# Normal curve equivalent

File:PRtoNCE.JPG
Normal curve equivalents (NCEs) compared to Percentile ranks (PRs or "percentiles")
A normal curve equivalent (NCE), developed for the United States Department of Education by the RMC Research Corporation,<ref name="All">AllPsych Online statistics primer.
NCE stands for Normal Curve Equivalent and was developed [for] the [US] Department of Education.
</ref><ref>Mertler, C. A. (2002). Using standardized test data to guide instruction and intervention. College Park, MD: ERIC Clearinghouse on Assessment and Evaluation. (ERIC Document Reproduction Service No. ED470589)
Normal curve equivalent (NCE): A normalized standardized score with a mean of 50

and a standard deviation of 21.06 resulting in a near equal interval scale from 0 to 99. The NCE was developed by RMC Research Corporation in 1976 to measure the effectiveness of the Title I Program across the United States and is often used to

measure gains over time. (p. 3)
</ref> is a score received on a test based on the percentile rank. It is a measurement of where a student falls on a normal curve, indicating a student's rank compared to other students on the same test.<ref name="roc">Rochester School Department webpage</ref>

The percentile rank scale is not an equal-interval scale; that is, the difference between any two scores is not the same between any other two scores (see below or percentile rank for more information).<ref name="roc"/> Normal curve equivalents solve this problem by converting percentile ranks to an equal-interval scale (see [1] and [2] for examples). Thus, NCEs are equal-interval scale conversions of percentile ranks. The equation for converting this scores is as follows:<ref name="All"/>

```     NCE = 21.06z + 50
where z = z-score```

Thus, NCEs are based on the standard score. NCEs range from 1 to 99 with a mean of 50. The major advantage of NCEs over percentile ranks is that NCEs can be averaged.<ref name="roc"/> The Rochester School Department webpage describes how NCE scores change:

"In a normally distributed population, if all students were to make exactly one year of progress after one year of instruction, then their NCE scores would remain exactly the same and their NCE gain would be zero, even though their raw scores (i.e. the number of questions they answered correctly) increased. Some students will make more than a year's progress in that time and will have a net gain in the NCE score, which means that those students have learned more, or at least have made more progress in the areas tested, than the general population. Other students, while making progress in their skills, may progress more slowly than the general population and will show a net loss in their NCE ranks."

## Caution

Careful consideration is required when computing effect sizes using NCEs. NCEs differ from other scores, such as raw and scaled scores, in the magnitude of the effect sizes. Comparison of NCEs typically results in smaller effect sizes, and using the the typical ranges for other effect size (XXXXX) may result in interpretation errors.<ref>McLean, J. E., O'Neal, M. R., & Barnette, J. J. (2000, November). Are all effect sizes created equal? Paper presented at the Annual Meeting of the Mid-South Educational Research Association, Bowling Green, KY. (ERIC Document Reproduction Service No. ED448188)</ref>

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