*2.5. Statistical Analysis*

Data were analyzed with SPSS 17.0 (SPSS Inc., Chicago, IL, USA). Distributions of excretion rates for Cd, NAG, and β2MG were examined for skewness, and those showing rightward skewing were subjected to base-10 logarithmic transformation before analysis. Departure of a given variable from normal distribution was assessed with the one-sample Kolmogorov–Smirnov test. For continuous variables not conforming to a normal distribution, the Kruskal–Wallis test was used to determine differences among the three localities in ECd/Ccr, ENAG/Ccr, <sup>E</sup>β2MG/Ccr, and other parameters. The Mann–Whitney *U*-test was used to compare mean differences between two groups. The Chi-Square test was used to determine differences in percentage and prevalence data. *p*-values ≤ 0.05 for two-tailed tests were assumed to indicate statistical significance.

Polynomial regression was used to fit lines and curves to the scatterplots of five pairs of variables, including eGFR versus ECd/Ccr, eGFR versus ENAG/Ccr, ENAG/Ccr versus ECd/Ccr, <sup>E</sup>β2MG/Ccr versus ECd/Ccr, and ENAG/Ccr versus <sup>E</sup>β2MG/Ccr. A linear model, *y* = *a* + *bx*, was adopted if the relationship was monotonic. A quadratic model (second-order polynomial), *y* = *a* + *b*1*<sup>x</sup>* + *<sup>b</sup>*2*<sup>x</sup>*2, was used if there was a significant change in the direction of the slope (*b*1 to *b*2) for prediction of the dependent variable *y*. In both types of equations, *a* represented the *y*-intercept.

The relationships between *x* and *y* were assessed with *R*<sup>2</sup> (the coefficient of determination) and with unstandardized and standardized β coefficients. In linear and quadratic models, *R*<sup>2</sup> is the fraction of variation in *y* that is explained by the variation in *x*. In linear models, the unstandardized β coefficient is the slope of the linear regression, and the standardized β coefficient indicates the strength of the association between *y* and *x* on a uniform scale. To examine quadratic curves relating eGFR to ECd/Ccr and ENAG/Ccr, we performed slope change analyses with a linear regression method.
