OF ATT1MIII ll> IN STATISTICS 



an instance, but the figures I found most suitable to my purpose are attack-rates not 

 death-rates. The following table gives the (percentage) small-pox attack rate, in 

 houses actually invaded by small-pox, of persons under and over 10 years of age, in 

 five towns in which small-pox epidemics have recently occurred.* 



From these data we can work out the association between " lack of vaccination " and 

 " attack," for children and persons over 10 years of age. If we call attack A, " non- 

 vaccination" B, the data given are 100 (A/3)/(/3) and 100 (AB)/(B) ; subtracting each 

 percentage from 100, we get 100(a0)/() and 100 (aB)/(B). Thus for the coefficient 

 of association in Sheffield for children we have 



67-6 x 92-1 - 32-4 x 7'9 



" 67-6 x 92-1 

 = -92 



+ 324 x 7-9 



where we have divided through numerator and denominator of the ordinary expres- 

 sion for Q by (B)(/8), leaving its value unaltered. This seems rather an interesting 

 case, as the form in which the data are presented does not give the surplus ratio for 

 non-vaccination, i.e., the ratio of non-vaccination to vaccinated, but does give the 

 association coefficient Q. The whole series of values are given below, and form a 

 striking addition to the previous table. The association between non-vaccination 

 and attack is very high indeed for young children *8 to '9 but drops sharply to 



Association between Non-vaccination and Attack in Infected Households. 



* I have taken the table from Mr. NOKI. A. HUMPHREY'S paper, "Vaccination and Small-Pox Statistics," 

 'Journal Royal Statistical Soc.,' vol. 60 (1897), p. 525. It is quoted by him from the 'Final Report of 

 the Yttccitiation Commission,' p. 65. 



VOL. CXCIV. A. 2 P 



