XXXV- \\.\VI] lntrtnlin-ti,ni cl\\\i 



It will !>< rioted that if n be not too small the system of curves (in) t< nd to 

 \\ith the contours of the (if, &) frequency ^mtui.- (ii), or 



In :iny ;_;i\'ii jtrol.lrm, if n<50, the following pro-<-duiv should In- parried <.ut : 

 (a) Find M = (.7 a)/<r = w/er and S' = /<7. 



(6) Using M arid $ as coordinates, obtain a valno for / from Diagram* 1 or 2 

 over page. A more accurate value for k could be ol.tained from equation (iiij, but 

 an estimate to two decimal places obtained from the diagrams will gcm-mlly lx? 

 (jnite sufficient. 



(c) Find P x by entering Table XXXV with n and k. 

 If however n > 50 we may proceed as follows : 

 (a') Find k as in (b). 

 (b'} Calculate X from the relation log, X= |(log w e k). 



(c') Obtain the ratio P A /X by entering with k the auxiliary Table XXXVI 

 (p. 223). 



(d 1 ) Multiply this ratio by the \ of (b') and so find P A . 



Illustration, (i) Measurements of 884 Egyptian skulls (XXVI XXX Dynas- 

 ties)* gave for the distribution of cephalic index, mean = 75-06, standard deviation 

 = 2'68. Would it be justifiable to consider that the 10 skulls with cephalic indices 

 as follows 667, 69'4, 67-8, 73'2, 79'3, 80'7, 64'9, 82'2, 72-4, 78'lf were a random 

 sample from this population ? 



The distribution of cephalic indices is in general found to be symmetrical but 

 somewhat leptokurtic; we shall assume however that if /Si = but/9 = 3 < 4 to 3'5, 

 the use of the P A test is still valid J. It is found that 



x = 73-47, 5=5-942, M=-'593, S=2'217, 



and the sample point falls near the contour k = TOO in Diagram 2 (p. clxxxiii). (N.B. 

 in the diagrams m/a- is written for 3f and */<r for S.) A reference to Table XXXV sho\\s 

 that for ?i=10, ^ = 1'60, P A is less than '0001. From the position of the point in the 

 diagram it will be seen that the divergence is mainly due to a very large value of* 

 compared with a-; the mean is not exceptionally divergent from the supposed jkipu- 

 lation mean 75-06. We should conclude that it was very improbable that the 10 

 skulls were a random sample from the Egyptian population, and that probably the 



* Values taken from Sionutrika, Vol. xvi. Tables II and III, pp. 337 and 338. 

 t Ten crania selected from a London graveyard of the 17th century. 



| Neyman and Pearson showed experimentally that in the case of samples of ten from a population 

 for which /3 1= -2193, /3 2 = 3-1677, the use of the test was still valid. 



