NATURE OF STATISTICAL KNOWLEDGE 97 



variations due to random sampling distribute 

 themselves according to a definite law of mathe- 

 matical probability. Knowing this law, it is 

 clearly possible to state the mathematical proba- 

 bility for (or against) any particular deviation or 

 variation occurring as the result of random sam- 

 pling. Exactly this is what the probable error does. 

 It says, in the particular case here considered, 

 that it is an even chance, that a deviation or 

 variation in the value of the mean as great as or 

 greater than .02 mm. above or below will occur 

 as a result of random sampling. Or, put in 

 another way, if we took successive samples of 

 1000 each from this crab population, it is an even 

 bet that the value of the mean from any sample 

 would fall between 30.14 + .02 = 30.16, and 

 30.14 - .02 = 30.12. 



Now all the knowledge that this probable 

 error furnishes is this : that if a man were to say, 

 "I'll bet a thousand dollars that the mean thoracic 

 length of the next sample of fiddler crabs you 

 measure will be either over 30.16 mm. or under 

 30.12 mm.," one would not be justified in offering 

 odds. He could wager on even terms. Either 

 party involved in the transaction would be as 

 likely to lose (or to win) as the other. 



Putting the case in this way, it is clear that this 

 is the same kind of knowledge which comes from 

 an examination of probable errors as that dis- 

 cussed in the preceding section. It is a knowledge 



