In educational statistics, a normal curve equivalent (NCE), developed for the United States Department of Education by the RMC Research Corporation,[1] is a way of normalizing scores received on a test into a 0-100 scale similar to a percentile rank, but preserving the valuable equal-interval properties of a z-score.
The reason for the choice of the number 21.06 is to bring about the following result: If the scores are normally distributed (i.e. they follow the "bell-shaped curve") then This relationship between normal equivalent scores and percentile ranks does not hold at values other than 1, 50, and 99.
The number 21.06 was chosen because Normal curve equivalents are on an equal-interval scale.
[2] Careful consideration is required when computing effect sizes using NCEs.
Comparison of NCEs typically results in smaller effect sizes, and using the typical ranges for other effect sizes may result in interpretation errors.