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around the best half part of the observations in each step of 
linear adjustment. 
The number could be increased until 2/3 of the observations, 
preserving the reliability of the observations, globally and 
locally, according to geodesists community suggestions, if the 
amount of suspected outliers isn’t too large. The breakdown 
point desreases, obviously, but not too much, so that the 
procedure continues to be effective. 
These methods are grouped together and generalized by means 
of the definition of the S-estimators. 
The strategy of application of the presented procedure is an 
adjustment of the best observation, after a prelimunary least 
squares adjustment. Successively the suspected outliers which 
don’t show blunders, leverages or small outliers are forward 
accepted by using the Hawkins test. The degrees of freedom are 
equal to the number of observations actually processed at the 
present step of adjustment (remember that this number is always 
less than the number of observations) minus the number of 
unknowns parameters. 
The expected value is computed taking into account the 
residuals, the recursive, tire variances of the residuals and the 
squares sigma zero. Furthermore the critical values, for a 
parametric test on two sides, are derived from the extremal 
Hawkins probability distribution. 
A. Distribution- free inference (Mussio, et al, 1994) 
Distribution-free significance tests (sometimes called noil- 
parametric significance tests, although the two terms are not 
synonyms) collect a broad category of significance tests which 
can be used instead of classical significance tests. 
There exist many different significance distribution-free tests, as 
above mentioned. Nevertheless for the sake of brevity, only 
few multiple significance distribution-free tests are presented in 
the follows, concerning : 
• goodness of fit of population distributions 
• independence against interdependence or dependence (e.g. 
collinearily) 
• homogeneity of variance components for several variances 
• variance analysis of several means, 
Where the last two tests are repeated for independent and 
correlated samples, respectively. 
A. Kolmogoroff-Smimoff s test on the goodness of fit of 
population distributions. 
UUU It is a powerful test and its use is rccommendable instead 
of classical chi-square goodness of fit of population 
distribution test 
UUU The test criterion compares the largest absolute difference 
between cumulative sample frequencies and population 
distribution with Kolmogoroff-Smimoff s extremal 
distribution critical values, where the degress olT freedom 
are the size of the samples 
13-1 MU Kolmogoroff-Smimoffs test on the independence 
against interdependence. 
MU The same test performed for the goodness of fit of 
population distributions can be used to the test the 
independence against interdependence. Indeed because 
the goodness of fit hasn’t limitations concerning the 
dimension of domain of population distributions, these 
could be derived by multiplying marginal frequencies. 
UUU Thus comparing each multidimensional frequency with the 
product of the coiresponding marginal frequencies, the 
test on the independence against interdependence is 
performed. 'Hie test criterion is, obviously, the same 
explained for the test on the goodness of fit of population 
distributions, moreover because the uniqueness of the test, 
its power is conserved. 
13-2 Modified Wilcoxon-Wilcox’s tes according Lawlay on tire 
independence against dependence (e.g. collinearity) 
This lest must be used instead of classical Hotelling’s test, 
when population distributions aren’t normal. It is a 
generalization of Spearman’s rank tes for one Spearman’s 
rank correlation coefficient under the same hypotheses. 
Let remember that the Spearman’s rank correlation 
coefficient is a function of the sum of rank difference 
squares, where the ranks are assigned separately to the 
largest one and then compared, element by clement, in 
terms of their difference. Furthermore when the null 
hypothesis is the standardized value of the Spearman’s 
correlation coefficient with the student’s t distribution 
critical value, where the degrees of freedom are the size of 
sample minus two 
The test criterion compares a quadratic function of the 
standardized Spearman’s rank correlation coefficient 
squares with chi-square distribution critical value, where 
tire degrees of freedom are the number of terms of the 
quadratic combinations. 
C-l UUU Kruskall-Wallis’ test on the homogeneity of variance 
components for several variances of independent samples 
This test must be used instead of classical Barlctt’s test, 
when population distributions aren’t normal, although 
samples must be independent. It is a generalization of 
Siegel-'furkey’s rank lest for two variances under the 
same hypotheses. 
Therefore the ranks are assigned from the smallest 
absolute residual to the largest one, after having put all 
samples together and sorting their residuals, so that the 
dispersion of each appears immediately. The test criterion 
compares a quadratic function of the sums of the ranks of 
the samples with chisquare distribution critical value, 
where the degrees of freedom are the number of samples 
minus one. 
C-2 Friedman’s test on the homogeneity of variance 
components for several variances of correlated samples 
UUU 
This test is less powerful than the above mentioned 
Kruskall-Wallis’ test, but it penniLs to analyze correlated 
samples. This is a generalization of Thompson’s sign test 
for two variances under the same hypotheses. 
Therefore the rank are assigned to the absolute residuals, 
element by element across the samples in increasing 
order, after having paired all samples. The test criterion 
compares a quadratic function of the sums of the ranks of 
the samples with chi-square distribution critical values, 
where the degrees of freedom arc the number ot samples 
minus one.