5

begrijpelijk aanschouwelijk voor te stellen. Evenals de kwaliteitscontr61e gedurende den oorlog aan Engeland en Amerika onschatbare diensten be- wees, omdat het met behulp daarvan mogelijk was met minimum contrdle- kosten en met het relatief kleinere aantal meetinstrumenten de kwaliteit te beheerschen van millioenen en millioenen voor de oorlogvoering onmis- bare producten van hooge kwaliteit, zoo kan Nederland daarvan met groote vrucht gebruik maken bij de vreedzame, maar daarom niet minder felle slag, welke geleverd moet worden om door een snel herstel onze materieele welvaart te herwinnen en daardoor ons geestelijk herstel te bevorderen.

Applied statistics in England

door E. D. van Rest B.A., B.Sc.

It may be of interest to the members of the “Vereeniging voor Statistiek” to have this account, a stock-taking as it were, of the position of the science of applied statistics in England.

T h e science of statistics touches upon and provides tools for many other sciences so that its field is a tremendously wide one and its exponents are drawn from many sciences. There is thus the danger that workers will be isolated in their own subject and not be able to take advantage of the advances in the science of statistics as applied to other sciences.

We have thus been fortunate in England that in 1933 the Royal Statistical Societ)l formed an Industrial and Agricultural Research Section which formed a focal point for scientists using statistical methods. Papers were read at public meetings and these and other papers published in a Supplement to the Journal of the Society. The wisdom of this step was confirmed by the increase in the number of Fellows of the Society. Now, in 1945146 the Society is experiencing a great influx of Fellows and a greatly increased attendance at meetings, both of the main Society and of its sections. These sections have been reformed as a Research Section and a series of Industrial Applications Groups formed at local centres wherever interest is suffidiently dtrong. They are affiliated to the parent society. These Groups hold meetings locally, four or five during the year, which are less formal than the meetings of the Research Section and the papers read are not alwayspublished, being designed to promote discussion rather than to convey new information.

I propose briefly in this paper to survey the uses made of statistical science during the war; to touch on the changing status of statisticians; to survey the provision for teaching the subject and to indicate some of the trends of new work.

6

1. Statistic. in the Governmeat Service

(a) During the war The war naturally brought a demand for statistical work; for wherever

information is available in a numerical form statistical methods are needed to draw valid conclusions or to make predictions. Of the many kinds of work in which statisticians were engaged during the war we may mention the following; -

Operational Research Work of this kind was undertaken by each of the three Services for its

own information. It consisted of the collection of the kind of information a commander needs as a basis for his tactics. The efficiency of a technique (of flying, of bombing or of training, to quote examples) can only be assessed Scientifically if scientifically gathered information is available.

Probability Problems A number of probability problems arise in operational research and else-

where. Examples are the probability of achieving hits on a given target with a given size of bomb; the number of bombs which should be dropped to allow a given chance of success in a given operation; the effectiveness of anti-aircraft fire under given conditions; the location of obstacles to give the greatest defence. Calculations such as these assume importance when it is necessary to partition a limited total effort among a number of targets.

Design and analysis of experiments Experiments were undertaken by the Service departments in widely

different fields such as the selection of flying personnel, or the clearing of minefields by explosives; all these needed statistical methods in their inter- pretation and therefore in their design. The need for fairly rapid decisions on the basis of fairly small scale experiments made the scientists engaged on these experiments quickly aware of the need for these methods.

Control of production The need to work to closer limits than usual brought difficulties to many

firms engaged in the production of war stores. A system based on statistical methods and known as “quality control’’ was succesfully used by many. Briefly it consists of making a study of the frequency distribution of the dimension being produced and then subsequently throughout production keeping a watch on this distribution, by taking samples only, to see that it does not change. Changes indicate a need for re-setting the machine.

7

Statistical methods enter into the initial study and into the theory of the sampling process.

Inspection A good deal of effort was often expended during the war in inspection;

the inspection often being repeated by the service department purchasing the stores. The system of quality control mentioned above was sometimes able to replace a part at least of this expensive final inspection because the results of a continuous system of inspection during production were available. In other cases total inspection could be replaced by inspection of samples only; the necessary scheme being designed on statistical principles. Heavy ammunition presents a special difficulty because of the great expense and the few items which can be inspected by actual firing tests.

(b) After the war

There is no evidence of any intention on the part of either the Government or industry to abandon this new found aid. The creation of posts of Chief Statistician, Principal Statistician and Executive statistician in the government service which are desctibed in a later paragraph are indications.

That branch of the Ministry of Supply which during the war provided an advisory senfice on appGed statistics both for Government departments and for industry engaged on munition production is to be retained though its function will be confined to the Service departments. For other departments and for industry generally there has been formed a statistical section of a new Mathematics Division at the National Physical Laboratory where it will have extensive computing facilities. This section will be available to advise and sometimes to work for others in all fields of applied statistics and should prove of value to those specialists who wish for a specialist knowledge of statistics to be brought to their own problems.

2. S b t i a t i a in Industry The advance in the application of statistics to industrial problems is well

refleoted by the formation of the Industrial Applications Groups of the Royal Statistid Society in three centres: London, Birmingham and Sheffield. The London one has been running throughout the war, the Birmingham one is a transformation of a number of study groups also formed during the war and the Sheffield one is no doubt a development from the lecturing and advisory work done by Dr. B. P. D u d d i n g of the General Electric Company’s Research Staff.

Many of the large corporations and combines are aware, through their

8

research staff, of the usefulness of statistical methods to their work and have taken care to employ statisticians on their staff. Among those who are known to do so may bequoted: Imperial Chemical Industries, United Steel Co, Ferranti Ltd ind Philips Lamps Ltd. The function of a statistician on the staff of such an organisation may be on the economics side but there is ample indication that statisticians are also being brought into production problems and into the interpretation of research and development experiments. A special field is the biological assay of vitamin products, drugs and insec- ticides etc.

The British Standards Institute whose members cover the whole of in- dustry is concerned to apply statistical methods to its work on specifications. The methods enter into the preliminary exploration of what is to form a satisfactory batch of the product and into the design of a sampling test which shall reject undesirable batches while not rejecting the acceptable ones. The Institute has one of its numerous committees dealing entirely with statistical methods and available for consultation by the others.

This industrial work is by no means confined to “quality control” though many of the discussion groups start with this subject. Their interests sub- sequently range over sampling problems for inspection, analysis of variance, design of experiments and accounts of special investigations requiring sta- tistical work. As already mentioned the newly formed statistical section of the Mathematics Division of the National Physical Laboratory will be avail- able to industry for advice and work as required.

3. The Status of Statisticians With the growth of employment of statisticians as such and not under

some other name there has come a recognition of their status. Hitherto, the compilation and collation of data in government departments has been handled by “statistical officers” not necessarily with any particular qualification though many of them have acquired an aptitude for the work and have indeed helped to develop the science. The dangerous ease with which false con- clusions can be drawn has contributed to the desire to set some standard of qualification for these posts and it is now envisaged that there shall be posts of “Executive, Principal and Chief Statistician”. The qualifications for the Principal and Chief Statistician posts are to be a first or second class degree in either mathematics or statistics as a principal subject. A recent adver- tisement in “The Times’’ invites applications for twelve of these posts.

It is to be expected that with these developments in the use of statistical methods in science, in industry, in commerce and in the business of govern-

9

ment there will be a demand for teaching and examination in the subject and some steps are being taken to meet this.

There have been for some time facilities far students to take a B.Sc. dzgree in Statistics at London University. Although University College London is the maip centre of teaching of mathematical statistics in England, other London colleges and other English universities do offer courses and several othersaremakingpreparations to do so. Most universities already offer degrees or diploma’s for which statistics is an optional subject but in only a few cases is it a compulsory subject and only at London is there a degree in the subject.

Although unforeseen difficulties have prevented its publication, it is now generally known that the Royal Statistical Society have prepared a scheme for an examination for the award of a Diploma and of a Certificate which shall form a professional qualification at two levels. The committee of the Statistical Society which is dealing with this proposal will also report on the teaching of the subject in universities, schools and elsewhere.

Agriculture was, of course, the subject in which statistics applied to ex- periment developed and the Cambridge School of Agriculture has for some time had a statistical post (now a Readership of the University) on its establish- ment. New ground has been broken by Oxford University by the creation of a lectureship in the Design and Analysis of Experiments sponsored by the biological departments and attached to the Forestry Department.

4. Recenc Trend. Among noticeable trends in the science of applied statistics is a renewed

interest in the analysis of time series. The orthodox analysis of the Fourier kind into harmonic components is not always appropriate (on physical grounds). An alternative analysis supposes that the nth observation has a component correlated with the (n-k)th observation. By plotting the corre- lation coefficients between terms at interval k against k one obtains the

The “dosage-mortality” technique has a widespread use among biologists for testing the potency of drugs etc. but has really a much wider application, though this is not always realised to all kinds of experiments in which the reponse is not capable of measurement but is all or nothing. For example, the explosion of a cartridge by another cartridge exploded at a distance. The observed result is either “exploded” or “not exploded”. The data will be in the form of the fraction of the number of cartridges which exploded when exposed at a given distance from the originating explosion. The method determines the frequency distribution for individual cartridges of the maximum

correlogram” characteristic of the series. ‘,

I0

distances for individual cartridges at which sympathetic detonation takes place.

Sequential Inspection is a fairly recent development. A sample will, within limits, give information about the fraction of the population possessing a certain attribute. In order to narrow these limits of uncertainty to a useful size it is often necessary to use rather large samples. On the other hand it will be agreed that the information contained in the sample accumulates step by step as each item is examined. So that, depending on the population from which the sample is being taken and on the result of inspecting each item, a given confidence that the population has less than a given fraction possessing the attribute may be reached at various steps in the sampling process. For e‘xample if we wish to devise a sampling scheme to reject batches of an article when the batches contain as many as 25% bad we could fix a sample size at, say, 90 and if no more than two bad are found in the sample we can be reasonably sure (99,5y0) that the batch does not contain more than 25% bad. If however by the time the first 70 have been inspected none or only one bad has been found we are equally sure (99,504) that the batch does not contain more than 25% bad articles so that we can safely stop the inspection. Thus it may be more economical to s u m up the information gained in sampling as the inspection proceeds; the sequential method provides the information necessary for this to be done.

5. New books

war years are the following: Among the books of interest to statisticians which have appeared in the

Statistical Mathematics. A. G. A i t k e n. Oliver & Boyd, Edinburgh 1942,

This is a short text book, one of a series called “University Texts”, which sketches the mathematical theory behind statistics. It requires a knowledge of higher mathematics.

51- sh.

StatisticaI Methods for Research Workers. R. A. F i s h e r. Oliver & Boyd (an 9th edition has appeared 1944) 161- sh. This is the classic well-known to research workers, especially those in

biology.

Regression Analysis of Production Costs and Factory Operation. P h i l i p L y 1 e. Oliver & &yd, Edinburgh 1944, IS/- sh. This is a very practical book. Besides a very readable account of the

methods it shows how and why the calculations are carried out.

The.4dvanced Theory ofstatistics. Vol. I . M. G. K e n d a 11. Charles Griffin & Co. London 1943 42!-sh. With volume 2, shortly to appear, it forms a very complete reference book

of the mathematics of the subject.

Indtistrial Experimentation. K. A. B r o w n 1 e e. Ministry of Supply, DOF/X

First Guide to Q-uality Control for Engineers. H. M. Stationery Office London, London 1945.

I / - sh.

There is not a large provision for the publication of statistical papers in England. The main papers, except for the applications which appear under their main subjects appear in , ,Biometrika” (published by the Biometrika Office, University College London) and in the Journal and the Supplement to the Journal of the Royal Statistical Society. The Supplement has not yet resumed publication but it is hoped that it will do so shortly. The Annals of Eugenics which previously contained a number of statistical articles is now to be more purely ,,eugenic”.

Over tolerantier en parringen in den maehinobouw door’J. Siftig

Het werk van den constructeur op een machinefabriek is veelzijdig. Het kiezen van de juiste vormen voor een bepaald onderdeel, de uitvoering van de noodige sterkteberekeningen, het aandacht schenken aan den eisch van gemakkelijke bewerkbaarheid, het vermijden van spanningen, de keuze van het meat geschikte materiaal - dit alles vereischt grondige theoretische kennis, groote technische ervaring en behoorlijk economisch inzicht.

Het is, psychologisch gezien, alleszins natuurlijk dat de constructeur op de verschillende vragen waarvoor zijn werk hem telkens plaatst, een positief, ondubbelzinnig, precies omschreven antwoord tracht te geven. Hij geeft dit antwoord in de teekening.

De teekening is ondubbelzinnig en exact. Als de constructeur de lengte van een pen aanduidt door ,,60 mm”, dan is Z;j 60 mm, geen mikron meer of minder; het koolstofgehalte van het staal is op de teekening precies 0,30%; de trekvastheid exact 72 kg/mm%. Maar zoodra de teekening uit de theore- tische sfeer van het constructiebureau verhuist mar d e ruwe werkelijkheid van de werkplaats, blijkt dat de volledige bepaaldheid en exactheid, waar- van hierboven sprake is geweest, slechts theorie is. In de werkplaats doet