6.2 Constant errors. 
  
meter | 6.20 We shall use the following notations 
: | S, — the standard deviation of the total error within a single model (the constant error excluded), 
. S, — the standard deviation of the random error within a single model, 
S2, — S*, — S?, = an estimation of the systematic error (the constant error excluded), 
2 19 
12-1 -— = = = — (he multiple correlation coefficient. 
) 1 
6.21 The constant errors were calculated twice, as the mean M (Tables 1: I—III) and as the constant term 
of the regression function (5.4). These two calculations were identical. The standard deviation S, of the 
. residuals around the regression function was calculated at the regression analysis. The expression S5:n is 
an estimate of the dispersion of the constant error. The following tests were made. 
6.22 Hypothesis. The means of the errors for X, Y, Z; L4,,p and L4 g within a single model can not 
  
  
  
M—O 
* . qut * ry * . 4 0 ^w 
differ significantly from zero. The hypothesis was tested with u — n , where s = S,, or s = Sa (only 
for X, Y and Z) and may be rejected as false at the significanse level of L % if u = uy (u; = 1.96; 
uj = 2.58; Up; = 3.89). 
The results were given in the following table. 
Table 6. Test of the hypothesis that there were no constant error within a model. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
S Number of models 
Strip 
and X Y Z L4,p and Lap | Remark 
model 
No 5% 1% 0.1%| No 5% 1% 0.1% | No 5% 1% 0.1% | No 5% 1% 0.5% 
A 6 2 | 3 5 2 6 1 5 1 
I B 5 1 1 1 3 1 4 4 1 3 3 5 
= 11 1 1 3 | 6 1 9 6 1 9 4 5 6 
A Se a6 isd wl igi à | 4 2 2 3]: Test 
IT B 4 4 3 2 9 2. 2.1.5 4. 1 1 4 with 
> 7 5 1 9 3 19 1 3 1 13 8 3 3 7 S 
A 2 2 3 1 6 | 1 1 4 5 1 
III B 3 1 3 7 1 5 1 1 1 3 
à ging vy 6 1 13 | 1:2 9 6:1 23 
A 6 2 5 1 1 6 
I B 3 1 1 3 1 ] 6 3 l — 1 
x 9 ] 1 5 1 1 11 4 1 1 10 
y the T 
A 3 8 1.10 2 1 8 l'est 
IT] B 2 1 3 + ] 1 9 2 1 1 6 with 
V X 6 1 3 12 1 1 1 19 4:2 1M 8; 
listri- 
e le- A 2 5 1 6 1 — 5 
IH B 1 6 7 1 5 
- 2 11 1 13 1 1. 10 
"he conclusion must be, that there were constant errors within every model and strip for each of X, Y, 
Z. LA-B and LA. p. 
6.93 It must however be studied if those constant errors within single models remain constant in a set of 
repeated measurements or if they change eventually to random character within the set. It was tested with 
takes ue : 
the t-distribution. 
le in 
here. The result was given in the following table.