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.     

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.     

Identificeren op grond van waarnemingen

This paper is an exposition of some elements of Wald's decision theory. Concepts like a priori distribution, decision function, loss function, risk, Bayes procedures, admissible procedures, minimax procedures, least favourable distribution are introduced all in connection with the problem of classification of observations into two given populations. The exact treatment of the procedures and their mutual relations are illustrated by numerical examples concerning univariate and multivariate normal populations. The extension towards the classification into more than two given populations concludes the paper.     

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.     

Produktiviteitsverhoging op grote schaal: Maatnormalisatie van kleding

The article contains a short review of a campaign, undertaken in Holland during the last 12 years to arrive at standardized sizes for women's and men's clothing. The first campaign was undertaken by a department store, the second one by the clothing industry.
The operational value of a sizing system depends on the value of three parameters which are not, of course, independent of each other: coverage of the system, number of sizes and average cost of alterations.
The basis of the standardization is furnished by measuring a sample of the population of customers and by measuring the fitting-tolerances of clothing.
The proposed sizing systems are:
a. Ladies' dresses — a two-dimensional system based on waist girth and length of back, containing 14 sizes and giving a coverage of 90%.
b. Men's suits — a system with a variable number of dimensions (2 to 4). The identification dimensions are waist girth, length of leg, hip girth and inclination of shoulder. The proposed system gives a coverage of 90% with 34 sizes. Both systems have been experimentally verified.
Stress is laid on the necessity of an international sizing standardization.     

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.     

Tabel en nomogram voor het aflezen van jaarlijkse groeipercentages van grafieken op semi-logaritmisch papier

Summary  A table and a nomogram are given to find the growth rate of a regression line drawn on so-called semi-logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is explained.     

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.     

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.     

Tabel en nomogram voor het aflezen van jaarlijkse groeipercentages van grafieken op semi-logaritmisch papier

Summary A table and a nomogram are given to find the growth rate of a regression line drawn on so-called semi-logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is explained.     

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.     

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).     

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.     

Over prijsraming en prijsvorming op de bouwmarkt

The analysis deals with the ratio of actual to predicted prices of building projects for a big city in the Netherlands in the period 1946–1953. These forecasts had been made by the city's civil servants as a guide to building policy. It appears that the ratio of actual to predicted prices was of the order of 0.85 on the average, which implies a tendency to overestimate the actual prices to be paid. This ratio has an average which is closer to 1 for large projects than for small ones, and the standard deviation around the mean is smaller for large projects. Further more it appears that this standard deviation decreased systematically in the course of time.     

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.