Sten Scores and Their Use in Rescaling Test Scores

Many times in order to make easy comparisons between individuals, test scores are rescaled. One such rescaling is to a ten point system. The result is called sten scores. The word sten is formed by abbreviating the name "standard ten."

Details of Sten Scores

A sten scoring system uses a ten point scale with a normal distribution. This standardized scoring system has a midpoint of 5.5. The sten scoring system is normally distributed and then divided into ten parts by letting 0.5 standard deviations correspond to each point of the scale. Our sten scores are bounded by the following numbers:

-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2.0

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Stanine Score Example

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Each of these numbers can be thought of as z-scores in the standard normal distribution. The remaining tails of the distribution correspond to the first and tenth sten scores. So less than -2 corresponds to a score of 1, and greater than 2 corresponds to a score of ten.

The following list relates sten scores, standard normal score (or z-score), and the corresponding percent of ranking:

• Sten scores of 1 have z-scores less than -2 and consist of the first 2.3% of ranked scores.
• Sten scores of 2 have z-scores greater than -2 and less than -1.5 and consist of the next 4.4% of ranked scores.
• Sten scores of 3 have z-scores greater than -1.5 and less than -1 and consist of the next 9.2% of ranked scores.
• Sten scores of 4 have z-scores greater than -1 and less than -0.5 and consist of the next 15% of ranked scores.
• Sten scores of 5 have z-scores greater than -0.5 and less than 0 and consist of the middle 19.2% of ranked scores.
• Sten scores of 6 have z-scores greater than 0 and less than 0.5 and consist of the next 19.2% of ranked scores.
• Sten scores of 7 have z-scores greater than 0.5 and less than 1 and consist of the next 15% of ranked scores.
• Sten scores of 8 have z-scores greater than 1 and less than 1.5 and consist of the next 9.2% of ranked scores.
• Sten scores of 9 have z-scores greater than 1.5 and less than 2 and consist of the next 4.4% of ranked scores.
• Sten scores of 10 have z-scores greater than 2 and consist of the last 2.3% of ranked scores.

Uses of Sten Scores

The sten scoring system is used in some psychometric settings. The use of only ten scores minimizes small differences between various raw scores. For example, everyone with a raw score in the first 2.3% of all scores would be converted into a sten score of 1. This would make the differences among these individuals indistinguishable on the sten score scale.

Generalization of Sten Scores

There is no reason that we must always use a ten point scale. There may be situations in which we would want to have use of more or fewer divisions in our scale. For example, we could:

• use a five-point scale, and refer to stafive scores.
• use a six-point scale, and refer to stasix scores.
• use a nine-point scale, and refer to stanine scores.

Since nine and five are odd, there is a midpoint score in each of these systems, unlike the sten scoring system.