^RESIDENTIAL ADDRfeSS. 630 



Tke method of sampling is, of course, only one of many instances of the 

 application of the theory of probability to statistics. 1 have taken it at length 

 because the method is so persistently neglected, and even when it is used the test 

 of precision is ignored. We are thus throwing aside a very powerful weapon of 

 research. It is I'requeutly impossible to cover a whole area, as the Census does, 

 or as Mr. Rowntree here and Mr. Booth in London successfully accomplished, but 

 it is not necessary. We can obtain as good results as we please by sampling, and 

 very often quite small samples are enough ; the only difficulty is to ensure that 

 every person or thing has the same chance of inclusion in the investigation. 



The use of such methods must remain for some time in the hands of specialists 

 for several reasons. The theory is still in the making ; no general rules can be 

 laid down, and considerable judgment is needed as to how far a particular theory 

 is applicable to a given problem. There is still some difference of opinion as to 

 the best method of grounding the theory, and there is not complete agreement as 

 to the meaning to be attached to the technical terms or as to the best terms to be 

 used. Again, the observations we are able to make are so few and so rough that 

 special skill is required to handle them; the worse the tools, the better must be 

 the workman. So far, too, there is dearth of raw material for educative or 

 laboratory work, though suitable groups of statistics are now accumulating rapidly. 

 These conditions strengthen, rather than weaken, my demand for an adequate 

 supply of specialists, and for the proper preparation of those whose duty it will be 

 to handle statistics in a few years' time, when the methods will be more perfect. 

 On the other hand, they support the general practice of the non-inclusion of the 

 more advanced mathematical methods iu undergraduate courses ; but I could wish 

 that the line were not drawn quite so low. 



The use of the methods I have indicated can be illustrated from almost any 

 branch of statistical inquiry. In dealing with wages we have to determine 

 whether the samples we have are sufficient. In studying trade records we need 

 to know the precision of our index numbers, the theory of weighted averages, and 

 the measurement of trend and of fluctuations. In questions of income and 

 income-tax we have to consider what help Pareto's law of graduatioa can give. 

 In sociological and anthropometrical investigations, whether we are considering 

 the malnutrition of children, or the alleged deterioration of national physique, or 

 the birth-rate, or the employment of women, we have again and again to take 

 mathematical means for describing the groups or estimating the precision of the 

 averages and the significance of observed differences. In most cases of cause and 

 efiect, and in general in testing the interdependence of phenomena, we have to 

 use the mathematical measure of correlation, a subject whose importance demands 

 much more than the brief mention here given. 



For illustration of the immense practical importance of such methods I offer a 

 brief analysis of the most important and pressing of modern economic problems, 

 showing in what respects mathematical statistics ai'e needed. What do we 

 actually know of, and how should the nation deal with, the classes who do not 

 fit in with the ordinary and normal economic life of society — who do not, as a fact, 

 attain any reasonable standard of life in our regime of free competition : the 

 sweated, the casual labourer, the frequently unemployed, the permanently 

 unemployed, and their forerunner, the underfed and uneducated child ? 



As economists and statisticians we are not concerned with palliatives or 

 methods of expediency, but with a correct knowledge and true diagnosis of the 

 extent of the evils, on which can be built reasoned and permanent remedies. 



As is generally the case, our information as to the facts is hopelessly incom- 

 plete. There is no agreement as to scientific classification, no complete estimate 

 of numbers; nothing but most limited records, supplemented by ill-informed 

 guesswork. This is the case at the present moment, when public attention has 

 been focussed on these questions for some time. Still less do we kno^v auything 

 about conditions thirty, twenty, or even ten years ago. In these circumstances 



