cxviii Tables for Statisticians and Biometridans [XXI XXII 



which W n is the limit at which, for a sample of n, the chance of obtaining a range 

 greater than W n (measured in terms of the population standard deviation as unit) 

 isp(p=-10, -05 and '02). 



Illustration. In the paper referred to "Student" has discussed some of the 

 problems involved in routine analysis, and has suggested criteria for determining 

 whether a given observation should be discarded and repetitions undertaken. The 

 reader who wishes to use this method must refer to the original paper, but the 

 following example will illustrate the use of the tables in the simplest form. 



In the ordinary course of business a firm needs repeatedly to undertake a certain 

 form of analysis, let us suppose to measure the moisture in a sample of grain. Five 

 analyses are made of the same material, giving values 



22-8, 23-9, 25-5, 26-0, 26'6. 



Far the greater part of the variation between these values will be due to errors 

 of analysis, and it is advisable in taking the mean values to discard any particularly 

 erratic observation. Previous work has shown that the standard error of analyses 

 of normal accuracy undertaken at the same time upon the same sample of grain is 

 0'675. In the present case the range in terms of this standard error is 



w 5 = (26-6 - 22-8)/(-675) = 5'63. 



If it be assumed that the distribution of repeated analyses follows approxi- 

 mately a normal curve*, then the tables show that in samples of 5 the distribution 

 of w has the following constants : 



w= 2-326, <r w 



From the small table above (based on the Pearson curve with these moments) 

 it is seen that W 5 corresponding top = '02 is only 4'3; that is to say a sample with w 

 as large as 4'3 will only be expected to occur in two random samples out of 100, 



* That is to say the distribution of normal or reliable analyses. Experimental work by E. S. Pearson 

 and Adyanthaya, Biometrika, Vol. XX A . pp. 357 358; "Sophister," ibid. pp. 394 395, and other un- 

 published results suggest that while w in sampling remains very constant whatever the population may 

 be, ff w and /3j and fa alter considerably with changes in population form. 



