122
B. M. J. K. Balasooriya et al.
significant parameters (Razmkhah et al. 2010). Further, it redistributes the variance
of each factor to enhance the relationship between the independent variables.
5.2.6 Discriminant Analysis
Discriminant analysis (DA) was applied to identify discriminations between two or
more groups in terms of the discriminating variables (Usman et al. 2014). DA consists
of finding a transform, which gives the maximum ratio of difference between a pair
of group multivariate means to multivariate variance within the two groups (Davis
1986). It is concerned with the relationship between a categorical variable and a set of
inter-related variables based on the set of measurements. These coefficients represent
the maximum distance between the means of the dependent variable (McLachlan
2004).
Eigenvalues, Canonical-R, Wilks’ Lambda, Chi-square, and p-value tests are used
to produce the discriminant function table. These tests help to determine whether
discriminant functions are statistically significant. The eigenvalue is a measure of
ratio of importance of the dimensions, which classify cases of the dependent variable.
Canonical correlation (R) is a measure of the association between the groups which
are formed by the dependent variable and the given discriminant function (Nosrati
and Van Den Eeckhaut 2012). If the values are close to 1, it is considered as a strong
association. Further, Nosrati and Van Den Eeckhaut (2012) explain the functioning
of Wilks Lambda in discriminant analysis. Significance of the discriminant function
as a whole will be assessed by Wilks’ Lambda test. Wilk’s Lambda is an indication of
the proportion of the total variance in the discriminant scores which are not explained
by differences among the groups. Test values range between 0 and 1. If the value is
close to 0, group means are different. A Chi-square transformation of Wilks’ Lambda
is used along with the degrees of freedom to determine significance of the test. If the
value is <0.10, group means differ (Davis 1986).
5.3 Results
5.3.1 Spatial Clustering
All sampling wells were grouped into two major clusters in the analysis; 298 wells
were grouped into cluster 1, and 964 wells were grouped into cluster 2 (Fig. 5.2).
Almost all of the points in cluster 1 lie on intermediate zone or dry zone of the
country, while only two points lie on the wet zone; one is in Galle district, and other
one is at the boundary of Matara district. Both points have been grouped into cluster
2 due to the extreme values in some parameters. One sampling well (Galle) had
extreme concentrations of chromium (6.07 mg/L) and nickel (14.8 mg/L), while the
B. M. J. K. Balasooriya et al.
significant parameters (Razmkhah et al. 2010). Further, it redistributes the variance
of each factor to enhance the relationship between the independent variables.
5.2.6 Discriminant Analysis
Discriminant analysis (DA) was applied to identify discriminations between two or
more groups in terms of the discriminating variables (Usman et al. 2014). DA consists
of finding a transform, which gives the maximum ratio of difference between a pair
of group multivariate means to multivariate variance within the two groups (Davis
1986). It is concerned with the relationship between a categorical variable and a set of
inter-related variables based on the set of measurements. These coefficients represent
the maximum distance between the means of the dependent variable (McLachlan
2004).
Eigenvalues, Canonical-R, Wilks’ Lambda, Chi-square, and p-value tests are used
to produce the discriminant function table. These tests help to determine whether
discriminant functions are statistically significant. The eigenvalue is a measure of
ratio of importance of the dimensions, which classify cases of the dependent variable.
Canonical correlation (R) is a measure of the association between the groups which
are formed by the dependent variable and the given discriminant function (Nosrati
and Van Den Eeckhaut 2012). If the values are close to 1, it is considered as a strong
association. Further, Nosrati and Van Den Eeckhaut (2012) explain the functioning
of Wilks Lambda in discriminant analysis. Significance of the discriminant function
as a whole will be assessed by Wilks’ Lambda test. Wilk’s Lambda is an indication of
the proportion of the total variance in the discriminant scores which are not explained
by differences among the groups. Test values range between 0 and 1. If the value is
close to 0, group means are different. A Chi-square transformation of Wilks’ Lambda
is used along with the degrees of freedom to determine significance of the test. If the
value is <0.10, group means differ (Davis 1986).
5.3 Results
5.3.1 Spatial Clustering
All sampling wells were grouped into two major clusters in the analysis; 298 wells
were grouped into cluster 1, and 964 wells were grouped into cluster 2 (Fig. 5.2).
Almost all of the points in cluster 1 lie on intermediate zone or dry zone of the
country, while only two points lie on the wet zone; one is in Galle district, and other
one is at the boundary of Matara district. Both points have been grouped into cluster
2 due to the extreme values in some parameters. One sampling well (Galle) had
extreme concentrations of chromium (6.07 mg/L) and nickel (14.8 mg/L), while the