BOYCOTT: LOCAT, VARIATION OF CT-AUSIT.IA BIPENTATA. T3 



variable population ; if it is more, it is tolerably certain that the 



populations from which our samples have been collected are really 



different in size. In the present instance, the difference between 



the means is o"i m.m., i.e., only oS times the standard error, and 



we conclude that this is not significant, i.e., there is no evidence 



that the snail communities from which the samples were taken 



differ in length. Two samples from A or B might easily have given 



means differing by ci m.m. Suppose a third sample from locus C 



had consisted of nine specimens measuring 10*4, io'5 1 1 '3, 



mean lo'S : then the difference A/C would have been o"4 m.m., 



0.4 

 which is = T,"x tunes its standard error and siunificant, and 



0'122 & ' 



we should judge that the population in locus C did really differ 

 from that in locus A ; C would not, however, be significantly 

 different from the sample from locus B, as the difference would be 



° 3 

 only = 2't: tniies its standard error. 



■^ 0"I22 ^ 



This curious series, A different from C, A not different from B, B 

 not different from C, emphasizes a point of importance. A significant 

 difference means a difference ; a non-significant difference does not 

 mean identity, but only that on the evidence we have we cannot con- 

 clude that there is a difference. The influence of the number of 

 specimens examined on the standard error of the difference points 

 this still more clearly, and, as I take it, it would be impossible to 

 demonstrate identity of size unless we could measure with infinite 

 accuracy the whole community under examination. The conclusion, 

 therefore, that " M is not different from N," is not the same as that 

 " M is the same as N," though for many practical purposes we look 

 on them as interchangeable. 



Why these things should be so, I do not pretend to understand. 

 It is evident that making three times the standard error of the differ- 

 ence the limiting value is fixing an arbitrary limit, and it will occasion- 

 ally happen that significant differences will be found between samples 

 collected from the same population, just as non-significant differences 

 may be determined for lots of shells taken from communities known 

 to differ in the size of the individuals which compose them. But the 

 rule seems to work very well in practice, and some of the material 

 collected at Portmadoc enables us to put this particular pudding to 

 what will appeal as the soundest test to those of a pragmatical turn 

 of mind. 



Thus from one locus (A) I have five fairly large collections, the 

 germane particulars of the length of which are — 



