CORRECTION OF DATA TOR ERRORS 



313 



bution of s's, as we might expect, is asymmetrical; the most probable 

 standard deviation s, to be obser\ed is not the average 5. Of course, 

 the customary theory assumes that the average 5 is the most probable 

 5, and that the distribution of 5 is normal. We should therefore expect 

 to tind the s's distributed normally for values of n such that the dis- 



1.4 

 1.3 



1.2 

 1.1 



1.0 



Ol 



PHOBABLE ERROR 



10 15 20 



SIZE OF SAMPLK - n 



3.5 

 3.0 



2.6 



o 



§ £.0 

 a 



1.5 

 1.0 . 



99.73'!j ERROR 



10 15 2( 



SIZE OF SAMPLK - n 



Fig. 5 — Chart showing magnitude of correction for size of sample — ratio of the errors 

 to their customarily accepted values 



tribution of obser^•ed standard deviations is approximately normal. 

 Now, Professor Pearson ^ has developed the theory underlying the 

 distribution of 5. He finds that as n increases, the distribution of ^ 

 rapidly approaches normality. Even for n greater than 25 the distri- 

 bution has approached normality to such an extent that we should 

 expect the z's to be distributed approximately in normal fashion. 

 The study of the distribution of z shows this to be true, as we shall 

 see below. 



In passing, we should note how closely the theoretical curve. Fig. 4, 

 fits the observed points and also note two other checks between theory 

 ' Log. cit. 



