96 MODES OF RESEARCH IN GENETICS 



prediction of future events, gives only a knowl- 

 edge of betting odds, one may ask : what about 

 the whole concept of probable error? The value 

 of this concept in scientific research is unquestioned 

 (cf. p. 59, supra). Yet plainly the whole concept 

 has its basis in the calculus of probability. Has 

 not our discussion led us unwittingly into a serious 

 contradiction ? 



I think not. Let us examine the probable error 

 concept a little more carefully than we have yet 

 done. Suppose we read that the mean length of 

 the thorax of a thousand fiddler crabs is 30.14 ± .02 

 mm. Just what does this actually mean ? Ac- 

 cepting the figures at their face value, or, put 

 another way, assuming that the mathematical 

 theory on which the probable error was calculated 

 was the correct one, the figures mean something 

 like this : If one were to take, quite at random, 

 successive samples of 1000 each from the total 

 population of fiddler crabs and determine the mean 

 thoracic length from each sample, these means 

 would all be different from each other by varying 

 amounts. In other words, no single sample 

 would give us the absolutely true value of the 

 mean thoracic length of the whole fiddler crab 

 population. This true value is in an absolute 

 sense unknowable, because, for one reason, always 

 we must come at the finding of it by the way of 

 random sampling, and sampling means variation. 

 Now it is an observed fact of experience that the 



