ccxliv Tables for Statisticians and Biometricians [LII LII 6 '* 



Owing to the great range of values it is possible for N to take, the Tables only 

 contain a series for N proceeding by units from 3* to 25, and then by values up 

 to 400 admitting of logarithmic calculation. For values of N >400, Hall's formulae* 



(v), 

 (vi), 



will suffice, except when p is very small, when it is better to take the first few 

 terms of Wishart's hypergeometrical expression for 72. 



Illustration (i). For a sample of 400 from a normal population with five 

 variates, and p = '4, what are the values of R z and o- 2 ^? 



Here without interpolation we find from (i) and (ii) by aid of our Tables LII 

 and LII to : 



fi?= -16776, (rV = -001,129, 



and from Hall's formulae (v) and (vi): 



]R2 = -16773, <rV = -001,086, 

 the two sets of results being close enough for most practical purposes. 



Illustration (ii). Dr Wishartf gives the following example: -AT=101, n = 7 

 and p z = -5. What will E 2 be ? 



We take p = '7071, and first interpolate for p corresponding to ^=100 and 



We shall use Everett's Central Difference formula to S 2 terms (see p. xlv) with 



6 = -071, <f> = -929. 

 For JV= 100 we have from Table LII: 



2 =-509,8429, ^ = '360,9965, S z z = - "020,5732, S 2 ^ = - -020,9530. 

 Hence : 



z e = -929 x -509,8429 + "071 x -360,9965 



- i (-929 x -071) {1-929 (- -020,5732) + l'07l (- -020,9530)} 

 = -499,9578, 



which is 7! for N= 100. 

 Similarly for JV=200: 

 * = -929 x -509,9355 + -071 x '360,5013 - '010,993 



x {1-929 x (- -020,2884) +1-071 (- -020,4733)1 

 = 499,9970, 



which is 71 for N= 200. 



Clearly linear interpolation will suffice to find 71 for N= 101, and we have 



7j = -499,9582. 



* Biometrika, Vol. xix. pp. 100 109, 1927. t Biometrika, Vol. xxn. pp. 357 and 360. 



