PRESIDENTIAL ADDRESS. . 669 



is, of course, not free from incidental dangers. It is clearly possible to lean on 

 the third foot of our tripod more heavily than it will bear, and it is not only 

 possible but probable that the public demand for quantitative information will fin- 

 some time outrun the available means of supply. Certainly the pressure for more 

 and better statistics is increasing very rapidly at the present time, and not always 

 with due regard to the limitations of what is practicable. In order to form a 

 sound and sober judgment of the true possibilities of advance along this line it is 

 necessary to recognise frankly the chasm which separates the crude and primitive 

 means of measurement, or rather of quantitative estimate, which alone are open 

 to the economist, from the relatively perfect apparatus and methods which are 

 available to the physicist. 



But the more imperfect our data and the more primitive our means of 

 enumeration and measurement, the more perfect and complex needs to be our 

 scientific apparatus for criticising the results and enabling positive inferences to 

 be drawn therefrom. In other words our dependence on statistical science is pro- 

 portionate to the defects of our means of direct and accurate measurement. 



Statistics is often classed with economic science (and, indeed, the two names 

 are linked in the title of our Section) as though there were some essential connec- 

 tion between the two. But this, of course, is not the case, statistical methods 

 being used to a greater or less extent in all the branches of science which occupy 

 the other Sections of the British Association. In fact, it is probably in connection 

 with biology rather than economics that the most important original research by 

 statistical methods has been recently carried out. 



Quantitative measurement is the backbone of science, and whenever the 

 quantities handled are in any way indeterminate or inexact, either in regard to 

 their definition or enumeration, we need the assistance of scientific rules and 

 criteria to enable us to correct, or neglect, or at least to limit the error introduced 

 into our results by the faulty nature of the data. The mere direct measurement, 

 counting, or weighing of quantities is scarcely worthy of being called a statistical 

 operation : statistical science properly so-called is mainly concerned with estab- 

 lishing the conditions under which approximately true inferences may be drawn 

 from imperfect data. On this problem the modern statistician brings to bear 

 the powerful engine of the mathematical theory of probability. 



It is no part of my intention to attempt to discuss the methods of modern 

 statistical science : I only wish to emphasise the close connection between the 

 elaboration of these methods and the imperfection of the data to which they are 

 applied. 



Now the data of economic statistics are almost all liable to error either through 

 defects of definition or extension. Either the only data available are not precisely 

 of the nature required for the purpose of the particular investigation, so that we 

 have to do the best we can with second or third best materials, or the data 

 obtainable only cover a comparatively small portion of the total field, and there 

 may be formidable questions as to how far the results based on such limited data 

 are really representative. Sometimes we suffer from both these difficulties, and 

 statistical inquiries oscillate habitually between the two dangers as between 

 Scylla and Charybdis — the danger on the one hand that over-insistence on 

 elaborate precision of data may so narrow the field that the results obtained from 

 the sample may be unrepresentative of the whole, and the danger on the other 

 hand that the ' common statistics ' which alone cover the whole field are neces- 

 sarily obtained not only for one but lor many diverse purposes, and are therefore 

 unlikely to be entirely appropriate to any particular inquiry. Between these 

 characteristic dangers of the intensive and extensive methods respectively we have 

 to steer our difficult course as best we may. 



The peculiar dangers of the intensive method are so obvious as net to need 

 special emphasis. Everyone is aware that better results are obtained from a wide 

 than from a narrow range of observations, and indeed I think that the besetting 

 error of the public is to attach too much rather than too little importance to this 

 defect. It requires a trained observer to understand how few samples if honestly 

 chosen at random suffice to give a good approximation to the truth. 



But one special difficulty which attends the extensive method often receives, 

 I think, less attention than is its due. 



Statistical investigations which cover very large masses of returns and are 



1910. x x 



