Take two things we know are highly correlated- the age of boys (0-18) and their height. As age increases, height tends to increase. If you measured a sample of boys of different boys ages 0-18 and measured their heights, you would find a strong relationship.
Instead, imagine if a researcher undermined the experiment with the following, invalid procedure. First the researcher divides all of the children by the independent variable- age group. She puts all the 1-year-olds in a group, all the 2-year-olds in a group, etc. Then, within each small group, the researcher ranks the boys by height- the tallest in the group is 1, the second tallest is 2, etc. Now she tries to correlate these rankings with age, and finds little or no relationship. Within the narrow band of 14-year-olds, for example, being a few weeks or months older might have little or no relationship to height. You have taken a relationship that clearly exists and obscured it by pre-sorting the subjects.
In exactly the same way, your SAT research uses pre-sorted students. Students get sorted into different colleges, largely based on test scores and academic ability. Harvard is akin to one age group in the height/age analogy. DePaul is like a different age group. The GPAs kids earn are relative to other kids at the same school who have similar scores to begin with. Within these narrow bands, SAT might not predict the sorting of GPAs. In other words, whether a kid scored a 1000 or a 1050 might not predict how that kid fares at, say, Indiana State University, relative to the competition of other kids with just about the same SAT score. But do you really think that the kid will succeed at an ivy league school? If so, you are deluding yourself.
Look at the 25th-75th percentile SAT scores of various schools- they are about 200 points apart. Just as in the invalid height/weight experiment, you have obscured a relationship by pre-sorting subjects according to a narrow band of the independent variable. You can tell me about your off-the-record conversations about what the ivy league admissions people KNOW all you like, but on the record, they know very well that a kid with an average SAT score is not going to excel at Columbia or Princeton.
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