Let's say I measure the height of 100 individuals every week in both Illinois and Texas while allowing for the same individual to be measured multiple times in the following weeks. This way, my samples within each state are not completely independent as there is some overlap in the composition of individuals over time.
For example, sample 1 included 100 individuals. Sample 2 included 100 individuals, but 2 individuals were also measured in sample 1. Sample 3 can be fully independent. Sample 54 can have 5 individuals that were also measured before. Thus, my 100 samples from each state can have some overlap. (I have an ID for each individual, so I know in which weeks they appear.)
In this scenario, the samples are neither fully dependent nor fully independent. What test can I perform to test for statistical significance in the mean height differences between Illinois and Texas. I imagine both t-test and Wilcoxon assume samples are completely independent of each other.