A new study argues that the nation’s focus on helping students who are furthest behind may have produced a Robin Hood effect, yielding steady academic gains for low-achieving students in recent years at the expense of top students.

The study, to be released on Wednesday, compared trends in scores on federal tests for the bottom 10 percent of students nationwide with those for the top 10 percent and said those at the bottom moved up faster than those at the top.

In tests of fourth-grade reading from 2000 to 2007, for instance, the scores of the lowest-achieving students increased by 16 points on a 280-point scale, compared with a gain of three points for top-achieving students, according to the study, by the Thomas B. Fordham Institute, a research organization in Washington.

The period of big gains for low achievers and minimal ones for high achievers coincides with the federal education law known as No Child Left Behind, which took effect in 2002. The study said that while it was impossible to know whether the law caused those scoring patterns, such a result would hardly be surprising, since the law made it a goal to reduce the gap separating low-scoring, poor and minority students from higher-scoring white students.