" PHESIDENTIAL ADDRESS. 633 



chief of a department to which a situation belongs . . . shall consider that the 

 qualifications in respect of knowledge and ability deemed requisite . . . are . . . 

 professional, or otherwise peculiar, and not ordinarily to be acquired in the Civil 

 Service,' a person ' who has acquired such qualifications in other pursuits ' may to 

 appointed. 



I have dealt with this subject at length in order to ask the question : Have 

 we any guarantee that the public service, whether official or unofficial, will be 

 supplied with a sufficient number of persons who are qualified to handle statistics 

 expertly, to follow the rapid mathematical developments which alone can get the 

 full significance of records, and to inform the public with reasoned knowledge of 

 the measurable phenomena of national life ? There is no dearth of capable mathe- 

 maticians streaming from our universities, but there are relatively few who apply 

 their special knowledge to public aflTairs ; they rather dissipate it in elementary 

 teaching or put it aside as a useless weapon. There is a veiy plentiful supply of 

 expert arithmeticians entering the lower grade of the public service, but there 

 is no provision for their developing into educated statisticians. 



The use of mathematical reasoning in statistics is very imperfectly understood, 

 partly because the passage from numbers to symbols and back to numbers suggests 

 an air of mystery, or even of prestidigitation, to the unmathematical mind ; partly 

 because, even with mathematicians, the application of the theory of probability to 

 the determination of the precision of an estimate is unfamiliar ; partly because the 

 method, though fully sixty years old,' has only recently heen developed, and the 

 methods and limitations of its use are still a matter of analysis and discussion 

 among its advocates. In many respects its position resembles that of mathematics 

 in economic theory, a subject handled at length by Professor Edgeworth, my 

 predecessor in this chair in 1889. There are those that hold, in both ca.=es, 

 that verbal or numerical reasoning, unassisted by symbols, is sufficient for the 

 elucidation of all truth. Whatever may be said in favour of this view as regards 

 economic theory — a discussion so familiar to my audience that I need not dwell 

 on it — I do not think that in the case of statistics the argument can be seriously 

 maintained, and it is my intention to give such reasons for this statement as the 

 limitations of a presidential address make possible. 



Scientific measiu'ement is in general approximate, and in the physical sciences 

 much attention is given to the determination of the accuracy of experiments, and 

 their result is given as not absolute, but as correct to so many significant figures. 

 Statisticians frequently find that their second significant figure is doubtful, as in 

 the case of the national income, which is estimated as between 1,700,000,000/. and 

 2,000,000,000/. Sometimes even the first figure is doubtful, as in the en'oneous 

 quotation that 1 3,000,000 persons are on the verge of hunger. In such cases as this 

 the physicist would stop, and set to work to elaborate his measurements. Not so the 

 popular statistician, who delights in guessing in tens of millions and mixing up these 

 bold round numbers with others correct toten significant figures. These guesses must 

 be rigorously excluded from serious work, and, lest they should come in unawares, 

 the exact limitation of the quantity actually measured and its relation to the 

 total in question must always be carefully studied. We must candidly accept 

 the fact that our raw material is imperfect, and our business is to remove the 

 imperfections so far as we can, and, above all, to measure those we cannot remove. 

 It is in these two directions that mathematical methods are generally necessary, 

 and sometimes sufficient. The material is improved by methods of interpolation 

 and graduation ; the general law of grouping or direction of movement is dis- 

 covered, and the accidental variations eliminated ; or, conversely, the general 

 direction is neutralised and the variations measured. The adequacy of the 

 material is discovered from internal evidence of consistency and conformity to 

 the laws of continuity, and improved by carefully selected samples. The last- 

 named method will be dealt with presently. 



When the material is improved and tested there arise questions of causation — 



, ' Quetelet's Z/ettrpg sur la Thi'orie ties Probabilities was published in 1846. 



