where 
: -i - 
Mia 7 (Pss)an(Pss)11(Pss)12(Pss)22 . (14a) 
as =1/2 -1/2 E 
Ko Us UR. = 102 0 (IL) 
Because of the quadratic dimension of statistic T4 and To» the 
following global correlation 
pe Prt, (15) 
  
G 
  
  
  
is defined, in order to compare it with the others which are 
normally defined. 
The value »g describes a global correlation between two multi- 
dimensional alternative hypotheses. When it is equal to 100%, 
the two alternative hypotheses are in any case not separable. 
For each given direction s,and 89 of parameter vector VS, and 
vs, à correlation coefficient P12 can be obtained from 
ena si (Pss)1252 
12 STONE * (16) 
(SiPss)1$1 ^ "S2(Pss) 2252 
According to the derivation from Fórstner(1982) and Li(1985) 
the maximum value of Py» and the corresponding direction 8; and 
  
  
  
  
  
8 are determined as following: 
: 4 177 
(012 max 7 * max 12) ! (17) 
and 3 -T 
C (Pss Yi Pss is (Pss) jj (Pss) ji 7 PmaxU hal 150 7 955 (18) 
  
  
  
which are the solutions of the eigenvalue and eigenvector 
problem. 
2.5 Reliability measures under two alternative hypotheses 
The reliability measures under a single alternative hypothesis, 
i.e. internal and external riliability from Baarda are well 
known. By means of the separability multiplying factor we can 
Obtain the similar measures for the case with two alternative 
hypotheses. 
As a measure of controllability Or internat reliability for 
a single alternative hypothesis the lower bounds for detectable 
errors or the estimability of additional parameters are already 
- 191 =