What is the best way to compare population of children age 0-6 years old (head counts) across various regions? Population density (population per sq km) seems to make sense. A colleague mentioned looking at population per capita. Does that make sense? Any help is much appreciated. Tx!
It depends on what, exactly, you're interested in. All of your proposals can make sense given different research aims. Population density is also measuring the area of the territory that the children are in, which might not be relevant to your research question -- unless, e.g., you think there are some interesting urban vs. rural effects -- so you could inadvertently introduce some weird biases to your analysis.
The same arguments go for children per adult or children per total population.
Alternatively, is there any reason that you can't just compare the number of children directly?
In each case, 0-6 population is the numerator, and you will have something else in the denominator. The question you are trying to answer determines what goes into the denominator.
If you want to know the gross child population of different regions, the denominator is 1. Presumably you don't want this method because your regions have different sizes.
If you want to know something about regional fertility, then total population might make sense in the denominator - this is population per capita, and tells you how many children there are as a function of population size. To get closer to fertility, you might choose women aged 15-50 in the denominator, telling you the number of children per child-bearing woman.
Population density (regional surface area in the denominator) seems like a strange choice. For instance, you would likely conclude that Miami has more children per square kilometer than Atlanta, but this would be mostly driven by urban sprawl.