It is very important to remember three things:
1. some schools go to considerable lengths to avoid reporting scores at all
2. an impressive number of schools limit the number of potentially low-scoring students
3. there is no incentive for students to strive for their best scores
As working statisticians, we consider not testing everyone unethical. Period.
We are not flexible about everyone taking tests to measure English language proficiency. Of the
world's six thousand-odd languages, English has to rate as one of the most awful to learn. Yet, billions
have done so. William Shakespeare, among others, managed to transcend its limits. If a student
wants to take an additional test to measure proficiency in another language and report the better
scores, that's fine with us.
That said, if someone wants to take arithmetic tests in Spanish or Hmong or Braille, bully for them.
There has been a notable lack of first-rate Hmong and Spanish mathematicians for centuries.
As to item 3, there are two objectives: almost everyone would like each individual student's score to
improve year over year. Assuming, of course, the tests are actually measuring something. So what is
needed is an inexpensive but visible token of accomplishment.
We would also favor recognizing top scorers in a subject by school, district, county and state.
The Governor posing with the student, the subject teacher, the principal and the superintendent
while handing over the keys to a SmartCar or a sparkling new laptop whose case has the state seal
embossed sounds like a memorable photo opportunity to us. Five subjects times fifty-eight counties
times four years. Cheap at the price. We doubt that someone like Dell or Intel or an automaker would
mind being able to say "When the State of California recognizes its top students, they are given one of
our machines."