A stanine is an integer score from 1 through 9 obtained by dividing an approximately normal distribution
into nine ordered categories. The scale has mean 5 and standard deviation 2. A common conversion assigns
scores using z-score boundaries at 
, 
,
, 
, 0.25, 0.75, 1.25, and 1.75 (Gulliksen et al. 1951).
Under an exact normal distribution model, the resulting category proportions, expressed in percent and rounded to whole numbers, are 4, 7, 12, 17, 20, 17, 12, 7, and 4 for stanines 1 through 9. Stanines give a coarse normalized ranking rather than retaining the full precision of the original score.
