Y; sometimes it means Y=>X; sometimes it means W=>X, W=>Y. And sometimes it’s an artifact of people’s beliefs about corr(X, Y). With intelligent agents, perceived causation causes correlation.>
Sometimes the issue could be the choice of the appropriate Y to correlate with your X. In the Montessori example, rather than looking at test scores or even at rate of graduation from high school, it could be argued that it would be more meaningful to look at career performance. However choosing something as general as career performance requires a great deal of “narrowing down”. For example: First choose your career to compare, say law. Narrow it down to one, hopefully very large, law school. Further narrow it down to one demographic—all students graduating from similar performing high schools, who themselves performed similarly in their admission tests. Continue to narrow your study down even farther—similar race, religion, family income, number of siblings, birth order, parents’ careers and educations, etc. Then you can look at the pre-high school education—Montessori vs. other private educational methods. Ouch!
Y; sometimes it means Y=>X; sometimes it means W=>X, W=>Y. And sometimes it’s an artifact of people’s beliefs about corr(X, Y). With intelligent agents, perceived causation causes correlation.> Sometimes the issue could be the choice of the appropriate Y to correlate with your X. In the Montessori example, rather than looking at test scores or even at rate of graduation from high school, it could be argued that it would be more meaningful to look at career performance. However choosing something as general as career performance requires a great deal of “narrowing down”. For example: First choose your career to compare, say law. Narrow it down to one, hopefully very large, law school. Further narrow it down to one demographic—all students graduating from similar performing high schools, who themselves performed similarly in their admission tests. Continue to narrow your study down even farther—similar race, religion, family income, number of siblings, birth order, parents’ careers and educations, etc. Then you can look at the pre-high school education—Montessori vs. other private educational methods. Ouch!