gill1109 wrote:minkwe wrote:It is similar to claiming that the expression "women are shorter than men" is not true, by using height data from one set of randomly selected people without regard for gender, and gender data from a disjoint set of randomly selected people without regard for height. Its bad statistics.
This is amusing. Let me turn it around. Suppose we are interested in the average difference in height between a husband and wife. We could take a sample of married couples, and average the differences.
But ... we could also take a random sample of married couples, and average the heights of the women; we could take another, independent, random sample of married couples, and average the heights of the men. The difference between the two averages is a decent estimator of the average difference in height within married couples.
Statistics is a powerful tool.
Maybe you can describe to us exactly how you "selected a random set of couples" then you may start seeing the problem. It is very easy to lie using statistics. But only the uninitiated will be fooled. For any description of your random selection method you can come up with, I will be able to come up with a new hidden variable that defeats it. Up for the challenge? It is impossible to screen-off a hidden variable in your sample selection. You should know this.