Stanine Scores

Stanine scores are area-normalized standard scores that are standardized to have a mean of approximately 5 and a standard deviation of approximately 2. They are simple to define but may discard some of the detail in the original data.

Many statistical procedures assume that the data are normally distributed. Sometimes, nonlinear algebraic transformations such as logistic or arcsin transformations will produce the desired result, but when the non-normality is due to sampling or to the features of the measuring instrument itself, an area-normalizing transformation may be required. The stanine transformation provides a quick and simple way to accomplish this goal.

As with other area normalizations, the stanine transformation assigns transformed scores to be equivalent to the raw scores rather than computing the new scores. To obtain stanine scores, carry out the following steps:

• 1.
  Make a frequency distribution of the raw scores.
• 2.
  Assign stanine scores as follows: Assign a value of

  • 1 to the lowest 4% of scores,
  • 2 to the next 7% of scores,
  • 3 to the next 12% of scores,
  • 4 to the next 17% of scores,
  • 5 to the next 20% of scores,
  • 6 to the next 17% of scores,
  • 7 to the next 12% of scores,
  • 8 to the next 7% of scores,
  • 9 to the top 4% of scores.

Stanine scores have two main advantages over other area-normalizing transformations. First, they are easy to compute and do not require a table of the normal distribution z scores. Second, because single scores cover a relatively wide portion of the score distribution, stanine scores tend to discourage users from overinterpreting relatively small differences in scores. This is one reason many test publishers offer stanines as one metric in which test results are provided.

A third advantage, which is no longer very relevant, is that stanines require only one column. At the time they were invented, when punch cards were the primary means of data storage and sorting and hand computation was required, single-digit data values offered a major saving in space and computational labor. The primary disadvantage of stanines is that they may discard some useful detail in the data.