That a pair of attributes doesn't necessarily exhibit independence within the universe at large, even if it exhibits independence within each sub-universe is a

That a pair of attributes doesn't necessarily exhibit independence within the universe at large, even if it exhibits independence within each sub-universe is a powerful observation, and it's a troubling one to anyone who has attempted to design a sales and marketing strategy, a drug trial, or frameworks to encourage social equality: To have it suggested I can say nothing less about these thousand students other than a thousand different things, just sounds so absurd, and yet here it is true. Sometimes people use the term "paradox" simply to a contradictory statement which upon investigation turns out to be true. In that way, "Simpson's Paradox" is absolutely a paradox.