The LMS power transformation required to achieve normality constrains the maximum z-scorethat is obtainable at a given sex and age, making the LMS-derived z-scores ill-suited foridentifying extreme values. No matter what the value of BMI is, the maximum obtainable zscorefor a given sex/age is (-1) / (L × S). This occurs because as BMI becomes very largerelative to M, (BMI ÷ M)L in equation #1 approaches 0. (L is always negative.) Given a verylarge BMI, the maximum obtainable z-score depends only on the values of L and S, not on BMI. Now, suppose that this BMI was incorrectly entered as 333 kg/m2.
Her BMIz would now becalculated to be 3.1, which is close to the theoretical maximum z-score for this sex/age. This 300kg/m2 difference (33 vs. 333) in the 2 BMIs correspond to only a 1.1 SD difference (1.
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97 vs.3.08) between the 2 BMIz values. In addition to limiting the maximum z-score value that can beobtained at any sex/age, the LMS transformation results in the mapping of a wide range of veryhigh BMIs into a narrow range of high z-scores.This precludes the use of the LMS z-scores in the identification of values that are may be dataerrors.
Modified z-scores were introduced to address this limitation.