3
$\begingroup$

I wonder if it's possible to estimate a child's age given the child's measured height.

I have found this height chart: http://resource.nhi.no/resource/4281-21-hoyde-gutter-5-19-who.pdf

Is it possible to use the information in this chart to estimate what the probability for a child to be of a certain age when the height is known?

I'm sorry, but my knowledge in statistics are very small.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

In short, no.

This graph depicts the conditional percentiles of height given age. Overall, you know approx what the distribution of height is for a specific age, but not about what the distribution of height is in the population overall: this is the marginal distribution of height. Neither do we know the marginal distribution of age in the population. If we were interested in estimating some probability of age given height (the converse), we would need to know one of these two distribution functions in order to get a conditional plot of age given height. This is a consequence of Bayes' Theorem.

Improve this answer
$\endgroup$
6
  • 1
    $\begingroup$ Although the argument is correct, in practice (within most sizable populations) the distribution of children's ages will be close enough to uniform that reasonable estimates of age can be made based on height. Maybe, then, it would be more constructive to say "In short, yes, provided you look up additional information or make some assumptions," and then describe how to use that information to achieve the desired results. $\endgroup$
    – whuber ♦
    Commented Apr 10, 2013 at 17:42
  • $\begingroup$ Uniform age seems like a rather strong assumption to me. But I don't know, I'm not experienced in demography. I also think the details of actually obtaining such a distribution given the poster finds age information would be too complicated for someone without a background in statistics. $\endgroup$
    – AdamO
    Commented Apr 10, 2013 at 17:56
  • $\begingroup$ What is required for a uniform age distribution is that the size of the cohorts of potential mothers remains fairly constant and that their fertility behaviour remains fairly constant. If the curve in the OP was of infants, and cohorts differ in months rather than years, then that is a fair enough assumption. However, the curve in the OP was of children between 5 and 19 years old. I just looked at that distribution for Germany in the 1987 census (that is what I had readily available on my computer), and that distribution deviates quite a bit from a uniform distribution. $\endgroup$
    – Maarten Buis
    Commented Apr 11, 2013 at 7:22
  • $\begingroup$ Thank you for the quick replies! If I assume that the age distribution is uniform for the ages, how can I then make the estimates of age based on height? Can you please provide me with an example? $\endgroup$
    – Jompa234
    Commented Apr 11, 2013 at 9:07
  • $\begingroup$ Conceptually the easiest way to achieve that is to bin the graph you showed into squares defined by age-height combinations. Each square has an associated unconditional probability of observing a randomly selected child in that age-height category (a joint probability distribution). The marginal sums of the probabilities in the age direction would be constant since they are uniform. By taking the sum of heights in a similar fashion, you would get a marginal distribution of heights in that population. $\endgroup$
    – AdamO
    Commented Apr 11, 2013 at 17:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.