# Sten scores

The results for some scales of some psychometric instruments are returned as sten scores, sten being an abbreviation for 'Standard Ten' and thus closely related to stanine scores.

## Definition

A sten score indicates an individual's approximate position (as a range of values) with respect to the population of values and, therefore, to other people in that population. The individual sten scores are defined by reference to a standard normal distribution. Unlike stanine scores, which have a midpoint of five, sten scores have no midpoint (the midpoint is the value 5.5). Like stanines, individual sten scores are demarcated by half standard deviations. Thus, a sten score of 5 includes all standard scores from -.5 to zero and is centered at -0.25 and a sten score of 4 includes all standard scores from -1.0 to -0.5 and is centered at -0.75. A sten score of 1 includes all standard scores below -2.0. Sten scores of 6-10 "mirror" scores 5-1. The table below shows the standard scores that define stens and the percent of individuals drawn from a normal distribution that would receive sten score.

 Z-scores Percent Sten Stafive Stasix < −2.0 −2.0 … −1.5 −1.5 … −1.0 −1.0 … −0.5 −0.5 … −0.0 +0.0 … +0.5 +0.5 … +1.0 +1.0 … +1.5 +1.5 … +2.0 > +2.0 2.3% 4.4% 9.2% 15.0% 19.2% 19.2% 15.0% 9.2% 4.4% 2.3% 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 1 2 3 4 5 6

Sten scores (for the entire population of results) have a mean of 5.5 and a standard deviation of 2.[1]

## Calculation of sten scores

When the score distribution is approximately normally distributed, sten scores can be calculated by a linear transformation: (1) the scores are first standardized; (2) then multiplied by the desired standard deviation of 2; and finally, (3) the desired mean of 5.5 is added. The resulting decimal value may be used as-is or rounded to an integer.

For example, suppose that scale scores are found to have a mean of 23.5, a standard deviation of 4.2, and to be approximately normally distributed. Then sten scores for this scale can be calculated using the formula, $\frac {(s - 23.5)}{4.2} 2 + 5.5$. It is also usually necessary to truncate such scores, particularly if the scores are skewed.

An alternative method of calculation requires that the scale developer prepare a table to convert raw scores to sten scores by apportioning percentages according to the distribution shown in the table. For example, if the scale developer observes that raw scores 0-3 comprise 2% of the population, then these raw scores will be converted to a sten score of 1 and a raw score of 4 (and possibly 5, etc.) will be converted to a sten score of 2. This procedure is a non-linear transformation that will normalize the sten scores and usually the resulting stens will only approximate the percentages shown in the table. The 16PF Questionnaire uses this scoring method.[2]

## References

1. ^ McNab, D. et al Career Values Scale: Manual & Users' Guide, Psychometrics Publishing, 2005.
2. ^ Russell, M.T., & Karol, D. (2002). The 16PF Fifth Edition administrator's manual. Champaign, IL: Institute for Personality and Ability Testing