Toevals-frequenties, een hulpmiddel bij de constructie yan kunstmatige steekproeven van grote omvang

The construction of large-size random samples by means of random sampling numbers in the usual way requires much tedious labour. This paper describes a short-cut technique by which artificial samples, of say 500 or 1000, can be obtained in about one tenth of the time. Use is made of previous records of the frequencies of two-digit random sampling numbers; these are called the random sampling frequencies'.     

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.     

Over correlatierekening en de herleiding van klimatologische reeksen

Summary  (A useful climatological application of regression theory) It is often required to estimate the 24th mean temperature from a few known temperatures, e.g. at 8h, 14h and 19h, when a sample of accurately known 24h means is available. The usual method is to add a constant to the mean of the three temperatures.
It is better however to compute a regression equation of the accurate 24h means on the three temperatures.
An example is given, showing that the efficiency of the regression method is about 6 times as great as that of the usual method.     

Mogelijkheden en moeilijkheden bij het toepassen van de sequentietest

Summary  (Possibilities and Difficulties in Applying Sequential Sampling)
The application of sequential sampling schemes may be much simplified by chasing H and b ( in Barnard's notation ) in such a way that H/(b+ 1) = integer and (b + 1) = integer. A decision to accept can now be taken only after each (b + 1) items and samples of (b + 1) items may therefore be chosen from the batch.
A handicap of H/(b + 1) points is now allowed to the batch. One point is added to the score whenever no defectives are found in the sample; 0, 1, 2, points are subtracted whenever respectively 1, 2, 3. … defectives are found in a sample. The acceptance boundary is 2H/(b + 1) points; the rejection boundary is 0 points.
For given 1 in 20 producer's and consumer's risk points ( p ₁% and p ₂%), values of H and b are given in table 1 and fig. 3.     

Maxima voor de eenzijdige overschrijdingskans en voor de grootte van de gemiddelde overschrijding bij discontinue en continue, eentoppige verdelingen

The well-known inequality of Bienaymé-Tschébyschef (for short B-T), generalized by Camp and Meidell (for short C-M) for continuous, unimodal distributions gives specific limits for total probabilities outside the ± to limits.
In many cases however, especially in the field of industrial applications we are interested only in the probability of one tail of the distribution, which of course must be smaller than the limits given by the B-T and C-M formula.
For these cases the maximum probability of surpassing the to limit on one side equals under B-T conditions and under C-M conditions instead of the two-sided values of 1/t² and 47/9 · 1/t² respectively (cf e.g. Uspensky: "Introduction to mathematical probability", 1937, p. 198) These results set upper limits for the value of

Alternatively we may also set an upper limit for the integral

which measures in terms of σ the average amount by which the limit + tσ is exceeded. This problem is also discussed and under C-M conditions an upper limit

is derived.
Some practical applications of these results are considered.     

Tabellen en nomogrammen voor het onderscheidingsver-mogen van de 5% en 10%-F-toets voor het gebruik bij de gewarde blokkenproef

Tables and graphs of the power of 5% and 10%-F-tests for use in randomized block experiments.
As randomized block experiments occur so often in agricultural and other research, it was thought worth while to adapt existing tables of the power of 5% F-tests for this special case: The author hopes that in this way the design of experiments in terms of power will be facilitated. Moreover new tables were computed for the power of 10%-F-tests.
The tables have been summarized in graphs that greatly facilitate their use. Illustrations are given in practical problems.     

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.     

Enkele opmerkingesn over de mogelijkheid van toepassing van mathematisch-statistische methoden bij tijdstudieproblemen en in het bijzonder bij het Bedaux-systeem

Summary  (Some remarks on the possibility of applying mathematical-statistical methods to time-study problems and in particular to the Bedaux system.)
Time and motion study are based on observations of the workman's movements and an estimation of his efficiency.
The time spent on a certain action in mass-production is not constant but shows a considerable variation, due to various causes. The time-study-man who investigates this action and expresses it in a rate, causes still more variations by certain inaccuracies in using the stopwatch and calculating the rate itself. Considered from a statistical point of view, these cumulating variations result in a standard-error in the calculated rate; this gives rise to some interesting phenomena.
A more statistical approach tot the whole problem is shown in this article to be possible.
In the discussion, the application of the Beaux-system is assumed, but the conclusions hold good for all time study systems.     

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.     

Optimale rantsoenering van aardolie en aardolieprodukten in Nederland; een toepassing van input-outputanalyse en lineaire programmering

Samenvatting Bij een invoerrestrictie van ruwe olie ontstaat het probleem van de optimale verdeling van de olie over de verschillende bedrijfstakken. Met behulp van input-outputanalyse kan dit probleem worden getransformeerd in een lineair-prograrnmeringsvraagstuk. In het navolgende artikel worden een aantal oplossingen gepresenteerd die men verkrijgt bij verschillende veronderstellingen omtrent bezuinigingsmogelijkheden, verbruiksminima enz.     

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.     

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.     

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.