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Associations between any two variables were addressed using Pearson's correlation.
The chi-square (χ2) test was used to confirm whether respondents were uniformly distributed or not among the groups for each variable or, for the two-way tables, to measure the interaction or strength of association between any two variables.
The relationship between any two variables will be deduced by applying the previous statistical concepts especially for the carbonate aquifer at this study which is controlled by several factors such as porosity (fractures) including the density of fractures, TDS, water resistivity, shale content, and amount of water.
Using these methods we were able to examine the correlation between any two variables in addition to which, we also conduct a partial mantels test where partial correlations provided us the significance of correlation of two variables while controlling for the effect of the third variable.
We quantified the strength of the correlation between any two variables using Pearson's ρ correlation coefficient.
Chi squared was used to determine association between any two variables.
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The information matrix is employed to 1) derive the covariance between any two random variables; and 2) establish a novel weighting covariance formula to address the quadratic terms associated with the random matrices.
Spearman's coefficient of rank correlation, denoted as ρ is a nonparametric measure of statistical dependence between any two ranked variables, which are assumed to have a monotonic relationship.
Certain theorems establish a mathematical link between a causal diagram and the expected association between any two displayed variables.
Clearly, additional data and analysis are required to understand the relationship, if any, between these two variables.
Significance values for the effects of genotype, treatment, and/or any interaction between two variables have been included in each figure, where appropriate.
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