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.     

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.     

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 plaats van de statisticus in het bedrijf

Summary  (The position of the statistician with regard to general management).
Analysis of the statistical work to be done in a great concern leads to a determination of the position of the statistician in the usual organisation scheme.     

De omvang van de steekproef bij een enkelvoudig steekproefsysteem

Summary  (Sample size for a single sampling scheme).
The operating characteristic of a sampling scheme may be specified by the producers 1 in 20 risk point ( p ₁), at which the probability of rejecting a batch is 0.05, and the consumers 1 in 20 risk point ( p ₂) at which the probability of accepting a batch of that quality is also 0.05.
A nomogram is given (fig. 2) to determine for single sampling schemes and for given values of p₁ and p ₂ the necessary sample size ( n ) and the allowable number of defectives in the sample ( c ).
The nomogram may reversedly be used to determine the producers and consumers 1 in 20 risk points for a given single sampling scheme.
The curves in this nomogram were computed from a table of percentage points of the χ² distribution. For v > 30 Wilson and Hilferty's approximation to the χ² distribution was used.     

De statistische basis van de planning in een machinefabriek

The normal or jigsaw-puzzle method of planning cannot be applied to the production of an engine factory. One has to fall back upon a kind of statistical automatism, like in the planning of road traffic as opposed to the planning of railway traffic.
In order to do this kind of planning efficiently, it is necessary to know the statistical relationships between the degree of occupation (number of working hours divided by number of available hours) of the machines, the waiting time and the velocity of flow through the factory.
The statistical analysis of some of these quantities in an Amsterdam plant, manufacturing medium size diesel engines, showed that Erlang's formulas of waiting time in telephone traffic (with exponential distribution of holding times) are applicable.
These formulas are used to prove that the highest degree of occupation is not the best one from an economic point of view. Formulas and graphs are given for finding the optimum degree of occupation in engine factories and other works where the same conditions apply.     

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 ontwikkeling van de inkomensongelijkheid gemeten volgens informatietheoretische maatstaven

Summary Some years ago Theil introduced new inequality measures, originating from information theory. He applied them 8.0. to income distributions in the United States. This inequality coefficient is - in contrast to Pareto's constant - based on the whole income distribution. Moreover, the inequality can be disaggregated into inequalities for groups of population. The numerical value of the inequality depends on the chosen class intervals; this may be inconvenient when making comparisons between countries, between different periods and the like. Hence we suggest an appropriate standardizing procedure. The inequality of income distributions has been calculated for the period 1950–1964 and a cornparison is made with Pmm's constant. The investigation relates to three groups of population: wage earners, self employed and others. A remark is made about between-province inequalities.     

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).     

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.