Smackdown Revisited

After tackling the z-score:percentile issue, I thought it might be interesting to graph how different z-score equations look in this light. Here is what I derived as the cumulative density function for the aortic valve z-score (1.0 m²; male) using data published from Boston, Wessex, Cincinnati, and Detroit:

I think that because I have explained z-scores to our students and fellows so many times, and made use of my own roughly drawn bell-shaped curve, this next depiction of the probability density function highlights the differences most strikingly for me:

The mean (50th percentile) of the Wessex data is clearly and importantly different than the others... and only the Cincinnati data demonstrates an appreciable degree of skewness, with a long right tail. Of course, none of the investigators mention how they tested for skewness (mean/median/mode?).

(This post is an elaboration of an earlier comparison of different published z-score equations that graphically depicted the predicted mean values of the aortic valve annulus.)

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Validation and re-evaluation of a discriminant model predicting anatomic suitability for biventricular repair in neonates with aortic stenosis.

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J Am Coll Cardiol. 2006 May 2;47(9):1858-65. Epub 2006 Apr 17.

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Regression equations for calculation of z scores of cardiac structures in a large cohort of healthy infants, children, and adolescents: an echocardiographic study.

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J Am Soc Echocardiogr. 2008 Aug;21(8):922-34. Epub 2008 Apr 11.