297 
included are 
parent dis- 
ples (Si, S2) 
Lbution a 
Lfference be- 
Dtained as 
(2) 
amber of 
an estimate 
but ion given 
(3) 
of S-| , S2 . 
(2) , has 
The second is an accurate procedure, by testing the 
normality of sample distribution, equality of 
variances and finally significance of differences in 
mean values. The samples Sj do not necessarily belong 
to a normal parent distribution and, if so, the 
variances of their parent distribution are not neces 
sarily equal. The goodness of fit of Si, S2 to a 
normal distribution can be assessed (Steel and Torrie 
1960) by calculating the value of the criterion: 
(4) 
where o^, e^ are the observed respectively expected 
occurrences in class i. To calculate e^, the normally 
distributed variable: 
(X - Xj) 
(5) 
is applied, with xj, Oj being the mean respectively 
the variance of sample Sj. Then the expected number 
of sample elements e^ in the i-th class, i.e. between 
zi and z^ + i are calculated on the basis of a normal 
distribution and of the total number of occurrences 
l i0i . Finally, the thus obtained x 2 ~value is compared 
with threshold x 2- values, corresponding with pre-set 
probabilities, to assess whether the observed dis 
tribution significantly deviates from a normal dis 
tribution. 
Assuming that the observed distributions belong to 
normal parent distributions, we have now to test the 
equality of variances. The following criterion can be 
applied (Kenney and Keeping 1959): 
F = 
(6) 
2 . 2 
where U is the larger and V the smaller estimated 
variance between: 
N 1 - 1 
and 
2 2 
s 2 = nT^-T 
(7) 
The F-value thus obtained is compared with the select 
ed threshold F, e.g.^with a probability P = 0.01 of 
F being larger than F. 
After having established that both samples belong 
to the same normal distribution, the Student's t-test 
can be applied according to the first procedure. If 
not, the following procedure has to be applied (Steel 
and Torrie 1960) : 
t = 
and 
(0) 2 _ V? + V2 
N 
1 + N 2 
(8) 
(9) 
The threshold t-value is obtained as: 
t* = 
Vi + V 2 
(10) 
with Wl = J- and w 2 = Л 
threshold t-values at the 
while t^ , t^ are the 
same level of probability 
Table 4. Goodness of fit of observed distributions 
against the normal distribution; observed values of 
TVI in field plots in the Grande Bonifica Ferrarese 
and East Sesia irrigation districts (Po valley, Italy); 
reflectance measurements obtained with the LANDSAT 
TM, band 4 and 3; x 2- values having a probability 
P = 0.05 respectively 0.01 to be exceeded are in 
dicated (s = significant, ns = not significant) 
Variable 
Plots 
ВАЗ 
CA4 
CA2 
IA2 
0B2 
Total frequency 
4 
25 
49 
25 
77 
Skewness 
-0.1 7 
-0.05 
-2.4 
-0.05 
1.41 
Kurtosis 
317.1 
664 
2289.9 
44.7 
3.81 
X 2 
0.24 
7.4 
32 
6.9 
18.4 
X 2 (P = 0.05) 
3.84 
11.1 
7.8 
6.0 
7.8 
X 2 (P = 0.01) 
Deviation from 
6.63 
15.1 
11.1 
9.2 
1 1.3 
normal distr. 
ns 
ns 
s 
ns 
s 
Table 5. Significance of differences in TVI-values, 
as obtained with LANDSAT TM 4 and TM 3 measurements 
(2 May 1985), Grande Bonifica Ferrarese, Po-valley, 
Italy; significance assessed by applying the accurate 
procedure respectively the simplified procedure 
(within brackets); ns = not significant, s = signif 
icant at probability P = 0.05, hs = highly signif 
icant at P = 0.01; for plot coding see text; largest 
observed differences in seeding dates: BB1, 30 April; 
BB2, 16 May; 0B1, 5 April; 0B2, 12 May; IB1, 10 April; 
IB2, 7 May 
Plots 
BB1 
BB2 
0B1 
0B2 
IB1 
IB2 
BB1 
hs (hs) 
hs(hs) 
hs (hs) 
hs(hs) 
hs(hs) 
BB2 
- 
hs(ns) 
s (ns) 
hs (hs) 
s( s) 
0B1 
- 
s( s) 
hs(hs) 
hs( s) 
0B2 
- 
hs (hs) 
hs( s) 
IB1 
- 
hs(hs) 
IB2 
- 
Table 6. Significance of differences in TVI-values, 
as obtained with LANDSAT TM 4 and TM 3 measurements 
(30 April 1985); East Sesia, Po-valley, Italy; for 
explanation of plot coding see text: ns = not sig 
nificant, s - significant at P - 0.05, hs = highly 
significant at P = 0.01; samples include between 20 
and 77 pixels; largest observed phenological dif 
ferences: CA1, full cover = 20 March; CA2, full cover 
= 30 April; BA1, seeding date = 15 April; BA2, seed 
ing date - 24 April; LA1, seeding date = 1 April; 
IA2, seeding date = 5 May 
Plots 
CA1 CA2 
BA1 
BA2 
IA1 
IA2 
CA1 
- s 
hs 
hs 
hs 
hs 
CA2 
- 
hs 
hs 
hs 
hs 
BA1 
- 
ns 
hs 
hs 
BA2 
- 
hs 
hs 
IA1 
- 
hs 
IA2 
-