XXV] Introduction cxx \ \ i i 



Kiitcring our Table XXV with n 10, we hn\ 



x Function S 1 d 1 



64 -998,4448 -215 Negligible 



G5 -!>!)8,<;380 -196 



= -57, < = -43, 0</> = -04085. 

 Required value = -998,5549 + -000,0025 



= 998,5574. 



"Student" gives the value "9985, quite in keeping. 

 The chance therefore that x' will not lie between the limits 1*35 



= 2 x -00144 = -0029 nearly, 

 or the odds are 997 1 to 29 against it or 344 to 1 against it. 



Now let us suppose the 10 patients who had dextro-hyoscyamine hydrobroraide 

 were not identical with those who had the laevo- form, and that the standard 

 deviations remained the same. Then there is no doubt about the application of 

 formula (e). If we suppose them to be independent samples of the same population 

 r = 0, and u = v. In this case m u m v = 2*33 0'75 = T58, and 



0) 2 + (l-90) a 

 = 2-5495. 

 Thus x' = T58/2-5495 = -6197, #' 2 = -3840, 



r /a 



and x-~ ^ = '2775, and n = 10. 



1 + x 6 



We have from Table XXV : 



x Function 8- d 4 



27 -949,3108 -2475 Negligible 



28 -952,9130 -2318 



# = 75, < = -25, 00 = -0336. 

 Required value = -952,0124 + -000,0224 = -952,0348, 

 or the odds are about 9'4 to 1 that x' does not lie in the range -6197. 

 These odds are by no means great. 



A further test which has been provided* to determine whether two samples, 

 of which the means are m lt w 2 and the standard deviations si and , have been 

 drawn from the same normal population, has been further discussed recently by 

 J. Neyman and E. S. Pearson f. 



_ / 



3V 



We take x' = 



and its distribution curve is 



.('). 



* B. A. Fisher, Metron, Vol. v. p. 7. t Biometrika, VoL XX A . pp. 175 et teq. 



B. II. * 



