Sten scores

The results for some scales of some psychometric instruments are returned as sten scores, sten being an abbreviation for 'Standard Ten'.

When the population of results for a scale comes from a normally distributed population with known parameters (or those results can be transformed in such a way that this is the case) then sten scores can be calculated for the results for each individual to whom the scale is administered. Sten scores are calculated in such a way that, for the entire population of results, the mean sten score is 5.5 and the standard deviation of them is 2.

For example, suppose that a scale of some notional characteristic is administered to each member of some large reference population and its values are found to have a mean of 23.5 and a standard deviation of 4.2, and to be approximately normally distributed. Then sten scores for this scale can be calculated using the formula, 2( s - 23.5 ) / 4.2 + 5.5.

A mean score is thus 5.5.

There is some ambiguity in the way that sten scores are defined. Some authors use these real-valued scores, possibly rounding them off to the first decimal point as a reflection of level of precisions often seen in psychometric instruments. However, it is much more common for authors to derive scores from the 'raw' scores which assume only the values in the set, {1, 2, 3, ..., 10 }, according to the following scheme:

values less than 2 -> 1 values between 2 and 3 -> 2 values between 3 and 4 -> 3 . . . values between 9 and 10 -> 9 values above 10 -> 10

Thus these sten scores represent ranges of values.

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.