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.     

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 vervaardiging van een systeem functie-ponskaarten

While making a series of 10,000 "function" -punched cards with the data of the well-known Barlow's tables and with the logarithms of the integers from the tables of Schrön, we took the opportunity to examine the accuracy with which our personnel and machines are working under normal conditions. We examined for instance in how many cases the first punching operator did not notice an error she made and how many of those errors remained after control-punching. These last-mentioned errors were traced by control-calculations with the punched cards, e.g. by calculating and checking n × n²= n ³ or by the calculation of differences. In this way it appeared that the first punching operator did not notice 270 errors in the part coming from Barlow's tables, being 0.055% of the number of punched columns or 2,7% of the number of cards. Further it was found, that only one error of the first operator was not noticed (or not corrected) by the controling operator.
Besides this a number of printing-errors, or anyway errors which were the result of the bad legibility of the digits, were found in Barlow's tables, where the punching operator and the controling operator had come to the same interpretation.
The article gives in some detail what precautions were taken by wiring the machines to attain that an error would be noticed as such.     

Een criterium voor het kiezen van een proefopzet

A characterization of D-optimality is given together with several examples where D-optimal designs are computed.     

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 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.     

Een opmerking over het aanpassen van functies aan een groot aantal waarnemingsuitkomsten

Note on the fitting of a function to a large number of observations.
The paper deals with various ways in which a set of functions may be chosen to describe a given body of observations, the parameters determining the function being determined by the data.
The special case when the functions of the set are given in the form of a table or a graph is emphasized.     

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.     

Poisson-proces met interrupties, een waarschijnlijkheids-model voor het machinaal dunnen van bieten.

Starting from the assumption that {even in case of dense precision sowing), the occurence of beet plants in a row can be taken as a realisation of a Poisson proces, the influence of mechanical thinning is studied.
The distribution of the distance between two plants, originally exponential, is changed by mechanical thinning in a way, dependent on the lengths of the intervals a (the potential survivor-zone) and b (the length of the thinningblade).
The distribution of the distance between plants after mechanical thinning, is examined, and the "best" way of thinning, leading to the distribution of the distance between plants with the smallest variance, is derived.     

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 simpele grafische iteratiemethode voor het schatten van een betrekkingtussen kwantitatievestochastische variabelen.

A simple graphical iteration procedure for estimating a relation between quantitative stochastic variables.
For the estimation of a relation which will predict values of one stochastic variable from known values of a number of other ones, a simple graphical iteration procedure, applicable under rather general conditions, is demonstrated by means of an example. The method amounts to plotting the values of the dependent variable against one (or one pair) of the initial variables, after correction for the influences of the other initial variables as far as these have already been estimated. An approximation (or improved approximation) for the influence of the variable considered can then be made.     

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.     

Het vergelijken van twee verschillende schatters voor een percentiel P van een normale verdeling

A comparison is made between two different methods to estimate the probability that a normally distributed observation is less than a certain value. One method is based on the binomial distribution, the other one on HALD'S maximum likelihood estimates of the parameters of a censored normal distribution. For large sample sizes a graph of the relative efficiency of these two estimates is constructed. A sampling experiment was performed in order to investigate for one particular situation the possible bias of HALD'S maximum likelihood estimate, which is only asymptotically unbiassed.     

Statistische eigenschappen van een vlambeveiliging met behulp van een gasontladingsbuis welke gevoelig is voor ultraviolet licht

Summary The output voltage of a detector circuit containing a gas-filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov-process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special circuit.     

Statistische eigenschappen van een vlambeveiliging met behulp van een gasontladingsbuis welke gevoelig is voor ultraviolet licht

Summary  The output voltage of a detector circuit containing a gas-filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov-process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special circuit.