I have what seems like it should be simple statistics problem. Given anthropometric data (height, weight, BMI, age, etc.), determine if a sample population has significantly different anthropomorphic characteristics than the larger population. The difficulty however lies in that this test must be done for a pediatric population, thus the anthropometric data is a function of age.
For example, consider the following null-hypothesis:
"The sample's height-per-age (growth-curve) is not significantly different than the World Health Org (WHO) database."
The WHO produced growth-curves (height as a function of age) for children, and offers a simple calculation to determine the z-score of an individual observation. But I want to make a claim about the sample as a whole, rather than individual measurements. This led me to believe I could simply take the mean of the z-scores from individual measurements, and look up the corresponding p-value on a z-table to test for significance, i.e. if Zmean < -1.96, then the sample is significantly different than the population. However, this calculation does not consider the sample size (n). I can't imagine making a statistical claim about the sample as a whole without considering the sample size. How can this null-hypothesis be evaluated?
Also, the WHO software produces a the below graph from the z-scores, which leads me to wonder if I could simply perform a t-test from the z-scores to determine if the sample is statistically different than the WHO data population.