aC- 
vue 
Hay leads, to 
~ 2 -. ^ 2 
Ele, /Han) = Ble [WJ + Won (15a) 
2 X 2 
Yoke = Sef (15b) 
Ap depends on the type I error size o, on the type II error size B(Ap) 
(B(Xp) * 1-P(II), P(II) = probability of accepting a false hypothesis) and on the 
degrees of freedom r, =, For a given a ,8(Ap); r we can find Ap by using Baarda's 
nomograms in /3/, pp. 21-23. 
If HA is true, then the estimators x and 6 are no more unbiased. If the effect 
of a gross error vector vl, in the observations upon the residual vector v has to 
p 
be computed then we obtain 
E(v/HR 197-9 EOv2[/030€ veu 1 (16) 
p 
vv. 7 71 
p yP Vlp ° (17) 
V 
Although in practical projects we normally don't know anything about the vector 
ep?- it indicates the relationship of the gross errors - equation (17) enables 
us to study the effect of an a-priori supposed gross error vector vi, upon the 
residual vector v. From (14), (15), (17) and from the idempotency of the matrix 
product Qn9r it follows for small gross errors 
An 7 N e 
I 
p pp 5 Np = cpPQ, ,PCp . (18) 
The vector vl; contains all assumed gross errors of the pth alternative hypothesis. 
If we suppose only one gross error in the observation i we get 
Tr 
> 
+ 
«1 
-—À 
Pt 
~~ 
— 
— 
" 
e cl" ; (19) 
and with c1 s (0,...0,1,0,...,0) 
Hay: MC e 827) : (20) 
combining (18) and (20) we obtain 
for diegonal P: 
m. d 
Hay: Vl O6 N1 , Ni = pit quivi ; (21) 
qyiv; = 1th diagonal 
element of Qyy 
Te pr) is the minimal gross error which can be detected with the probaility 
s{x17). Thus for a constant 34 for all possible i vr, (1) represents a suitable in- 
dividual reliability indicator ("measure for internal reliability" in Baarda /3/). 
Furthermore, Baarda /3/ has developed a test criterion for testing the residuals 
of an adjustment ("data-snooping"). If Ho is rejected, we get 
T 
-CpPv 
= : 22 
"o^ s Np (22) 
  
With one of the possible alternative hypotheses (615. Cp) s i from (14) and by 
using a weight matrix of diagonal form we obtain