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Studies that assess the co-variation between two variables: for example, co-variation of functional or structural properties of the brain and a behavioural variable, such as reported stress.
The purpose of ATE is to capture information transfer between two variables for a particular association of their states.
The G2 test is commonly used to test independence and conditional independence between two variables for discrete data.
Pearson correlation or Spearman correlation coefficients were used to measure the strength of the association between two variables for parametric and nonparametric data, respectively.
The former represent algebraic relations between variables as in quantitative mathematics, for instance, addition, subtraction, and multiplication; the latter describes incomplete knowledge between two variables, for example, the monotonically increasing and decreasing relations, which state that one variable will monotonically increase with the increase/decrease of another.
One of the most widely applied causal inference approaches is MR. If the direction of the association is previously known between two variables (for example, a metabolite and a lipid in a SNP-MET-LIP set), MR can measure the extent of the unconfounded causal relationship using genetic variants as instrumental variables.
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Linear regression analyses were performed to examine the relations between two variables, controlling for age, and standardised β coefficients are reported.
Thus, mutual information as a measure of intricate dynamics and information transfer between two variables is applied for analysis.
As a first step, correlation analysis which reveals the relationship between two variables is calculated for the major ion chemical data from the study area.
The partial correlation in the MLR analysis gives the correlation between two variables after controlling for the effect of all other variables in the equation.
The correlation between two variables was tested for statistical significance using Spearman rank order correlation test in Sigma Stat software (SPSS Inc. Chicago, IL).
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