

De oplossing van een kwaliteitsprobleem door het gebruik van proefschema's

Samenvatting  Het artikel geeft een beschrijving van de strategie en de methoden, die worden gebruikt voor het zoeken naar de oorzaak van een kwaliteitsvermindering bij dubbelspiralen voor gloeilampen. Er wordt niet alleen aandacht besteed aan de beschrijving en motivering van de gekozen proefschema's maar ook aan de praktische uitvoering van de experimenten. Het fabricage-proces is nl. dermate gecompliceerd dat niet kon worden volstaan met de instructie de experimenten in aselecte volgorde uit te voeren.
Het gehele onderzoek wordt uitqevoerd aan de hand van een drietal proefschema's. De keuze van het tweede en derde proefschema volgt logisch uit de uitkomsten van de voorafgaande proef. Na vol-tooiing van de derde proef is ondubbelzinnig aangetoond dat de belangrijkste oorzaak van de kwaliteitsvermindering is gevonden.     

Produktiviteit en statistiek

Productivity and Statistics.
Introduction to this special issue concerning productivity and statistics. Theauthor gives a brief general survey.     

Practische [berekening van de standaardafwijking van de constante term bij regressie-analyse

The formula arrived at in a previous article [1] is adapted to the usual computation schemes of regression analysis.     

Aantekeningen bij de herziening van de methodiek der prijsindexcijfers van het levensonderhoud

Momentarily (fall 196o) the Netherlands Central Bureau of Statistics is revising its price indexnumbers of family living. Some features of this revision are summarized below.
The old series is based on an expenditure pattern of 1951, whereas the new series will be calculated according to an expenditure pattern of 1959/'60. The latter data will be derived from a budget survey held among 250 households of manual and clerical workers consisting of 4 persons and grossing between four and eight thousand guilders a year (para. 6). The period covered was April 1959 till April i960.
The author indicates the way in which the varieties of the budget items to be covered by the monthly price surveys are chosen (para. 7). He discusses the principles and results of determining the number of price quotations (para. 8).
The choice of the municipalities in which price data will be collected is explained. An outline is given of the organisation of the new surveys apparatus (para. 14).     

De spreiding van inschrijvingsbedragen op openbare aanbestedingen

Summary
The Dispersion of Bids in Public Contracting
The analysis is concerned with the coefficients of variation (standard deviation divided by mean) of bids in public contracting by the municipal authorities of a big city in the period 1946–1953. Three factors are investigated as to their impact on these coefficients of variation. The first is time; it is shown that the dispersion decreased gradually, probably as a result of increased cartelization. The second is the nature of the object (road building and earth-work, waterworks, and sewerage); waterworks seem to be characterized by a smaller dispersion of bids. The third is the size of the object, and it is shown that the dispersion is smaller for large objects than for small ones, probably as a result of the greater care of cost calculation for large objects. An attempt is also made to ascertain the interaction of these factors.