8 HISTORY AND INTRODUCTION Ch. 1 



ful degree — is a method of reasoning which enables us to induce from 

 relatively few samples useful information regarding the population 

 sampled. 



Inductive reasoning based on evidence obtained from samples 

 necessarily runs some risk of error; but as long as the extent of this 

 risk can be measured, the process offers real hope for useful appli- 

 cation. Much of the recent research in mathematical statistics has 

 been devoted to the development of methods of reasoning based on 

 sampling observations. 



The reader should not feel from the preceding remarks that sam- 

 pling is useful only in scientific research, because everyone is con- 

 stantly being confronted with sampling studies of one sort or an- 

 other. Radio advertising is quite full of alleged sampling investiga- 

 tions during which various products presumably have been tested and 

 shown to be superior. Life insurance premiums are based on samples 

 of mortality rates among insurable persons. Public opinion polls, 

 economic polls, and the like, often reported in the newspapers, are 

 attempts to reason from a sample to conclusions about a whole 

 population of possible responses to one or more questions. Persons 

 who have visited other parts of the world return and, upon the basis 

 of relatively small samples, attempt to say how whole nations or 

 societies are reacting to certain world events. The reader un- 

 doubtedly can think of many other examples of sampling followed 

 by more or less valid applications of either inductive or deductive 

 reasoning, or what might be better described in this instance as 

 statistical inference. 



In closing these introductory remarks, it seems fair to warn the 

 student that, as in many other lines of thought, he cannot immedi- 

 ately jump into interesting applications of statistical methods and 

 reasoning. He must first learn some fundamental principles and 

 some statistical tools with which to work, a process which necessarily 

 occupies most of the time in a first course in statistics. There is, 

 however, nothing to prevent him from reading the rest of the book 

 for himself, and from taking other courses in statistics. 



