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Weight-for-height is not a ratio. You do not divide weight by height to get a number. Instead, each child measured is compared to a reference population of normally nourished children.
In the past, the reference population was a large group of children who were weighed and measured in the United States in the 1960s and early 1970s. This reference population is called the NCHS:CDC:WHO reference.
Recently, the World Health Organization has completed measurements and analysis for a new reference population of children living in six countries (Brazil, United States, Norway, Ghana, Oman, and India). Unlike in the first reference population, children in the new reference population were closely monitored to ensure they had optimal nutrition and health. For example, they were all exclusively breastfed for at least 4 months and were up-to-date on their vaccinations. As a result, these children are thought to demonstrate the ideal growth possible in young children. For this reason, this population is often called a standard population instead of a reference population.
For more information on the new WHO standard population, see the website www.who.int/childgrowth/en/.
As mentioned above, each child is compared to a comparable group in the reference population. That is, to assess weight-for-height for an individual child, that child's weight is compared to all children in the reference population who are of the same sex and the same height. For example, we weigh and measure an individual girl who is 80 cm tall and weighs 8.0 kg. The distribution of the weights of all girls in the WHO standard population who are 80 cm tall is shown below.
Now we plot plot this individual girl's weight relative to the weights of all the 80 cm tall girls in the WHO standard population.
Now we know that this girl weighs a less than most of the 80 cm tall girls in the reference population, but how to we quantify this difference between our individual girl and the average of all the 80 cm tall girls in the reference population?