ON THE AMOUNT AND DISTRIBUTION OF INCOME. 179 



sufficient information to form an approximate estimate; for others we 

 must proceed by results of common observation or by guesswork. It 

 is intended throughout this part of our Report to show clearly the basis 

 of our estimates, and to put them in such a form that it will be possible 

 for each item to be amended if further information can be obtained. Our 

 information is adequate as regards the Civil Service, Local Government, 

 the Army, Navy, the clergy, elementary teachers, banks, and railway 

 servants. It is sufficient for an estimate for clerks, farmers, and shop 

 assistants. In some other cases, viz., professional, under our classes b 

 and 8, and merchants, we may assume that the great majority pay income- 

 tax. In the remaining cases we must do the best we can to find limits 

 to the aggregate income, which will not contradict any of the general 

 data we have. The weak point of previous estimates of this intermediate 

 income has been that no attempt has been made to determine any limits 

 within which the aggregate may be definitely expected to lie. The late 

 Sir Robert Giffen and some other writers have been content to find a 

 lower limit and say, for example, that there is at least 200,000,000L in 

 this group. Others, following the example of Dudley Baxter, who 

 initiated this inquiry in 1868, have been content to make the best guess 

 they could, without attempting to assign its precision. We propose, on 

 the other hand, to state (wherever any check can be obtained) the superior 

 and inferior limits of the number and of the average income of the non- 

 tax-payers in each group, and hence to compute a measurement of 

 precision of the aggregate. 



The theory of probability, especially that part related to the Law of 

 Great Numbers and the normal Curve of Error, will afford some help. 

 In each case we have endeavoured to assign, in the light of all the in- 

 formation available, whether published in this Report or omitted as too 

 confidential or for want of space, limits within which it seems highly 

 probable that the true measurement must lie. The modulus in the Curve 

 of Error shows the deviation which will only be exceeded in either direc- 

 tion once in six times in the long run, and we believe that we can assign 

 the numbers, not differing greatly from such a modulus for the various 

 classes. This does not mean that we can assign definite odds of five to 

 one against the quantity measured being outside the limits we give, but 

 that we can obtain numbers whose ratio to such a modulus will not differ 

 greatly from unity. The numbers following the sign + in our estimates 

 are all to be interpreted in this sense. 1 Having obtained these moduli for 

 all the items it is a known problem to combine them by the theory of 

 error into a modulus for the total. Accordingly this section of the Report 

 will be devoted to assigning estimates for each of the thirty -one classes, 

 and then grouping them together. 2 



It must be clearly understood that the main purpose in this Report 

 is to tabulate our knowledge or our ignorance as to the Intermediate Group 



1 We use the modulus here in preference to the ' probable error ' or the ' standard 

 deviation ' which express smaller improbabilities. 



a It should be understood that the estimates in this section of the Report have 

 been made by the Secretary, who alone has had access to the information accumulated, 

 and that the other members of the Committee have only given a general assent to 

 them, 



