About 10 percent of American children attend private schools. That portion is somewhat larger for Washington area children, and even larger, I would guess, for students whose parents read The Post.

So whenever I put out my annual Challenge Index rankings of high schools, national and local, many readers ask why I don’t include private schools. It is a good question that reveals surprising differences not only between private and public schools, but also among private schools.

I called a few local private schools recently to make certain their attitudes about revealing their college-level course and test data had not changed. As they have in the past, spokespersons for the Sidwell Friends School and St. Albans School declined to tell me how many Advanced Placement exams they gave in 2010. That is a key figure for me, since I calculate the college-level test participation rate I use to rank schools by dividing the number of AP, International Baccalaureate (IB) or Advanced International Certificate of Education (AICE) exams given at a school by the number of students graduating that year.

I don’t include private schools on my lists because too many refuse to provide that data. (A few public schools in affluent areas have also resisted but usually acquiesce when I point out that freedom of information laws require them to release those numbers.) Many private-school educators say the rankings distort what they offer students. They want to be judged by the quality of their teaching and other factors that cannot be summed up by a number.

Sources inside those schools have given me a good idea of how they would rate. One school similar to Sidwell and St. Albans, the Roxbury Latin School in West Roxbury, Mass., even filled out my form recently at my request. In 2010 it gave 221 AP tests and had 50 graduating seniors, for a Challenge Index rating of 4.420. On the new Washington Post High School Challenge national list, which can be found at washingtonpost.com/highschoolchallenge, it would have ranked 97th, just above John L. Miller Great Neck North High on Long Island, a public school in a wealthy neighborhood. Among Washington area public schools, Roxbury Latin would have ranked 11th, wedged between two Montgomery County schools, Churchill and Wootton, that also have very few low-income students.

A West Coast private school, San Domenico in Marin County, Calif., also agreed to share its data. It estimated just 5 percent of its students were low-income. Its Challenge Index rating was 2.829, close to the 2.841 rating of Paul D. Schreiber High in Port Washington, N.Y., where 8 percent of students are from low-income families.

On most measures, including the Challenge Index, private schools produce numbers close to those of public schools that enroll children from similar backgrounds. Many of the most selective and expensive private schools seem reluctant to let this be known since it undercuts one of their selling points — the public schools just aren’t like us.

But some private high schools have been willing to release their data. Among those are some whose college-level test participation rates are much higher than public schools that share their demographic characteristics. The Eastbrook Academy in Milwaukee has a Challenge Index rating of about 5.600, even though 40 percent of its students are from families with incomes low enough to qualify for the city’s voucher program. Providence, a Catholic high school for girls in downtown San Antonio, has a large low-income population but a rating of 2.767. Only about 10 percent of U.S. public schools have ratings above 1.000.

A good local example of a Catholic school with unusual results is St. Anselm’s Abbey School in Northeast Washington, which gave 232 AP tests and had 32 graduates in 2010. That would give it a rating of 7.250 and a national ranking of 27th if I put it on the list. On the Washington area list it would have been No. 1.

St. Anselm’s officials say they are proud of their AP program. They have always given me their data. I asked spokesman James Leathers why the school wasn’t worried, as other private schools were, about being judged by just one number. “We think parents are smart enough to know that this is not the only determinant of the quality of a school,” he said.

As someone who has had children in both public and private schools, that makes sense to me. I wish all private schools had as much faith in their parents.