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also be explained by analyzing the same data which was used for the validation. Sometimes
sample size t used in the surveys is not appropriate for detecting a rare event like the
appearance of first necrotic spots (Roßberg , et al. , 2000). It can also be difficult to recognize
the first symptoms at the leaves (the first spots of Cercospora could be taken for Alternaria
sp ., Phoma sp . or bacterial spots).
For an appropriate statistical validation (Racca , et al. , 2010b, Rossi , et al. , 1997a, Teng, 1981)
simulation and field data were regarded as two independant random samples to compare
the distribution. It is possible to apply some parametric tests like the t-test (comparison of
mean values) and the F-test (comparison of standard deviation), but also a non-parametric
method like the Kolmogorov-Smirnov test (computing the maximum distance between the
cumulative distributions of two samples) (Tab.3)
first appearance 50% infected fields
t-test F-test Kol.Smirn. test t-test F-test Kol.Smirn. test
1999 25 n.s. * * n.s. * *
2000 16 n.s. n.s. n.s. n.s. n.s. n.s.
2001 16 n.s. n.s. * n.s. n.s. n.s.
2002 27 n.s. * * n.s. n.s. *
2003 30 n.s. n.s. n.s. n.s. n.s. n.s.
2004 22 n.s. n.s. * n.s. n.s. *
2005 35 * * * * * *
2006 36 * n.s. * * n.s. *
2007 28 * * * n.s. * *
2008 28 n.s. n.s. * n.s. n.s. n.s.
Table 3. CERCBET1: Statistical tests on the results for the simulation years 1999-2008
(Kol.Smirn.: Kolmogorov-Smirnov test, n.s. not significant, * = significant with p<0,05)
Considering the statistical analysis of model results, it must be concluded that the presence of
significant differences between the distributions does not show a good correlation according to
the data. However, analyzing the subjective validation method we conclude that the model is
satisfactory if we consider the principal aim of the model, determine the date of beginning of
the monitoring system. An early forecast can also be accepted (in only 12% of the total cases
the forecast was more than 3 weeks before the observed first appearance).
A similar validation was done for the SIMBLIGHT1 model. The model predicts the risk of a
potato late blight outbreak and recommends the date for the first treatment. A subjective
validation was done and the model results were considered valid when the predicted date
of the first treatment was earlier than the date of the field observation. More than 700
observations during the period 1994-2005 were recorded for the validation. For most years
the proportion of correct forecasts reached more than 90% and a statistical validation was
not done (Kleinhenz , et al. , 2007).
For models that provide results in a binary response it is possible to apply a different
statistical method of evaluation and validation. As one example in the model ERYBET1 the
dates of onset of the disease (powdery mildew on sugar beet) were classified into two
groups: early onset (before July 31) and late onset (after July 31). The two groups are
discriminated by a binary logistic regression model using the winter weather as input
parameters (Racca , et al. , 2010a).
year
n
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