# Understanding NCE (Normal Curve Equivalent) and Percentile Rank in Imagine Math

Norm-referenced interpretations—specifically the NCE (Normal Curve Equivalent) and Percentile Rank—can be viewed along with the student Quantile® measures in the Benchmark report. Norm-referenced interpretations express how a student performed on the test compared to other students of the same age or grade. They do not provide any indication about what a student can or cannot understand. Norm-referenced interpretations also provide minimal value at the student level but can be useful—and are often required—at aggregate levels for program evaluation and to ensure funding. The NCE, in particular, was developed specifically for use in the evaluation of Title I programs and is most commonly used to aggregate “gain scores” from different programs.

The primary difference between the percentile and NCE is that the percentile is limited in its use for comparing results across tests and student populations, while the NCE provides a valid and reliable framework to compare student scores individually, in aggregate, and on average across tests or student populations.

Percentile Rank: The percentile rank of a Quantile measure indicates the percentage of scores less than or equal to that score. Percentile ranks range from 1 to 99. For example, if a student scores at the 65th percentile, it means that the student performed as well as, or better, than 65% of their peers (the norm group). This also means that 35% of his or her peers scored higher than the student. Percentile rank does not refer to the percentage of items answered correctly. A limitation of percentile rank is that all the points along the percentile distribution do not represent equal intervals. As a result, percentile rank provides a limited ability to compare achievement for groups of students.

NCE: The NCE is similar to a percentile rank, but provides extensive ability to compare achievement for groups of students. Like the percentile rank, the NCE scale ranges from 1 to 99. Like the percentile rank, an NCE indicates the percentage of scores less than or equal to that score. Unlike the percentile rank, the NCE is based on an equal-interval scale, making it extremely useful in comparing student achievement. NCEs provide the ability to compare the results of different tests for a student or group of students. NCEs also provide the ability to compare results for different students or groups of students on the same test.

For example, if the same student received an NCE score of 45 on a math test and an NCE score of 65 on a reading test, it means that the student scored 20 points higher on the reading test as compared to the math test. Similarly, in Imagine Math, if the same student received an NCE score of 50 on Benchmark 1 and 70 on Benchmark 2, it means the student experienced a gain of 20 points between the two Benchmarks.