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Converting scores to national percentiles

New York State has a Mathematics test and an English Language Arts test for
the public schools. Each test gives the kid a score between 1 and 4, with 4
being the highest score.

How can I find out roughly what those scores are equivalent to in terms of
national percentiles?

I realize that this will vary from year to year and that it's controversial
and political - I just want to get a rough idea.

The reason I'm asking this is that sometimes parents who have been
homeschooling want to know what their kids' national percentile scores on
tests like the CAT (we homeschoolers get to choose from a list of approved
tests, and one of them is an old version of the CAT) can tell them about the
likelihood of the kid's getting into, for example, a sixth-grade gifted
program that requires a 4 in both English and Math on the NYS tests. I just
tell them, "It's complicated."

Any pointers?