The federal “No Child Left Behind” Act of 2001 allows states to determine when the number of students in a school or subgroup is too small to make accurate decisions about a school’s performance.
Many states have proposed a minimum subgroup size of 30 students to be included in calculations about adequate progress. Other states have added a test of statistical significance to increase the certainty of their decisions. States also are proposing to average several years of test data or to look at multiple years of performance to reduce the possibility of misjudging a school.
But the problem poses a particular challenge for very rural states with large numbers of small schools and districts. In 2001-02, for example, 40 percent of Alaska’s schools had 100 or fewer students, nearly 27 percent enrolled 50 or fewer pupils, and 16 percent had 25 or fewer. With statistics like those, even a minimum subgroup size of 30 would exclude large numbers of schools from the accountability system.
To address the problem and bolster the chances that it is classifying schools correctly, Alaska has proposed using an index that would combine reading, writing, and math results; the scores from students at all achievement levels; and measures of absolute achievement and growth.
By combining so many data points, said Mark A. Leal, the director of assessment and accountability for the state education department, “that helps to ensure the reliability of the system.”
Far to the east, Vermont is suggesting a similar approach. Although the proposals depart from the literal letter of the law, both states argue that a strict interpretation would be inappropriate, given their circumstances.
Both states also have proposed using a statistical technique, known as a “confidence interval,” rather than a minimum group size, to make decisions about whether schools and subgroups have met their targets. The approach—which at least eight states are considering—calculates how well the data being judged represent the “true” performance of the school.
The confidence interval expands or shrinks based on the number of students in the group and how far they are from the target. If a school’s or subgroup’s confidence interval extends above the state’s performance goal for that year, it would have made adequate progress.
“I really think this issue of using confidence intervals is going to be the way for most states to go,” said Richard Hill, the executive director of the Portsmouth, N.H.-based Center for Assessment, assuming federal officials give their blessing.
The statistical technique is particularly useful, he suggested, when using the “safe harbor” provisions in the act. Under those provisions, a school that fails to meet the state’s annual target for the percent of “proficient” students can still make adequate progress if it hits specified improvement targets from one year to the next and tests at least 95 percent of the students in each subgroup.
Because it is even harder to measure growth, Mr. Hill said, confidence intervals and other statistical techniques are even more necessary to gauge schools’ performance properly. Such techniques make it less likely that a state will misidentify the performance of schools or subgroups.
But other experts caution that depending on how such techniques were applied, they also could mean few subgroups would ever be identified as failing.