xxiv 



Tnlilta fur S/,iffxfii-fnnfi mill /if 



[IX 



TABI.K IX (pp. 2223) 



Values of the Incomplete Normal Moment Functions. (Calculated by Dr Alice 

 Lee, Biometrika, Vol. vi. p. 59.) 



The nth incomplete normal moment function is defined to be 



We take 



I B (x) = fin(x)/{(n I ) (n 3) (n - 5) ... 11 if n be even) 



) (xvi), 



= ,*(*)/{( -l)(n-3)(n- 5). ..2} if n be odd J 



and m n (.') is the function tabled. 



In multiple correlation (supposed normal), the frequency surface is 



X -ix* 



z ~ 1 



x (ivii), 



where X* = I? I (Rpp^p'/Gp") ~^~ 2<S ^Rpy-l'p^g/O'pO'q)} 



and Ji= 1, r,,, r u ...r ln (xviii), 



',, 'V., '... 1 

 while Rpp and 7? OT are the usual minors. 



%* = constant is the "ellipsoid" of equal frequency in n-dimensional space. 

 The total frequency, i.e. the volume of the surface, inside any ellipsoid % is 



7^= f*zdV 

 Jo 



J r Iff _ \2Tpn-l(X) 'f ] ,} 



*' = 2 4. JR ... (n-2} 



.(xix). 



if be odd 



Thus a knowledge of the incomplete normal moment functions enables us 

 to predict for multiple variables whether an outlying observation consisting of 

 a system of n variate values is or is not reasonably probable. 



If I X JN=%, we obtain the 'ellipsoidal' contour ^ within which half the 

 frequency lies. This x<> ' s fc he "generalised probable error" of Pearson and Lee. 



