Multivariate statistical methods for analysis of physicochemical and microbiological parameters of well water from the village M’Pody

The aim of this paper is to analyze well water from the village M’Pody using multivariate statistical analysis methods. Sixteen physicochemical and micro-biological parameters from four well water sampling campaigns in 2020 were analyzed. A descriptive statistical analysis was used to study the non-potability of these waters according to World Health Organization standards. Next, principal component analysis, factorial correspondence analysis are used to highlight the diﬀerent well proﬁles in the study area. Self-Organizing Map method was also used for data classiﬁcation. This method is needed for a better analysis of the data in order to remove any ambiguity. Finally, analysis of variance was used to prove the contribution of these wells on microbiological parameters.


Introduction
Water is an essential resource for humans, animals and plants.For good health, all people must have access to a source of drinking water.In fact, it can be a source of disease due to its pollution by industrial waste, wastewater, household or agricultural waste, excreta and various organic wastes (Eblin et al. 2014), (Scalon et al. 1994).Making drinking water available at the tap to all populations requires the catchment, control or treatment and distribution of drinking water.All these operations require major technical and financial resources that developing countries do not have.In Côte d'Ivoire, water distribution is the responsibility of the Côte d'Ivoire Water Distribution Company(SODECI).Unfortunately, many people still do not have access to drinking water.What's more, most people who do have access to this water are reluctant to use it as drinking water because of its often yellowish color, deposits, the smell of bleach and its bad taste.As a result, people have no hesitation in turning to other sources of water, such as rainwater, streams and wells, for everyday use.In Côte d'Ivoire, well water is used by the population as drinking water or for various activities such as agriculture and livestock rearing in general.People consider well water to be healthier based solely on its colorless appearance and clarity, without attempting to assess its physicochemical and microbiological parameters.However, studies of well water quality in the south and west of Côte d'Ivoire have shown that it is unfit for consumption (Ahoussi et al. 2010), (Yapo et al. 2010).For example, in January 2020, an epidemic of diarrhoea was detected in the village M'Pody in the Anyama district of southern Côte d'Ivoire as a result of the consumption of well water (Gbagbo et al. 2020).This village is located ten kilometers from Abidjan in Côte d'Ivoire.Its geographical coordinates show that it is located approximately at 5 • 34 ′ 29 ′′ North latitude and 4 • 14 ′ 8 ′′ West longitude.The authors (Gbagbo et al. 2020) carried out a study on the water from these wells.It showed that this water was the cause of the epidemic, as it was of poor microbiological quality.To do this, they used electrochemical and spectrophotometric methods to study the physicochemical parameters and a microbiological analysis by membrane filtration.They provided measures to be adopted.Our study is a continuation of their work, by using multivariate statistical analysis techniques (ACP, AFC and ANOVA).The main objective is to assess the quality of the physicochemical and microbiological parameters of well water in the light of WHO standards; to classify wells according to their profiles; to analyze the impact of the wells on physicochemical and microbiological parameters.Self-Organizing Map (SOM) method is used.Indeed, there is a linearity constraint in ACP that does not exist in SOM.This constraint, as well as the orthogonality between the principal axes, can be a handicap in the treatment of non-linear problems.Moreover, SOM is very often in two dimensions(2D), whereas ACP is not in 2D in most cases.It is therefore necessary to combine these different techniques for a better analysis of the data in order to remove any ambiguity.In this study, it appears as a complement to the ordinary classical analysis.This paper is structured as follows.Section 2 introduces the classification methodology used.We briefly define the Method of descriptive statistical analysis, Principal Component Analysis (ACP) Method, Correspondence Factorial Analysis (AFC) Method, ANOVA method and the Self-Organizing Map (SOM) Method.Section 3 presents the results obtained and the ensuing discussion.We conclude this study with a conclusion.

Methodology for classical data analysis
In this section, we present the multivariate statistical analysis techniques that we used to study the water quality of the wells in the village of M'Pody.To do this, we had to acquire field data on these wells.The methods of analysis that we present are: descriptive statistical analysis, Principal Component Analysis (ACP), Correspondence Factorial Analysis (AFC), Analysis of Variance (ANOVA) and Artificial Neural Networks (Kohonen Map).

Method of descriptive statistical analysis
A descriptive statistical analysis of the physical, chemical and microbiological parameters of the well water in the village of M'Pody was carried out in order to gain an overview of the situation of the well water.The World Health Organization standards were used as a reference for the detection of non-standard parameters.

Method of descriptive statistical analysis
We observe n individuals measured against p quantitative variables noted (X j ) (1≤j≤p) .The observation of the variable X j observed on individual i is X ij .These variables are mostly correlated with each other.The principle of ACP is to reduce the dimension of the initial data (which is p), by replacing the initial p variables with (q < p) new uncorrelated variables (factors) that we note (F k ) (1≤k≤q) .These factors are linear combinations of the initial p variables that will cause the least amount of information to be lost.These factors are linear combinations of the initial p variables that will lose the least amount of information (maximum dispersion).Indeed, the variables studied do not have the same unit of measurement, we first centred-reduced the initial data to obtain a new variable where X k and S k are respectively the mean and the standard deviation of the variable X k .A set of factors are constructed (F k ) (1≤k≤q) , linear combinations of variables whose quality of information restitution can be appreciated : Secondly, ACP makes it possible to calculate the variable-factor correlations.In other words, the linear correlation coefficients between each variable and each factor retained.The variable-factor correlations are used to draw up graphs of the variables, the detailed study of which leads to the significance of the axes.Finally, ACP can also be used to calculate the coordinates of the individuals on the axes, their contributions to the dispersion along each of these axes and the squared cosines.The coordinates are used to produce graphs of the individuals (1 or 3 graphs, depending on whether q = 2 or q = 3 is chosen).

Correspondence Factorial Analysis Method
Correspondence factor analysis (AFC) is an exploratory method for analyzing qualitative data tables such as contingency tables.It was introduced in the 1960s by JP Benzecri.The AFC is considered as a particular ACP with the metric of χ 2 (Chi-2) which depends only on the profile of the table columns.The analysis allows, in the plane of the first two factorial axes, a simultaneous representation of the similarities between the columns or rows of the table and the proximity between rows and columns.We study on N individuals the link between two qualitative variables X = (X i ) (i∈I) and Y = (Y j ) (j∈J) .The cardinal of I is noted n and that of J is noted p.We note by x ij the number of individuals having the modality i of X and the modality j of Y .The contingency table is given by the matrix (x ij ) (1≤i≤n;1≤j≤p) or (f ij ) (1≤i≤n;1≤j≤p) with f ij = xij N .Now, we define the profiles and the distance χ 2 between two profiles.
• The line-profiles form a cloud of n points in space R p and the array of line-profiles is fij fi.= P (X = i|Y = j) where f i. = p j=1 f ij = P (X = i),for i = 1, . . ., n.The associated marginal line profile is G L = (f .1 , . . ., f .p).The AFC compares the lines profiles to the marginal profile G L .
• The column-profiles form a cloud of p points in space R n .The table of profilescolumns is fij f.j = P (Y = j|X = i) where f .j= n i=1 f ij = P (Y = j) for j = 1, . . ., p.The associated marginal column profile is G C = (f 1. , . . ., f n. ).The AFC compares the columns profiles to the marginal profile G C .
• The distance χ 2 between two profiles lines i and i ′ is : 2 The distance χ 2 between the profile line i and its marginal profile G L is : In the same way, we define the distance χ 2 between two profiles columns j and j ′ by : . The distance χ 2 between the profile column j and its marginal profile G C by :
• The total inertia of the cloud of profiles lines with respect to G L is : (fij −fi.f.j ) 2 fi.f.j = χ 2 n = φ 2 , φ 2 measure the intensity of the linkage.This inertia therefore measure the intensity of the deviation from independence.Similarly, the total inertia of the profile-column cloud with respect to G C by : . This total inertia is decomposed into a sequence of axes of decreasing importance, each representing a synthetic aspect of the relationship between the two variables, and then a representation of the rows and columns is provided in which the position of a point reflects its participation in the independence gap.

ANOVA method
One-way analysis of variance(ANOVA) is used to study the effect of a qualitative variable (X) called a factor on a continuous quantitative variable (Y ).It allows us to see if the average of the quantitative variable is the same in different groups (Azaïs and Bardet 2005).The different values taken by the factor (X) are called level (or population).For factor (X), it is assumed that there are k levels, k samples of respective sizes n 1 , . . ., n k .The total number of samples is n = k i=1 n i .At each experiment, we measure the value of the variable Y = (Y ij ) 1≤i≤k;1≤j≤ni .The analysis of variance model is written as : The constraints, k i=1 n i α i = 0, ∀(i, j) = (k, l), ε ij and ε kl are independent.Then, the null and alternative hypotheses of the one-factor ANOVA are given by : The statistical test is used to determine whether the factorial variance is significantly greater than the residual variance.This is the F -test of the ratio of these two variances where F is defined as : , is the dispersion due to the factor and SCR = Under the assumptions of normality and homogeneity of the residuals (differences between the observations and the group means), the F statistic follows a Fisher distribution with k −1 and n−k degrees of freedom.If the value of F is greater than the theoretical threshold value according to the Fisher distribution, with a given alpha risk (usually 5 per cent), then the test is significant.In this case, the factorial variability is significantly higher than the residual variability.We conclude that the means are globally different.If these hypotheses are not verified, it is always possible to apply a transformation at the level of the responses (log for example), or to use a non-parametric ANOVA (Kruskal-Wallis test), or to carry out an ANOVA based on permutation tests.

The Self-Organizing Map Method
The Self-Organizing Map (SOM) is a method of classification, representation and analysis of relationships.It was defined by Teuvo Kohonen, in the 80's, from neuromimetic motivations (Kohonen 1984), (Kohonen 1995).Our data set is stored in a table with n(72) rows representing the individuals (or observations) and p( 16) columns corresponding to the variables describing the individuals.Each of the n observations (x 1 , x 2 , . . ., x n ) is therefore described by p quantitative variables.The SOM algorithm is a stochastic classification algorithm that groups the observations into K classes, while respecting the topology of the observation space.This means that, if we define a priori a notion of neighborhood between classes, neighboring observations in the space of observations of dimension p belong after classification to the same class or to neighboring classes.We consider hexagonal neighborhoods because they have the advantage of making the apparent distances in all directions equal.The classification algorithm is iterative.The initialization consists in associating to each class a code vector (or representative) of p dimensions chosen randomly.Then, at each step, an observation is randomly chosen, compared to all the code vectors, and the winning class is determined.The winning class is the one whose code vector is the closest in the sense of a distance given a priori.The codes of the winning class and of the neighboring classes are then compared to the observation.Practically speaking, we have a Kohonen network formed by N units arranged according to a certain topology.For each unit i of the network, we define a neighborhood of radius r noted V r (i) and formed by all the units located on the network at a distance less than or equal to r.
Each unit i is represented in space R p by a vector C i (called weight vector) which we call the code vector of unit i (or class i).The state of the network at time t is given by C(t) = (C 1 (t), C 2 (t), . . ., C N (t)).For a given state 4and a given observation x, the winning class i 0 (C, x) is the one whose code vector C (i0(C,x)) is the closest to the observation x in the sense of a certain distance.We have, For a given state C, the network defines an application ψ C which associates to each observation x the number of its class.After convergence of the Kohonen algorithm, the application ψ C respects the topology of the input space, in the sense that neighboring observations in the space R p are associated to neighboring units or to the same unit.The code vector construction algorithm is defined iteratively as follows : • at time 0, the N code vectors are randomly initialized, • at time t, the state of the network is C(t) and an observation x(t + 1) is presented according to a probability distribution P .
Then, we have : where 0 ≤ ε(t) ≤ 1 is the adaptation parameter (constant or decreasing), and r(t) (decreasing) is the radius of the neighborhoods at time t.After convergence of the algorithm, the n observations are classified into K classes according to the nearest neighbor method, relative to the distance chosen in R p .Then, we can build graphical representations according to the topology of the network.

Results and discussion
Our data consist of sixteen physicochemical and microbiological parameters studied on seventy-two wells of the village M'Pody.These parameters are : Chlorides (Cl − ), Conductivity (Cond), Coliform Thermotolerant (CTH), Total Hardness (DHT), Escherichia coli (E.col), Enterococcus faecalis (E.faecalis), Bicarbonate (HCO 3 − ), , Temperature (T), Total Alkalinity Titration (TAC), and Turbidity (Tur).Sampling was carried out over four months (February, June, August and October) of the year 2020.The results presented in the paper are obtained by averaging the measurements of the four samples taken for each parameter.

Results of the ACP
The results of the water quality of the wells are recorded in the Table 1.They contain several bacteria (Thermotolerant Coliform, Escherichia coli, Enterococcus faecalis).Moreover, a minority of the wells have less turbid water with a conductivity within the norms.The average turbidity of the water in these wells is 3.38 NTU with an average conductivity of 312.6325CFU/250 ml.In addition, the water from these wells are generally acidic.Without prior treatment, such well water must not be consumed.At last, principal component analysis is performed on the average of the physical, chemical and microbiological parameters of the water samples from each well.

Inertia distribution
Figure 1 shows the decomposition of the total inertia in ACP.The eigenvalues measure the amount of variance explained by each principal component.The inertia of these axes suggests the appropriate number of principal components to study.Thus, the first principal components correspond to the directions carrying the maximum amount of variation contained in the data set.In our case, we have sixteen principal axes.The first two principal axes of the analysis express 48, 37 percent of the total inertia of our data.It means that 48, 37 percent of the total variability of the individual cloud is represented in this plane.This is a relatively average percentage.Looking at the inertia decomposition plot, the break occurs at the 4th and 5th principal components.In addition, the cumulative inertia of the first five principal components is 75, 07 percent (see Table 2) of the total inertia of the data.This observations suggests that only these axes carry real information.Thus, only these first five axes will be considered in our analysis.

Description of the studied plans
We have the projection of the seventy-two wells observed on the five planes studied.
The wells are positioned according to their respective coordinates.Their representational qualities and contributions to the studied planes serve for a better analysis.An extract is given in Figure 2 and Table 3.The correlation matrix(See Table 4) gives an idea of the associations between the different parameters.The Table 5 presents the correlations (Cor) and contributions(Cont) of the parameters on the five dimensions studied.It appears that the : Dim1 summarizes information on the physicochemical parameters Tur, N O 2 − , TAC, DHT, SO 2 − 4 , HCO 3 − ; Dim2 summarizes information on the physicochemical parameters Cond, T, Cl − and the microbiological parameters CTH, E.coli, E.faecalis ; Dim3 summarizes information on the physicochemical parameters N O 3 − and the microbiological parameters CTH, E.coli ; Dim4 summarizes the information on the physicochemical parameter P O 3 − Fig. 2 Extracts from the graphs of individuals in ACP on the studied dimensions could give us information on the total hardness, the bicarbonate and sulphate concentration.Conductivity analysis alone could tell us about temperature, chloride and nitrate.Subsequently, the ACP allowed us to highlight the different profiles of wells according to their similarity.As shown in Figure 3, we have four types of well in the village of M'Pody.

Results of the AFC
The factorial correspondence analysis performed on our data set led to the following results.

Inertia distribution
The AFC gives us fifteen main axes (see Table 6).The decomposition of the inertia in AFC (Figure 4) shows that the first two axes of the analysis express 79, 79 percent of the total inertia of the data.This means that 79, 79 percent of the total variability of the row (or column) cloud is represented in this plane.This is quite a large percentage, and the first plan therefore adequately represents the variability contained in the data set.Thus, this plan alone summaries almost all the information.Consequently, the description of the analysis will be restricted to these axes only.

Description of the studied plans
The AFC yielded the following overlay plot of wells and parameters on the first principal plane (see Figure 5).Dimension 1 shows that wells P64, P34, P35 and P43 4 , TAC and HCO 3 − a low frequency of the parameter N O 3 − .Wells P10, P13, P12 and P16, characterized by a negative coordinate on the axis, share a high frequency of the parameters E. coli and CTH.These results allow us to deduce the characteristics of the well profiles.Profile 1 contains wells with soft, very turbid, slightly acidic (pH > 5.2) and highly mineralized water.Profile 2 contains wells with poorly mineralized water, with a pH of around 5.2 on average.These wells contain a high concentration of bacteria and very little chloride and are therefore greatly affected by microbiological pollution.Very soft waters (DHT < 80mg/L), with medium pH, low mineralization, low TAC and chloride and low microbiological pollution are in profile 3. Profile 4 is the warmest, most acidic, highly mineralized water with the highest concentrations of chlorides and nitrates.

ANOVA results
The ANOVA was performed to see if the wells have an effect on the parameters.To do this, we need to compare the variances.Note that correlated parameters will have similar responses in the ANOVA.Indeed, the results obtained with the conductivity parameter will be similar to those obtained with temperature, nitrate and chloride.Similarly, the result obtained with the parameter complete alkalinity titration will be similar to those obtained with total hardness, sulfate and bicarbonate.The result obtained with parameter Escherichia Coli will also be similar to those of thermotolerant coliforms and Enterococcus faecalis parameters.Three parameters (Conductivity, Escherichia coli, Complete Alkalimetric Titration) were therefore selected for testing.The tests of the validity conditions of the ANOVA are not conclusive.Indeed, the Shapiro-Wilk normality tests (Figure 6) and the histogram performed on the dependent variables, show that these parameters do not follow a normal distribution.Therefore we conclude that the residuals do not follow a normal distribution.Under these conditions we perform the non-parametric ANOVA (kruskal.test).These tests gave significant p-values (Figure 7).This indicates that the wells do have an effect on these parameters.This also means that the factors influencing the well parameters are different.In addition, multiple comparison tests carried out respectively on the Cond, TAC and E. coli parameters gave the results summarized in (Figure 8, Figure 9 and Figure 10).These results show significant differences between the wells in terms of the parameters studied.These results also show a classification of the wells by concentration level (from the most concentrated well to the least concentrated well).Thus, we have sixteen significant levels for conductivity, nineteen significant levels for Complete Alkalimetric Titration and eight significant levels for Escherichia coli.These results suggest that if three wells belong respectively to different significant levels namely a, ab and c for example, then, the well of level a is close to the well of level ab but different from the well of level b.Also, the well of level b is close to the well of level ab but different from the well of level a.

Results with Kohonen Map
In this subsection, we construct a Kohonen map based on the physicochemical and microbiological parameters of the wells in the village of M'Pody in order to identify groups of wells with similar characteristics.To get rid of scaling problems, we center and reduce the data using the scale command.We chose a hexagonal grid of size 4 × 4 with a circular neighborhood structure.The graph of the learning progression allows us to appreciate the convergence of the algorithm.It shows the evolution of the average distance to the nearest node in the map.We can see that after a strong decrease, we reach a plateau in the final part.We now display the wells of each node(Figure 11).We see that all nodes have at least one well.The darker the blue color, the higher the number of wells.The first four nodes (counting from left to right) are the ones in the last row.Figure 12, shows the sum of the distances to nearest neighbors for each node.Nodes in the same class tend to be close.Figure 13 shows the role of the variables in defining the different zones that make up the topological map.This graph represents the weight vectors (the profile) of each node.It allows us to distinguish the nature of the different zones of the map with respect to the variables.It can be seen that the western part of the map is characterized by the values high values of the variables (in green and yellow).The Southeast part is rather characterized by high values of the variables(in pink).Rather than making a single graph for all the variables, we made a graph for each parameter (Figure 14), trying to highlight the contrasts between areas with high (red) and low (blue) values for each variable.For example, for the variable turbidity, wells P25, P48, P58 have a high concentration while wells P26, P44, P55, P66, P27, P34, P35, P38, P41, P43, P60, P63, P64, P15,  7).

Discussion
The results of the descriptive statistics showed that the well water in the village of M'Pody is not drinkable.These waters are globally acidic, turbid and affected by microbiological pollution.These results are consistent with those of (Gbagbo et al. 2020).The application of ACP and AFC revealed four well types and their characteristics.Similar to the study conducted by (Lagnika et al. 2014), the analysis of physicochemical and microbiological parameters justified the possibility of reducing the dimensions of the study.Clearly, we can obtain information on the sixteen parameters by carrying out an analysis on just eight.In this way, the parameters of these waters can be monitored using only the following parameters : Turbidity, Conductivity, Hydrogen Potential, Nitrite, Ammonium, Phosphate, Complete Alkalimetric Titration and Escherichia coli.The ANOVA showed that these parameters evolved differently.It also showed that there is a significant impact of wells on conductivity, turbidity and the concentration of bacteria in water.This significant impact of wells on the presence of bacteria could be due to the presence of septic tanks near the wells which contaminate the water or poor maintenance of certain wells by the populations.Multiple comparisons using Duncan's test were used to classify the wells by level of significant concentration of the parameters conductivity, complete alkalimetric titration and escherichia coli.The ACP showed that these parameters are correlated with others.Thus, a significant difference between wells for one of these parameters implies that of the correlated parameters.In fact, a significant difference between wells for the conductivity parameter implies the same significant difference for the temperature, nitrate and chloride parameters.The same applies to the complete alkalimetric titration, escherichia coli and the parameters which are correlated to them respectively.Self-organizing maps are an alternative way to perform classification of data, when there are several dimensions as in our study.Contrary to ordinary classification methods, self-organizing maps organize the classes found on a map whose topology tries to respect the topology of the original data.They summarize the information in a two-dimensional space.They allow to associate the topological representation with the interpretation of the groups resulting from the typology.Looking at Figure 11 and Figure 12 of the Kohonen map and Figure 3 and Figure 5, we can say that the associations are the same.For example, Figure 3 gives the different profiles.The profile in green consists of wells P03; P07; P10; P11; P12; P13; P16.In the Kohonen map, P07 belongs to node 3, P03 and P11 belong to node 8, P10, P11, P13, P16 belong to node 4. Nodes 3, 8 and 4 are neighbors.We note that these wells belong to the same or neighboring nodes.Note that the Kohonen map is easier to read.With a single representation, it allows us to see the distribution of wells on all factorial planes.The Kohonen map therefore confirms the different ACP patterns because we have roughly the same proximities.The hierarchical ascending classification carried out on the set of code vectors of the map leads to retain three super-classes.These super-classes are sets that separate our data into homogeneous groups with common characteristics.This is another grouping of the four profiles obtained in ACP.For example, group three of the CAH is formed by wells P10, P12, P13 and P16 which are of the profile (green) of the ACP.They have the same frequency of E. coli and CTH parameters.Group one of the CAH is formed by wells P25, P28, P45, P48, P58, P61, P68, P70 and P71 which are of the (purple) ACP profile.Among these different wells, P21, P45, P68, P70 and P71 have the same frequencies of the parameters TAC and DHT.They have the same frequency of the parameters E. coli and CTH.Wells P25, P48, P58, P61 have the same frequencies of these parameters but in lower proportions.It should be noted that in the context of multidimensional data analysis, the two techniques give the same results or are complementary.These techniques should therefore be combined to improve data classification.

Conclusion
In this paper, we proposed two complementary statistical methods for an efficient analysis of water quality in the wells of M'Pody village.The classical linear methods (principal component analysis, factorial correspondence analysis, analysis of variance) and the Self-Organizing Map algorithm.The descriptive statistical analysis showed that the water from the M'Pody wells constitutes a health risk for the populations whose survival depends on it.The study of the thirteen physicochemical parameters showed that turbidity, conductivity, hydrogen potential and temperature are out of range for the majority of well waters.The same applies to the three microbiological parameters (Escherichia coli, thermotolerant coliform and Enterococcus Faecalis).In addition, all the seventy-two wells are affected by this bacteriological pollution.The Principal Component Analysis identified four well profiles.The Correspondence Factorial Analysis revealed the characteristics of these profiles.Then, the information given by the three microbiological parameters is summarized in the single analysis of Escherichia coli bacteria.On the other hand, from the analysis of the total alkalimetric titration, we can deduce that of the total hardness, the sulphate and bicarbonate content.Finally, the effects of wells on physicochemical and microbiological parameters were highlighted using ANOVA.Effects that prove a poor management of the wells by the population.We used Self-Organizing Map (SOM) method to classify the seventytwo wells according to the sixteen physicochemical and microbiological parameters.Indeed, there is a linearity constraint in ACP that does not exist in SOM.This constraint, as well as the orthogonality between the principal axes, can be a handicap in the treatment of non-linear problems.Moreover, SOM is very often in two dimensions (2D0, whereas ACP is not in 2D in most cases.It is therefore necessary to combine these different techniques for a better analysis of the data in order to remove any ambiguity.In this study, it appears as a complement to the ordinary classical analysis.We have established the role of the parameters in the different zones that make up the topological map.This allowed to define the profile of each node and to distinguish the nature of the different zones of the map with respect to the parameters.We performed an CAH for the understanding and identification of the classes.A grouping into three classes was made on the basis of the dendrogram.The groupings of the wells and the parameters explaining the partitioning was done.The main variables designating the three identified zones are Turbidity, Conductivity and Total Alkalimetric Titration.This study also showed the importance and usefulness of multivariate analysis techniques in the study and monitoring of well water quality and the prevention of all kinds of pollution.It could be further developed with other analytical techniques.For example, a linear regression model of Escherichia coli parameter could be constructed as a function of the parameters turbidity, conductivity, hydrogen potential, nitrite, ammonium, phosphate, Total Alkalinity Titration and thermotolerant coliform.

Fig. 3
Fig. 3 Plots of the wells with the four profiles on the first plan of the ACP

Fig. 5
Fig. 5 Overlay graphs on the dimensions studied

Fig. 16
Fig. 16 Representation of classes in the topological map

Table 1
Frequency of exceeding standards

Table 2
Eigenvalues and variances in ACP

Table 3
Correlations and contributions of the wells to the studied plans

Table 4
Correlation matrix between the parameters

Table 5
Correlations and contributions of variables on the different dimensions

Table 6
Eigenvalues and variances in AFC