Is there a test to compare a variable across time When using a cutoff value to select for observations with a particularly high or low value.
I can think of many simple examples for this:
- Did the richest persons (99th percentile) get richer between 2000 and 2010?
- Do persons with a blood pressure above 140mmHg show an increase in blood pressure when watching their favourite football team?
- Did the fastest runners get faster in the Olympics 2004 in comparison to 2000?
My own naive guess is something like a regression to the mean (I hope I am using the term correctly): If the times for running in the Olympics are just randomly correlated across years, then I would expect that those who were fast in 2000 are likely to be slower in 2004.
The other case when the rich become richer from year to year holds rather true for money.