Statistics for Environmental Engineers

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The variance of the log-transformed values in Table 7.5 is О)2(y) = 0.549. This cannot be compared directly with the variance from, for instance, a square root transformation unless the calculations are normalized to keep them on the same relative scale. The denominator of the Box-Cox transformation, Xyg , is a normalizing factor to make the variances comparable across different


TABLE 7.5


Cadmium Concentrations in Soil


Cadmium


(mg/kg)


ln


[Cadmium]


0.023


0.005


0.005


-3.7723


-5.2983


5.2983


0.020


0.005


0.032


-3.9120


5.2983


3.4420


0.010


0.005


0.031


4.6052


5.2983


3.4738


0.020


0.013


0.005


3.9120


4.3428


4.2687


0.020


0.005


0.014


3.9120


5.2983


3.9120


0.020


0.094


0.020


3.9120


2.3645


5.2983


0.010


0.011


0.005


4.6052


4.5099


3.6119


0.010


0.005


0.027


4.6052


5.2983


4.1997


0.010


0.005


0.015


4.6052


5.2983


3.3814


0.010


0.028


0.034


4.6052


3.5756


5.2983


0.010


0.010


0.005


4.6052


4.6052


5.2983


0.005


0.018


0.013


5.2983


4.0174


4.3428


Average =


= 0.0161


Average of ln[Cd] = -4.42723


Variance


= 0.000255


Variance =


0.549

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