Normal Curve Equivalent scores
Contents
Rationale for NCE scores
Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and statiscal analyses that can take place. However, this limitation can be overcome by converting data into normalized standard scores instead of percentile rank. The common normalized standard score used in educational research is the normal curve equivalent (NCE) score.
contributed by Frank LaBanca, EdD
Description of NCE scores
The NCE scores are on a scale of 1 to 99 with a mean of 50 and a standard deviation of 21.38. For the purposes of educational research the standard deviation is usually calculated using a value of 21. An NCE value of 1 corresponds with 1st percentile, 50 with 50th percentile, and 99 with 99th percentile. Other NCE scores are mathematically modeled and do not correspond with the exact percentile, because of variations of area under the normal curve. The NCE is considered an (equally-appearing) interval scale.
contributed by Frank LaBanca, EdD
Computing NCE scores
1. Convert ordinal data to a z score
2. Convert z score to NCE score using the formula below
contributed by Frank LaBanca, EdD
NCE formula
X'=(s')(z) + X(mean)'
NCE score = standard deviation (21) x z score + 50
Remember: the NCE score is a standard score with a mean of 50 and standard deviation of 21. NCE scores can range from 1 to 99 and are equally-appearing interval data.
contributed by Frank LaBanca, EdD; modified by Chris Longo & Chris Ruggiero
