51i ^ peeslde:n'i's address. — section" gi. 



immediately comparable with similar results for other countries. To 

 "be immediately comparable, the two populations must be identically 

 ccnstituted as regards all releA'ant particulars. 



In respect of bii'thrate, for example, in order to compare two 

 populations, they should be similarly circumstanced as regards con- 

 stitution according to sex and age, and, indeed, also as to mamage 

 rate at each age, and also as to general economic conditions, or else 

 the results must be so corrected as to represent what would have been 

 given if they were thus similarly circumstanced. 



Special inquiries may involve special treatment by way of correc- ' 

 tions to be applied. For example, fertility varies with age: con- 

 sequently, to ascertain whether the expression of the maternal instinct 

 is equally efficient in two countries, the birthrates must be referred to 

 that of a standard population definitely constituted as regards sex and 

 age, preferably to the mean of the tAvo, or better still to a population 

 which could be regarded as normal according to some specific 

 definition. Since fertility is greatly influenced by marriage, a really 

 valid comparison requires, further, that the distribution of marriage 

 according to age should also be identical, or should be corrected for, 

 and still further — forasmuch as marriage is profoundly affected by 

 economic conditions — the distribution of economic condition according 

 to age must also be regai'ded as a factor affecting fertility and, there- 

 fore, also birthrate. 



For many purposes, therefore, crude birth and death rates are 

 very misleading. For example, the crude death rate for 1907 in the 

 Commonwealth is only 10'90, but the index of mortality is 14'37, 

 and this would be the actual death rate, if, while the proportion of 

 deaths in each age-group remained the same, the Commonwealth 

 population was identically constituted with that of Sweden, the con- 

 stitution of whose population has been taken by statisticians as a 

 basis for comparisons. 



Another illustration — viz., one of an economic character — may 

 be taken. A comparison of the total trade or the exports or imports 

 of two years expressed in money value, is obviously vitiated by change 

 of price, since an increase in value may actually correspond with a 

 decrease in the quantity of commodities. For this reason it is 

 necessary to use index mimbers, or the ratios of the prices of 

 commodities at the two periods compared, in order to so analyse 

 the crude result as to know how much is to be attributed to increased 

 volume of trade and how much to mere change of price. 



The science of modern statistics, Ave thus see, tries to penetrate 

 beneath the first appearances of the data, and endeavours to eliminate 

 before comparison those elements which would vitiate the comparison, 

 or failing this, to so correct the crude data as to make them fully 

 comparable for any specific end in view. 



II [.—THE EAXGE OF THE PROBLEMS OF MODERN STATISTICS. 

 1. Classification of Statistics. — There is and can be no unique 

 classification of statistics, for the reason that the matter of its sub- 

 divisions, under A^arious schemes of classification or from A'arious 

 points of view, overlap. Broadly speaking, however, the facts may 

 be ranged under two great headings, Vital and Economic. Even in 



