cxxxiv Tables for Statisticians and Biometricians [XXV 



The integral there given is 



/; 



f 



Jo 



o 

 In our case p = \ (n 3) = 3'5, 



1 1 / <? \ 2 



u = -j=,z = -~ ^77=) =5-0516. 

 V4-5 4 V4-5 WV2w/ 



For interpolation in excess of mean we have from the above tables, under 

 p = 3-5 : 



Argument Entry S 2 s 4 



5-0 '988,2633 -2497 Negligible 



51 -989,8982 -2185 



6 = '516, < = -484, 00 = -041,624. 

 Required value = '989,1069,1 +'000,0292,1 



= -989,1361, 

 or the chance of values of s as great as or greater than 14'64 = '010,8639. 



If on the side of defect we take as limit 14'64 10 = 4'64, we find u = '5074. 

 Our tables give : 



Argument Entry 5 2 5 4 



0-50 -010,5995 +37648 -2442 



0-60 -020,3677 +43857 -2855 



#=074, </> = -926, #</> = -011,4207, ^(1 + 0)(1 + <) = -103,4202. 

 Required value = -011,3223,5 - "000,1366,1 - -000,0015,4 

 = -011,1842. 



Accordingly the probability that s will differ from the population value by as 

 much as or more than 4'64 



= 010,8639 + -011,1842 



= -022,0481, 



or the odds are about 44 to 1 against the occurrence of such a deviation from the 

 population standard deviation. Now it would appear that these two sets of odds 

 36 to 1 against such an excess in the mean and 44 to 1 against such an excess in 

 the standard deviation especially when we remember that by our hypothesis as to 

 the parent population these two results are independent are entirely screened 

 when we apply " Student's " test, with its odds of only 4"5 to 1. The fact is 

 that when the two characters, on the ratio of which " Student's " test is based, 

 deviate in the same direction, this test may be very misleading, when we use 

 it as an indication of the rarity of a particular sample ; it is the measurement 



