What is the test for establishing that race was a motivating factor in a school's decision?

Arlington Heights I, 429 U.S. at 265, 97 S.Ct. at 563 (footnote omitted). Rather, the plaintiff need begin only by showing that race was "a motivating factor." Id. at 266, 97 S.Ct. at 564 (emphasis added). Once it is shown that a decision was motivated at least in part by a racially discriminatory purpose, the burden shifts to the defendant to show that the same result would have been reached even without consideration of race. Id. at 270 n. 21, 97 S.Ct. at 566 n. 21; Mt. Healthy City School District Board of Education v. Doyle, 429 U.S. 274, 287, 97 S.Ct. 568, 576, 50 L.Ed.2d 471 (1977). If the defendant comes forward with no such proof or if the trier of fact is unpersuaded that race did not contribute to the outcome of the decision, the equal protection claim is established.