LI I LIT") /iitroi/uctitm cc\l\ 



I It-nee by (i): 



R* - 1 - H x 491),9.-)82 = 525/2f)i2, 



which agm-H with the value /,'- - -f>:>.v; tfiven by I)r WiHh.-irt Inm, the hyper- 

 "inrtrii-.-il series. 



Now turning to Table LIP" to find 7,, we have for tf=100, and 0= 071 

 = -!)29 aa before: 



*o= '265,0540, *t = -133,7050, % = f 010,6294, S**! = + "035,4198. 

 Hence : 

 zo = "929 x -265,0540 + "071 x "133,7050 - -010,!)!':; 



x {1-929 x (-016,6294)+ 1 071 x (-035,4198)1 

 = 254,9586, 



which is 72 for N = 100. 

 Similarly for JV=20(): 

 z e = -929 x -262,5877 H- -071 x -131,6374 - -010,993 



x {1-929 x (-017,8219)4-1-071 x (-036,2360)) 



= -252,4857 = 72 . 



Interpolating for JV= 101, linearly we find: 



71- -254,8889. 



Then by formula (ii) 



^V = 93 x T <$- x -254,9339 - (-474.7078) 2 



= -0047,2806, 

 or o-^a = -0688. 



Illustration (iii). In a sample of 24, the multiple correlation coefficient for four 

 variables was found to be "5836. What is the best value to give to the multiple 

 correlation in the sampled population? 



We cannot at present solve this problem fully. In any single sample we are 

 more likely to have found a coefficient at the mode of the distribution than else- 

 where. But as this modal value has not so far been tabled, we are compelled to 

 adopt the mean as the best substitute for it. Accordingly in this case we have: 



24, 4. 

 * 



or 7i = M x 1'5836 x "4164 = -725,3521. 



For ^=24, this value of 7l lies between the '5 and '6 values of p. We can 

 now apply the inverse interpolation formula (iv) of p. xiv of Part I of this book of 

 Tables. We have 



wo = -732,2999, 



M! = -630,821 7, Ai/ = -'101,4782, 



// 2 = -508,4988, Af/! = - -122,3229, A*M = - -020,8447. 



