Normal Curve Equivalent Score

Normal curve equivalent scores (NCE scores) are one type of normalized standard, norm-referenced scores. Norm-referenced scores report the results of standardized assessments and other instruments in a way that permits the comparison of an individual’s performance with a very well-defined norm group of similar individuals who have completed the same assessment. Publishers of norm-referenced assessments will typically transform scores so that they can be placed along a common distribution. This common distribution is called a normal distribution, normal curve, or bell-shaped curve.

There are numerous types of scores that are transformed for ease of interpretation in relation to a norm group. These include linear standardized scores (e.g., Z scores and T scores), which report how far a raw score is located from the mean score of a norm group, reported in standard deviation units. A distribution of linear standard scores will typically retain the same shape as the distribution of raw scores (i.e., not a normal distribution). A disadvantage of these types of scores is that they are often misinterpreted due to the nature of their respective scales (i.e., the majority of Z scores range from −3.00 to +3.00 and the majority of T scores range from 20 to 80). This problem can be overcome through a transformation of raw scores to normalized standard scores. Transformation to any normalized standard score type will, in essence, make the distribution conform to a normal distribution. Examples of these types of transformed scores are stanines, SAT scores, deviation IQ scores, and NCE scores.

[Page 1154]NCE scores have a mean of 50 and a standard deviation of 21.06. NCE scores range from 1 to 99. The somewhat “odd” value for the standard deviation has been established so that NCE scores will precisely align with percentile ranks at three specific points: at scores of 1, 50, and 99. The basic advantage of NCE scores is that they represent equal units across the entire continuum (i.e., 1–99), unlike percentile ranks. NCE scores are calculated in the following manner:

• 1.
  A Z score is calculated (from the obtained raw score) and multiplied by 21.06 (the “new” value for a standard deviation).
• 2.
  The value of 50 (the “new” value for the mean) is added to the resulting value in order to obtain the NCE score.

This can be expressed with the following formula:

$$\text{NCE}=21.06z+50$$

NCE scores, along with other normalized standard scores, allow for ease of interpretation of scores that have been transformed to the same normal distribution scale. Regardless of the specific score being used, all normal standardized score scales provide the same information about a particular individual’s performance.

See also Ability Tests; Achievement Tests, ACT; Aptitude Tests; Areas Under the Normal Curve; High-Stakes Tests; Iowa Test of Basic Skills; Normal Distribution; Norming; Percentile Rank; Reading Comprehension Assessment; SAT; Standardized Scores; Standardized Tests; Stanines; T Scores; Z Scores