100 REPORTING PROGRESS 



before, and the results compared. But there must 

 be no " jumping " to conclusions. It is quite insuffi- 

 cient to examine a hundred schoolchildren and to find 

 only two of them absent for fever, where formerly 

 five were laid up, and then to conclude that there is 

 a reduction in the town of three per cent. Such a 

 conclusion is quite unjustified. There would be such 

 a statistical error that the conclusion would be wrong. 

 This is random sampling, and it gives erroneous im- 

 pressions. Strictly speaking, all the schools in the 

 town should be examined at least once a year, and 

 more frequently if possible. Omit no detail, and be 

 careful and painstaking it will be well rewarded. 



Collect all the figures available, and correlate 

 them. The percentages must be worked out from the 

 whole, not from individual units. Remember that 

 " averages are numerical expressions of possibilities ; 

 extreme values are expressions of probabilities." 

 Also that " the value of a series of observations in- 

 creases with the number of observations ; the value 

 of the deductions with the square root of that 

 number." How frequently official reports claim the 

 reduction of a disease in a large community because, 

 out of a hundred in-patients treated in one hospital, 

 ten per cent, suffered from that disease compared with 

 fifteen per cent, the year before 1 Such an inference 

 is not only unjustified, but is actually incorrect. If 

 deductions are drawn from percentages or averages, 

 large numbers must be employed. 



An interim report should be published. It should 

 describe the area dealt with by the mosquito mea- 



