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).     

Het verdelen van steekproeven over subpopulaties bij accountantscontroles

Summary “Stratificationprocedures for a typical auditing problem”. During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n₀ is determined in such a way that the probability β not to find any mistake in the sample, if a fraction p₀ or more of T is incorrect, is smaller than a preassigned value β₀. So n₀ should satisfy (l-p)ⁿ⁰≤β₀ for p≥p₀. A complication arises if it is not possible to postpone sampling until the whole population T is available. One then wants to take samples from a population which is growing up to T. Suppose one is going to take samples n_i from e.g. r subpopulations Using the minimax procedure, it is shown, that in this case one should choose the sizes n_i equal to (T_i/T)n₀. The minimax-value of the probability not to find any incorrect guilder in the r samples, taken together is equal to β₀.     

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.     

Lineaire regressie-analyse, ook bij gegevens in strijd met het model

Samenvatting Robuuste lineaire regressie-analyse volgens A ndrews (1973) wordt behandeld. Deze methode is bestand tegen enige fouten in zowel de verklarende variabele(n) als in de te verklaren variabele. Zij levert
i. een opsplitsing van de waarnemingen in begrijpelijke en onbegrijpelijke bij het gekozen model, en ii. parameterschattingen met nauwelijks verlies aan doeltreffendheid bij Gauss-residuen ** en met grote winst aan doeltreffendheid bij residuen met langere staart. zulks vergeleken met de bekende kleinste kwadraten procedure, die optimaal is bij Gauss-residuen.
Aan de hand van getallen-voorbeelden wordt een en ander toegelicht.     

Inleiding over de verdeling van extremen

Summary This paper is an introduction to the exact and asymptotic distribution of univariate statistical extremes and gives the methods of estimation of the parameters of the double exponential distribution.     

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.     

Produktiviteitsverhoging bij accountantscontrole door toepassing van gelaagde steekproeven

The auditor's productivity: application of stratified sampling to an auditing problem.
In this paper it is shown that the use of stratified sampling can lead to a considerable saving of costs in auditing operations and thus increases the auditor's productivity.
The sampling method to be described will render it possible to say that the total value of the transactions will not differ more than a fraction φ, given in advance, from the correct total value, apart from a probability not surpassing a preassigned level e, on condition that a certain acceptance criterion is fulfilled. Taking into account the auditing costs, the author gives an optimal sampling design and calculates the savings obtained.
Finally the theoretical results are applied to a population of clerical transactions, with an exponential and a logarithmico-normal distribution respectively.     

De fout bij het gebruik van een tweetal benaderingsformules

Summary For the sake of efficiency, the use of simplified formulae in item analysis is recommended. For adequate use of such formulae the systematic error must be known. For two important formulae this error is estimated: the KUDER-RICHARD-SON-21 (instead of 20) and a formula for the correction of the spurious part-whole correlation. As for the KR, if itemscores are 1 andO, the KR20 is given in (I) and the KR21 in (2). The difference dr between them, given in (5), is directly proportional to the variance of the itemdifficulties. This variance turns out to be rarely greater than 0,05. If the distribution of itemdifficulties is unimodal, a value greater than 0,05 is indeed improbable in four-choice tests. The KR21, which does not need an item analysis, can be used as a substitute of the KR20. The KR21 coefficient itself is an lower limit, the KR21 plus dr - estimated by (6) - a probable upper limit of the KR20 coefficient. The part-whole correlation of tests is spurious. If one wants to correct for this spuriousness it is theoretically preferable to estimate the part-parallel test correlation instead ofthe part rest correlation. This is done here with the assumptions of classical test theory. The part-parallel test correlation is given in (12), the easily computed first approximation, called A, in (13) and the second approximation in (75), in which last formula the corrected correlation is expressed as a function of A, the standard deviations of part and whole, and the reliability of the test. One can compute with this formula a maximum A, below which the first approximation is sufficiently precise.     

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 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 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.     

Oneindige verwachting en de wet van de grote aantallen

De beide wetten van de grote aantallen (de zwakke en de sterke) vormen een centraal punt van de kansrekening. In het onderstaande wordt op eenvoudige wijze aangetoond, dat zij ook gelden voor steekproeven uit verdelingen met oneindige verwachting. Een minder eenvoudig bewijs is te vinden in M. LOÈVE, Probability Theory, Princeton 1963.
Dehiergebruikte bewijsmethode werddeschrijver aanbevolen door dr. J. FABIUS.     

Loten bij delicate vragen; een overzicht van "randomized response"-technieken

In een populatie wenst men de fractie personen te schatten, die een zeker kenmerk vertoont. Bij het interview krijgt men vaak een weigering of een ontwijkend of een bewust onjuist antwoord op vragen m.b.t. delicate kenmerken, waardoor de schatter van de fractie onzuiver kan worden. Door gebruik te maken van statistische technieken, die de laatste tien jaren in de V.S. zijn ontwikkeld, kan men deze fractie toch zuiver schatten. Ook van kwantitatieve kenmerken, zoals de hoogte van het inkomen, kan men m.b.v. deze technieken het populatiegemiddelde zuiver schatten. Een overzicht van deze “randomized response”-technieken wordt behandeld. Een bibliografie van de tot nu toe verschenen publikaties wordt gegeven.