I have a couple of specific questions regarding the underlying assumptions of the pearson's correlation. I have googled this question but I have not managed to find a consistent answer. In particular whether there is an assumption of sample by sample independence. I will give an example to clarify as I may not be using the correct nomenclature. Assume, I have taken 50 measurements of height and weight from 40 people. These measurements are:
-Measurement of weight and height of 10 people. -Measurement of weight and height of the same 10 people but repeated at a different point in time. -Measurement of weight and height of a different group of 30 people.
If I conduct a pearson's correlation for height and weight, using all 50 measurements, is there an underlying assumption of sample independence that is being violated? If there is no underlying assumption of independence being violated, how can generalisation of the result be interpreted?
Any responses are appreciated.