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SummaryKnowledge by measurement in the social sciences, address to the general meeting of the Netherlands Statistical Society.The motto "Knowledge by measurement" of the great Dutch physicist Kamerlingh Onnes is also valid in the social sciences. Knowledge about economic and social phenomena must be obtained to a large extent by measuring quantities, ratios, mutual relations and growth factors.During the past 20 years a considerable progress is made in this field, which is shown by two examples.In a certain sense the motto mentioned above is a euphemism: however much our measurements may be improved, our knowledge remains incomplete. The observation of social phenomena is unique, they cannot be reproduced and the research worker meets different kinds of restrictions in practical experience. A careful criticism of the results of experimental research is all the more necessary, particularly in the case that these results have to be used as a tool for general economic planning.

SummaryThe 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.

SummaryThe 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.

SummaryThe application of sampling in auditing.A sampling procedure is developped for the application in audit‐procedures of a very large number of entries. The procedures can only be applied in cases where fraud will lead to a booking of an entry at a too high amount; it consists of the following steps:1. to check all bookings, surpassing an amount of x02. to take a sample of the other bookings, and to check the items of the sample. The size of the sample and the amount x0 have been chosen in such a way that, in case no fraud has been detected, the maximum amount of fraud committed does not — with a predetermined confidence coefficient — surpass a likewise predetermined amount.

SummaryAn application of the occupancy theory on a coding problemFor large scale registration of certain medical phenomena it is very useful to have the disposal of a coding system which enables the reconstruction of the code number of a given person at any moment from the smallest possible number of personals. For this purpose, place and date of birth and sex may be used. These items, however, are not sufficient as they do not permit to distinguish between persons of the same sex, born at the same day in the same place. For Amsterdam this number is about 20. Therefore the Inspector of Public Health considered the possibility of including the birthday of the mother in the data and requested the Municipal Bureau of Statistics of Amsterdam to estimate the percentage of duplications which would occur when this enlarged system of personals were used. A special investigation for September 1951 turned out a rate of 10% which seemed to be rather high even if the number of twins for which duplications by their very nature would occur was taken into account. So it became interesting to know which rate theoretically might be expected.If we suppose the birthdays of the mothers of the persons born on the same day and in the same place to be evenly distributed over the days of the year, it is easy to calculate the expected number of duplications.We are then led to consider the following occupancy problem: n objects (number of births on a given day) are distributed over N places (possible birthdays of the mothers), the probability to occupy a certain place is the same for all objects and independent of the place. What is the probability that no places will be empty, n1 occupied by only one object, n2 by two objects etc.? It is shown that this probability is equal to From this formula the expectation and the variance of the number of persons with equal code numbers can easily be derived.The empirical results for 4 different months of 1951 (including the already mentioned month of September) proved to be in good agreement with these theoretical calculations.

SummaryThe genesis of frequency distributionsThe next set of six short papers reproduces the contents of a series of six talks given at the annual meeting of the 'Vereniging voor Statistiek' (Statistical Society) having 'frequency distributions' for their subject.In this first and introductory paper the various ways in wich we may conceive a frequency distributions to be generated aye briefly indicated, and the useful conclusions with regard to the underlying sources of variation that may often be drawn from the shape of an observed frequency distribution are pointed out.

SummaryIntelligence in Amsterdam in connection with demographic and sociological characteristics of the population.Since the end of the war Dutch recruits, after having passed a medical examination, have been submitted to five psychological tests, measuring general intelligence, aptitude for mathematics and languages, respectively, technical ability and ability to carry out orders. This investigation is based on the results of some 13,700 recruits examined in Amsterdam from 1947 up to and including 1949. It is restricted to the results of the test for general intelligence, as this test is supposed to be most free from environmental influences and as its results are available for all recruits. General intelligence has been measured by the test of progressive matrices devised by f. C. Raven. The correlation matrix for the five tests (based on approximately 9,500 recruits) has been calculated and although the correlation coefficients are all positive and highly significant, they vary between 52 and 76; showing that the possibility cannot be excluded of finding greatly deviating results when using the results of one of the other tests.In order to be able to compare intelligence with characteristics not available for the individual recruits, either as a consequence of lacking statistical data, or even due to logical impossibility (e.g. in the case of fertility), the average level of intelligence has been calculated for each of the 54 wards of Amsterdam for which the Amsterdam Municipal Bureau of Statistics regularly compiles statistical data. Consequently the assumption has been made that these averages may be considered as fair measures for the average intelligence of the whole adult population of the wards.The first part of the study deals with the statistical material, i.a. some defects in the scale by which intelligence is expressed, the advantages and disadvantages of the fact that test results were not available for the recruits rejected at the medical examination and the shape of the frequency distributions of the results per ward. The inter‐ward differences in intelligence are submitted to an analysis of variance and prove to be highly significant.The second part of the study gives an enumeration of the results obtained by correlating intelligence with various demographic and sociological factors. Very significant and positive correlations were found with income (average income assessed for income tax) and social status (measured by the percentage of unskilled workers among the occupationauy engaged population). The high correlation between intelligence and social status, in itself probably due to a process of social selection based on intelligence, may also be drawn upon to explain the results obtained as to political conviction. This conviction measured by the percentage of votes per ward as given to the various political parties, shows highly significant coefficients for the communists and the liberal party, negative in the former and positive in the latter case. For the labour party and the Roman‐Catholic party, two important groupings chiefly appealing to the middle classes, no significant correlations are found.Fertility in marriage, generally considered as having strong links with intelligence, gives rise to a hardly significant though negative correlation. This result, however, can considerably be improved, although still remaining rather low, by introducing the percentage of Roman‐Catholics among the population of the wards. This is in accordance with the well‐known fact that the fertility of the various religious groups in the Netherlands is strongly diverging, being highest among the Roman‐Catholics.A very high correlation again is obtained with the number of children begot before marriage as a percentage of the total number of first born (children born alive within J months after contracting marriage). Here probably the influence of changing social standards in the various wards makes itself felt.The last part of the article gives an interpretation of the results of the investigation. Although the significant correlations under certain reservations may be interpreted as being due to causal interrelationship, intelligence itself need not be a direct cause. A model may be conceived in which all characteristics together with intelligence are explained by a number of hereditary and environmental factors. Now assuming that intelligence as measured in this investigation is entirely free from environmental influences (there are some indications that this is not so) it can be interpreted as representing only one aspect of the hereditary complex. But even under this assumption many other factors may be involved in a complete explanation of the characteristics. A factor analysis which may perhaps partly clear up the complicated network of interrelations is under consideration.

Résumé MM. P. de Wolff et J. Mef.rdink avaient déjà attiré l'attention sur eux par une remarquable étude sur la mortalité à Amsterdam (Population, octobre-décembre 1952). Ils montrèrent comment la notion même de mortalité sociale évoluait avec le progrès social lui-même. Cette fois, les deux savants hollandais se sont attachés spécialement à la mortalité infantile. C'est la première fois qu'une étude a été aussi poussée dans cette voie. De ces recherches originales, faites dans une ville à l'avant-garde du progrès social, découlent des enseignements qui doivent se traduire en d'autres villes et d'autres pays par un nouveau recul de la mortalité, mieux dépistée.