L*~ d LIT"'! lnfi-uilii<-h,,i, Jiii 



'I'll. T\|M- I curve li.-us really been tilted to a hiMo^iMm ) presenting 



; in tins the frequencies corresponding ! j Oand j - \ \ irorepretv 

 by blocks Mandin- mi Insen 0'5 to -f - 5 and !()."> to I I -5 respectively. Dividing 

 theM I'l'H-U into |)ni|),.rl,i.inal parts at the dichotomies JC.HB (KH and ./.**, I I :;; 

 it will !> fiuiinl that, -01)50 of the histogram frequency lies below O'.'U an<l -0052 

 above ll'.'W, so that almost exactly !)!) / of the frequency licH between the In 



If it were assumed that the binomial might be represented by a normal 00 

 with mean and standard deviation ;is before, we should have 



-d.oo5 = 2-5758 = + d.96, #.006= -'01, z.t* =10-0 1, 



and it would be found that none of the histogram lies below #.005 while a proportion, 

 0100', lies above #.995. The limits taken separately are therefore not as accurate as 

 those found from the Type I curve, although taken together they do enclose nearly 

 99 /o f the frequency. 



TABLES Ll a ~ b . 

 See this Introduction, pp. clxx and clxxiii. 



TABLES LII AND LII 6 *. 



The distribution of the squared multiple correlation coefficient, 12*, in samples 

 from an indefinitely large normal population, in which this squared coefficient is p? 

 has been discussed by R. A. Fisher*, and the mean value of B?, which we call #*, 

 and its variance, o- 2 ^, have been shown by J. Wishartf to be given by the equations: 



(N-n)(N-n + 2) 



= - -*- 



where N is the size of the sample, n the total number of variates (i.e. R is the 

 multiple correlation of one variate on n 1 other variates), and, F being the 

 symbol for the hypergeometrical series: 



2 ) ..................... (iv> 



It will be seen that 71 and y 9 involve only the size of the sample and p 1 , but 

 not the number of variates. 71 and 72 had already been computed for another 

 purpose in the Biometric Laboratory and Tables of them were published as an 

 appendix to Dr Wishart's paper J. These are reproduced as Tables LII and LIP** 

 in the present work. 



* Proceedings Royal Society, A, Vol. 121, pp. 654673, 1988. 

 t Biometrika, Vol. MIL pp. 353861, 1931. 

 t Ibid. Vol. xxii. pp. 362367, 1931. 



y - 



