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| 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.
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| == Definition ==
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| 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.
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| <table border="0" cellpadding="2" cellspacing="1">
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| <caption>Standard/Z scores, percentages, and sten scores</caption>
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| <tr bgcolor="#dddddd" align="center">
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| <td>'''Z-scores'''</td>
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| <td width="7%">< -2.0</td>
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| <td width="7%">-2 to -1.5</td>
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| <td width="7%">-1.5 to -1.0</td>
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| <td width="7%">-1.0 to -.5</td>
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| <td width="7%">-.5 to 0</td>
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| <td width="7%">0 to +.5</td>
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| <td width="7%">+.5 to +1.0</td>
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| <td width="7%">+1.0 to +1.5</td>
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| <td width="7%">+1.5 to +2.0</td>
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| <td width="7%">> +2.0</td>
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| </tr>
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| <tr bgcolor="#eeeeee" align="center">
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| <td>'''Percent'''</td>
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| <td width="7%">2.3%</td>
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| <td width="7%">4.4%</td>
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| <td width="7%">9.2%</td>
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| <td width="7%">15.0%</td>
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| <td width="7%">19.2%</td>
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| <td width="7%">19.2%</td>
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| <td width="7%">15.0%</td>
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| <td width="7%">9.2%</td>
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| <td width="7%">4.4%</td>
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| <td width="7%">2.3%</td>
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| </tr>
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| <tr bgcolor="#dddddd" align="center">
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| <td>'''Sten'''</td>
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| <td>1</td>
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| <td>2</td>
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| <td>3</td>
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| <td>4</td>
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| <td>5</td>
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| <td>6</td>
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| <td>7</td>
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| <td>8</td>
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| <td>9</td>
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| <td>10</td>
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| </tr>
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| </table>
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| Sten scores (for the entire population of results) have a [[mean]] of 5.5 and a [[standard deviation]] of 2.<ref>McNab, D. et al Career Values Scale: Manual & Users' Guide, Psychometrics Publishing, 2005.</ref>
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| == Calculation of sten scores ==
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| 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.
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| 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, <math>\frac {(s - 23.5)}{4.2} 2 + 5.5</math>. It is also usually necessary to truncate such scores, particularly if the scores are skewed.
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| 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.<ref>Russell, M.T., & Karol, D. (2002). The 16PF Fifth Edition administrator's manual. Champaign, IL: Institute for Personality and Ability Testing</ref>
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| ==See also==
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| * [[Stanine]] - a similar system, but with 9 possible values
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| == References ==
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| <references />
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| [[Category:Psychometrics]]
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