cxxxviii Tables for Statisticians and Biometricians [XXV 



In the above case of " Student " HI = n% = 10, and s^ = 170, s z = 1'90, mi = 0'75, 

 ma = 2-33. 



I .KO 



Accordingly x' = - ^ = "4382, and x' z = 1920, 

 2-5495 V2 



x' 2 



while x=z 75 ='1611, 



1 + x 2 



and we must look up the column for n = 19 in Table XXV. We have : 



x Function 5 2 



16 -959,7231 - 6554 S 4 may be neglected 



"17 "964,5820 5745 for present purposes. 



# = 11, < = -89, 6ty = -016,3167. 



Required result = '960,2576 + '000,0306 

 = -960,2882. 



The chance accordingly of x' exceeding the limits '1611 is '0794, or the odds 

 against this are about 11*6 to 1. 



This is roughly in keeping with the previous determination. Or, we conclude 

 that there is some, but far from overwhelming, evidence that a population treated 

 with the laevo- form of the soporific would have longer hours of sleep than another 

 sample of the same population treated with the dextro- form. On the otlier hand, 

 if we can trust the application of formula (e) to the case where the samples are 

 not independent, then the odds are 344 to 1 that the same individual gets longer 

 hours of sleep from the laevo- than from the dextro- form. 



The difference lies and can lie only in the correlation in the individual between 

 hours of sleep due to the two forms. What real trust, however, can be put upon a 

 correlation due to 10 pairs ? We need, further, some more definite demonstration of 

 how (e) applies to this case with u v = 0, which seems to involve the assumption 

 that u and v are drawn at random from the same population. 



Now it is most important that the worker should understand what "Student" 

 is really supposing in this special illustration and in others like it. His first 

 hypothesis is that u = v, and he then seeks to find out whether m u = m v . Thus the 

 question he is asking is this: What is the probability that dextro- and laevo- 

 hyoscyamine hydrobromide will produce different soporific effects on the same 

 individuals provided they produce the same effect on different individuals from the 

 same population? Not unnaturally he finds a high improbability, because it is 

 excessively unlikely that the two drugs should produce identical effects on the 

 population at large. He is measuring that improbability as well as the improbability 

 of their producing the same effect on the same individuals. How much of the im- 

 probability is due to one or other source cannot be ascertained without duplicating 

 the experiment, i.e. by first experimenting on different individuals from the same 

 population to ascertain whether it is reasonable to put u = v, or if not, to get some 



