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This is a very interesting article that points to the need for explicit attention for the circumstances of disadvantaged groups in society, rather than trusting that a focus on the population mean will automatically take care of the ‘deviants’. Regardless of any findings, that conclusion seems eminently sensible.
I do wonder if the combination of the right-skewed shape of the distributions and measurement error may partly explain the finding that the correlation of the mean with right-sided deviance is stronger than with left-sided deviance.
The skew means that the distribution is much more ‘compressed’ on the left than on the right, which implies that the same absolute measurement error (say, 0.2 BMI units) affects correlations on the left more than on the right. Even if scales are accurate, weight fluctuates in individuals. Measurement error would also be larger when the proportion of ‘deviants’ of the total is smaller, which helps explain why the correlation for overweight (r2=0.98; range 5-80%) with the mean is so much higher than that for the most extreme form of undernutrition (r2=0.41; range 0-6%).
BMI is right-skewed but measurement is fairly precise. Blood haemoglobin is probably not right-skewed but measurement accuracy in these population surveys may be low. Unfortunately, the article does not show the shape of the entire distribution, does not present results on the mean-right hand side correlation, or discuss the possible influence of measurement error.
Notwithstanding the need for explicit attention for high risk groups like the poor, Rose and Day’s ideas may have more validity on the left side of distribution than this analysis gives them credit for.